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  • 1.
    Andersson, David
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bengtsson, Ingemar
    Stockholm University, Faculty of Science, Department of Physics.
    Blanchfield, Kate
    Stockholm University, Faculty of Science, Department of Physics.
    Dang, Hoan Bui
    States that are far from being stabilizer states2015In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, no 34, article id 345301Article in journal (Refereed)
    Abstract [en]

    Stabilizer states are eigenvectors of maximal commuting sets of operators in a finite Heisenberg group. States that are far from being stabilizer states include magic states in quantum computation, MUB-balanced states, and SIC vectors. In prime dimensions the latter two fall under the umbrella of minimum uncertainty states (MUSs) in the sense of Wootters and Sussman. We study the correlation between two ways in which the notion of ` far from being a stabilizer state' can be quantified. Two theorems valid for all prime dimensions are given, as well as detailed results for low dimensions. In dimension 7 we identify the MUB-balanced states as being antipodal to the SIC vectors within the set of MUS, in a sense that we make definite. In dimension 4 we show that the states that come closest to being MUS with respect to all of the six stabilizer MUBs are the fiducial vectors for Alltop MUBs.

  • 2.
    Andersson, Ole
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Dumitru, Irina
    Stockholm University, Faculty of Science, Department of Physics.
    Aligned SICs and embedded tight frames in even dimensions2019In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, no 42, article id 425302Article in journal (Refereed)
    Abstract [en]

    Alignment is a geometric relation between pairs of Weyl-Heisenberg SICs, one in dimension d and another in dimension d(d - 2), manifesting a well-founded conjecture about a number-theoretical connection between the SICs. In this paper, we prove that if d is even, the SIC in dimension d(d - 2) of an aligned pair can be partitioned into (d - 2)(2) tight d(2)-frames of rank d(d - 1)/2 and, alternatively, into d(2) tight (d - 2)(2) -frames of rank (d - 1) (d - 2)/2. The corresponding result for odd d is already known, but the proof for odd d relies on results which are not available for even d. We develop methods that allow us to overcome this issue. In addition, we provide a relatively detailed study of parity operators in the Clifford group, emphasizing differences in the theory of parity operators in even and odd dimensions and discussing consequences due to such differences. In a final section, we study implications of alignment for the symmetry of the SIC.

  • 3.
    Andersson, Ole
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    A symmetry approach to geometric phase for quantum ensembles2015In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, no 48, article id 485302Article in journal (Refereed)
    Abstract [en]

    We use tools from the theory of dynamical systems with symmetries to stratify Uhlmann's standard purification bundle and derive a new connection for mixed quantum states. For unitarily evolving systems, this connection gives rise to the 'interferometric' geometric phase of Sjqvist et al (2000 Phys. Rev. Lett. 85 2845-9), and for more generally evolving open systems it gives rise to the generalization of the interferometric geometric phase due to Tong et al (2004 Phys. Rev. Lett. 93 080405).

  • 4.
    Andersson, Ole
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Quantum speed limits and optimal Hamiltonians for driven systems in mixed states2014In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 47, no 21, p. 215301-Article in journal (Refereed)
    Abstract [en]

    Inequalities of Mandelstam-Tamm (MT) and Margolus-Levitin (ML) type provide lower bounds on the time that it takes for a quantum system to evolve from one state into another. Knowledge of such bounds, called quantum speed limits, is of utmost importance in virtually all areas of physics, where determination of the minimum time required for a quantum process is of interest. Most MT and ML inequalities found in the literature have been derived from growth estimates for the Bures length, which is a statistical distance measure. In this paper we derive such inequalities by differential geometric methods, and we compare the quantum speed limits obtained with those involving the Bures length. We also characterize the Hamiltonians which optimize the evolution time for generic finite-level quantum systems.

  • 5. Arutyunov, Gleb
    et al.
    Heinze, Martin
    Medina-Rincon, Daniel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Uppsala University, Sweden .
    Integrability of the eta-deformed Neumann-Rosochatius model2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 3, article id 035401Article in journal (Refereed)
    Abstract [en]

    An integrable deformation of the well-known Neumann-Rosochatius system is studied by considering generalised bosonic spinning solutions on the eta-deformed AdS(5) x S-5 background. For this integrable model we construct a 4x4 Lax representation and a set of integrals of motion that ensures its Liouville integrability. These integrals of motion correspond to the deformed analogues of the Neumann-Rosochatius integrals and generalise the previously found integrals for the.-deformed Neumann and (AdS(5) x S-5)(eta) geodesic systems. Finally, we briefly comment on consistent truncations of this model.

  • 6. Arutyunov, Gleb
    et al.
    Heinze, Martin
    Medina-Rincon, Daniel
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Uppsala University, Sweden.
    Superintegrability of geodesic motion on the sausage model2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 24, article id 244002Article in journal (Refereed)
    Abstract [en]

    Reduction of the eta-deformed sigma model on AdS(5) x S-5 to the two-dimensional squashed sphere (S-2)eta can be viewed as a special case of the Fateev sausage model where the coupling constant v is imaginary. We show that geodesic motion in this model is described by a certain superintegrable mechanical system with four-dimensional phase space. This is done by means of explicitly constructing three integrals of motion which satisfy the sl(2) Poisson algebra relations, albeit being non-polynomial in momenta. Further, we find a canonical transformation which transforms the Hamiltonian of this mechanical system to the one describing the geodesic motion on the usual two-sphere. By inverting this transformation we map geodesics on this auxiliary two-sphere back to the sausage model.

  • 7.
    Bargheer, Till
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Beisert, Niklas
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Loebbert, Florian
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    McLoughlin, Tristan
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Conformal anomaly for amplitudes in N=6 superconformal Chern-Simons theory2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 47, p. 475402-Article in journal (Refereed)
    Abstract [en]

    Scattering amplitudes in three-dimensional N = 6 Chern-Simons theory are shown to be non-invariant with respect to the free representation of the osp(6 vertical bar 4) symmetry generators. At tree and one-loop level these 'anomalous' terms occur only for non-generic, singular configurations of the external momenta and can be used to determine the form of the amplitudes. In particular we show that the symmetries predict that the one-loop six-point amplitude is non-vanishing and confirm this by means of an explicit calculation using generalized unitarity methods. We comment on the implications of this finding for any putative Wilson loop/amplitude duality in N = 6 Chern-Simons theory.

  • 8.
    Bengtsson, Ingemar
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Blanchfield, Kate
    Stockholm University, Faculty of Science, Department of Physics.
    Campbell, Earl
    Howard, Mark
    Order 3 Symmetry in the Clifford Hierarchy2014In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 47, no 45, p. 455302-Article in journal (Refereed)
    Abstract [en]

    We investigate the action of Weyl-Heisenberg and Clifford groups on sets of vectors that comprise mutually unbiased bases (MUBs). We consider two distinct MUB constructions, the standard and Alltop constructions, in Hilbert spaces of prime dimension. We show how the standard set of MUBs turns into the Alltop set under the action of an element at the third level of the Clifford hierarchy. We prove that when the dimension is a prime number equal to one modulo three each Alltop vector is invariant under an element of the Clifford group of order 3. The set of all Alltop vectors splits into three different orbits of the Clifford group, and forms a configuration together with the set of all subspaces invariant under an order 3 element of the Clifford group. There is a well-known conjecture that SIC vectors can be found in the eigenspace of order 3 Cliffords. This, combined with a connection between MUB and SIC vectors, suggests our work may provide a clue to the SIC existence problem in these dimensions. We identify Alltop vectors as so-called magic states which appear in the context of fault-tolerant quantum computing. The appearance of distinct Clifford orbits implies an inequivalence between some magic states.

  • 9. Berkolaiko, Gregory
    et al.
    Kennedy, James B.
    Kurasov, Pavel
    Stockholm University, Faculty of Science, Department of Mathematics.
    Mugnolo, Delio
    Edge connectivity and the spectral gap of combinatorial and quantum graphs2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 36, article id 365201Article in journal (Refereed)
    Abstract [en]

    We derive a number of upper and lower bounds for the first nontrivial eigenvalue of Laplacians on combinatorial and quantum graph in terms of the edge connectivity, i.e. the minimal number of edges which need to be removed to make the graph disconnected. On combinatorial graphs, one of the bounds corresponds to a well-known inequality of Fiedler, of which we give a new variational proof. On quantum graphs, the corresponding bound generalizes a recent result of Band and Levy. All proofs are general enough to yield corresponding estimates for the p-Laplacian and allow us to identify the minimizers. Based on the Betti number of the graph, we also derive upper and lower bounds on all eigenvalues which are 'asymptotically correct', i.e. agree with the Weyl asymptotics for the eigenvalues of the quantum graph. In particular, the lower bounds improve the bounds of Friedlander on any given graph for all but finitely many eigenvalues, while the upper bounds improve recent results of Ariturk. Our estimates are also used to derive bounds on the eigenvalues of the normalized Laplacian matrix that improve known bounds of spectral graph theory.

  • 10. Borsato, Riccardo
    et al.
    Ohlsson Sax, Olof
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Sfondrini, Alessandro
    Stefanski, Bogdan
    On the spectrum of AdS(3) x S-3 x T-4 strings with Ramond-Ramond flux2016In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 49, no 41, article id 41LT03Article in journal (Refereed)
    Abstract [en]

    We analyze the spectrum of perturbative closed strings on AdS(3) x S-3 x T-4 with Ramond-Ramond flux using integrable methods. By solving the crossing equations we determine the massless and mixed-mass dressing factors of the worldsheet S matrix and derive the Bethe equations. Using these, we construct the underlying integrable spin chain and show that it reproduces the reducible spin chain conjectured at weak coupling in Olof Ohlsson S, Bogdan S Jr and Torrielli A 2013 (arXiv: 1211.1952). We find that the string-theory massless modes are described by gapless excitations of the spin chain. The resulting degeneracy of vacua matches precisely the protected supergravity spectrum found by de Boer.

  • 11. Borsato, Riccardo
    et al.
    Ohlsson Sax, Olof
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Sfondrini, Alessandro
    Stefanski, Bogdan
    Torrielli, Alessandro
    On the dressing factors, Bethe equations and Yangian symmetry of strings on AdS(3) x S-3 x T-42017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 2, article id 024004Article in journal (Refereed)
    Abstract [en]

    Integrability is believed to underlie the AdS3/CFT2 correspondence with sixteen supercharges. We elucidate the role of massless modes within this integrable framework. Firstly, we find the dressing factors that enter the massless and mixed-mass worldsheet S matrix. Secondly, we derive a set of all-loop Bethe Equations for the closed strings, determine their symmetries and weak-coupling limit. Thirdly, we investigate the underlying Yangian symmetry in the massless sector and show that it fits into the general framework of Yangian integrability. In addition, we compare our S matrix in the near-relativistic limit with recent perturbative worldsheet calculations of Sundin and Wulff.

  • 12.
    Borsato, Riccardo
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Universidade de Santiago de Compostela, Spain.
    Wulff, Linus
    Marginal deformations of WZW models and the classical Yang-Baxter equation2019In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, no 22, article id 225401Article in journal (Refereed)
    Abstract [en]

    We show how so-called Yang-Baxter (YB) deformations of sigma models, based on an R-matrix solving the classical Yang-Baxter equation (CYBE), give rise to marginal current-current deformations when applied to the Wess-Zumino-Witten (WZW) model. For non-compact groups these marginal deformations are more general than the ones usually considered, since they can involve a non-Abelian current subalgebra. We classify such deformations of the AdS(3) x S-3 string.

  • 13. Budroni, Costantino
    et al.
    Cabello, Adan
    Stockholm University, Faculty of Science, Department of Physics.
    Bell inequalities from variable-elimination methods2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 38, p. 385304-Article in journal (Refereed)
    Abstract [en]

    Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here, we present an alternative method based on a combination of algebraic results on extensions of measures and variable-elimination methods, e. g., the Fourier-Motzkin method. Our method is shown to overcome some of the computational difficulties associated with the hull problem in some non-trivial cases. Moreover, it provides an explanation for the arising of only a finite number of families of Bell inequalities in measurement scenarios where one experimenter can choose between an arbitrary number of different measurements.

  • 14.
    Cabello, Adan
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Danielsen, Lars Eirik
    Lopez-Tarrida, Antonio J.
    Portillo, Jose R.
    Quantum social networks2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 28, p. 285101-Article in journal (Refereed)
    Abstract [en]

    We introduce a physical approach to social networks (SNs) in which each actor is characterized by a yes-no test on a physical system. This allows us to consider SNs beyond those originated by interactions based on pre-existing properties, as in a classical SN (CSN). As an example of SNs beyond CSNs, we introduce quantum SNs (QSNs) in which actor i is characterized by a test of whether or not the system is in a quantum state |psi(i)>. We show that QSNs outperform CSNs for a certain task and some graphs. We identify the simplest of these graphs and show that graphs in which QSNs outperform CSNs are increasingly frequent as the number of vertices increases. We also discuss more general SNs and identify the simplest graphs in which QSNs cannot be outperformed.

  • 15.
    Cagnazzo, Alessandra
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Sorokin, Dmitri
    Tseytlin, Arkady A.
    Wulff, Linus
    Semiclassical equivalence of Green-Schwarz and pure-spinor/hybrid formulations of superstrings in AdS(5) x S-5 and AdS(2) x S-2 x T-62013In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 6, p. 065401-Article in journal (Refereed)
    Abstract [en]

    We demonstrate the equivalence between the worldsheet one-loop partition functions computed near classical string solutions in the Green-Schwarz and in the pure-spinor formulations of superstrings in AdS(5) x S-5. While their bosonic sectors are the same in the conformal gauge, their fermionic sectors superficially appear to be very different (first versus second-derivative kinetic terms, presence versus absence of fermionic gauge symmetry). Still, we show that the quadratic fluctuation spectrum of 16 fermionic modes of the pure-spinor formulation is the same as in the Green-Schwarz superstring and the contribution of the extra 'massless' fermionic modes cancels against that of the pure-spinor ghosts. We also provide evidence for a similar semiclassical equivalence between the Green-Schwarz and the hybrid formulations of superstrings in AdS(2) x S-2 x T-6 by studying several particular examples of string solutions.

  • 16.
    Caputa, Pawel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Kyoto University, Japan.
    Kusuki, Yuya
    Takayanagi, Tadashi
    Watanabe, Kento
    Evolution of entanglement entropy in orbifold CFTs2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 24, article id 244001Article in journal (Refereed)
    Abstract [en]

    In this work we study the time evolution of the Renyi entanglement entropy for locally excited states created by twist operators in the cyclic orbifold (T-2)(n)/Z(n) and the symmetric orbifold (T-2)(n)/S-n. We find that when the square of its compactification radius is rational, the second Renyi entropy approaches a universal constant equal to the logarithm of the quantum dimension of the twist operator. On the other hand, in the non-rational case, we find a new scaling law for the Renyi entropies given by the double logarithm of time log log t for the cyclic orbifold CFT.

  • 17.
    Caputa, Pawel
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Rams, Marek M.
    Quantum dimensions from local operator excitations in the Ising model2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 5, article id 055002Article in journal (Refereed)
    Abstract [en]

    We compare the time evolution of entanglement measures after local operator excitation in the critical Ising model with predictions from conformal field theory. For the spin operator and its descendants we find that Renyi entropies of a block of spins increase by a constant that matches the logarithm of the quantum dimension of the conformal family. However, for the energy operator we find a small constant contribution that differs from the conformal field theory answer equal to zero. We argue that the mismatch is caused by the subtleties in the identification between the local operators in conformal field theory and their lattice counterpart. Our results indicate that evolution of entanglement measures in locally excited states not only constraints this identification, but also can be used to extract non-trivial data about the conformal field theory that governs the critical point. We generalize our analysis to the Ising model away from the critical point, states with multiple local excitations, as well as the evolution of the relative entropy after local operator excitation and discuss universal features that emerge from numerics.

  • 18. Chruściński, Dariusz
    et al.
    Sarbicki, Gniewomir
    Stockholm University, Faculty of Science, Department of Physics. Nicolaus Copernicus University, Poland.
    Exposed positive maps: a sufficient condition2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 11, article id 115304Article in journal (Refereed)
    Abstract [en]

    Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a sufficient condition for a positive map to be exposed. This is an analogue of a spanning property which guarantees that a positive map is optimal. We analyze a class of decomposable maps for which this condition is also necessary.

  • 19. Cooke, Michael
    et al.
    Dekel, Amit
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Drukker, Nadav
    The Wilson loop CFT: insertion dimensions and structure constants from wavy lines2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 33, article id 335401Article in journal (Refereed)
    Abstract [en]

    We study operator insertions into the 1/2 BPS Wilson loop in N = 4 SYM theory and determine their two-point coefficients, anomalous dimensions and structure constants. The calculation is done for the first few lowest dimension insertions and relies on known results for the expectation value of a smooth Wilson loop. In addition to the particular coefficients that we calculate, our study elucidates the connection between deformations of the line and operator insertions and between the vacuum expectation value of the line and the CFT data of the insertions.

  • 20.
    de Wijn, A. S.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Hess, B.
    Fine, B. V.
    Lyapunov instabilities in lattices of interacting classical spins at infinite temperature2013In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 25, p. 254012-Article in journal (Refereed)
    Abstract [en]

    We numerically investigate Lyapunov instabilities for one-, two-and three-dimensional lattices of interacting classical spins at infinite temperature. We obtain the largest Lyapunov exponents for a very large variety of nearest-neighbor spin-spin interactions and complete Lyapunov spectra in a few selected cases. We investigate the dependence of the largest Lyapunov exponents and whole Lyapunov spectra on the lattice size and find that both quickly become size-independent. Finally, we analyze the dependence of the largest Lyapunov exponents on the anisotropy of spin-spin interaction with the particular focus on the difference between bipartite and nonbipartite lattices.

  • 21.
    Fremling, Mikael
    Stockholm University, Faculty of Science, Department of Physics.
    Coherent state wave functions on a torus with a constant magnetic field2013In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 27, article id 275302Article in journal (Refereed)
    Abstract [en]

    We study two alternative definitions of localized states in the lowest Landau level (LLL) on a torus. One definition is to construct localized states, as the projection of the coordinate delta function onto the LLL. Another definition, proposed by Haldane, is to consider the set of functions which have all their zeros at a single point. Since a LLL wave function on a torus, supporting N-phi magnetic flux quanta, is uniquely defined by the position of its N-phi zeros, this defines a set of functions that are expected to be localized around the point maximally far away from the zeros. These two families of localized states have many properties in common with the coherent states on the plane and on the sphere, viz a resolution of unity and a self-reproducing kernel. However, we show that only the projected delta function is maximally localized. Additionally, we show how to project onto the LLL, functions that contain holomorphic derivatives and/or anti-holomorphic polynomials, and apply our methods in the description of hierarchical quantum Hall liquids.

  • 22.
    Fremling, Mikael
    Stockholm University, Faculty of Science, Department of Physics. National University of Ireland, Ireland.
    Success and failure of the plasma analogy for Laughlin states on a torus2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 1, article id 015201Article in journal (Refereed)
    Abstract [en]

    We investigate the nature of the plasma analogy for the Laughlin wave function on a torus describing the quantum Hall plateau at nu = 1/q. We first establish, as expected, that the plasma is screening if there are no short nontrivial paths around the torus. We also find that when one of the handles has a short circumference-i.e. the thin-torus limit-the plasma no longer screens. To quantify this we compute the normalization of the Laughlin state, both numerically and analytically. In the thin torus limit, the analytical form of the normalization simplify and we can reconstruct the normalization and analytically extend it back into the 2D regime. We find that there are geometry dependent corrections to the normalization, and this in turn implies that the plasma in the plasma analogy is not screening when in the thin torus limit. Despite the breaking of the plasma analogy in this limit, the analytical approximation is still a good description of the normalization for all tori, and also allows us to compute hall viscosity at intermediate thickness.

  • 23.
    Grøsfjeld, Tobias
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Shapiro, Boris
    Stockholm University, Faculty of Science, Department of Mathematics.
    Zarembo, Konstantin
    Level crossing in random matrices. II. Random perturbation of a random matrix2019In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, no 21, article id 214001Article in journal (Refereed)
    Abstract [en]

    In this paper we study the distribution of level crossings for the spectra of linear families A + lambda B, where A and B are square matrices independently chosen from some given Gaussian ensemble and lambda is a complex-valued parameter. We formulate a number of theoretical and numerical results for the classical Gaussian ensembles and some of their generalisations. Besides, we present intriguing numerical information about the monodromy distribution in case of linear families for the classical Gaussian ensembles of 3 x 3-matrices.

  • 24.
    Guica, Monica
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Institut de Physique Théorique, France.
    On correlation functions in J(T)over-bar-deformed CFTs2019In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, no 18, article id 184003Article in journal (Refereed)
    Abstract [en]

    The J (T) over bar deformation, built from the components of the stress tensor and of a U(1) current, is a universal irrelevant deformation of two-dimensional CFTs that preserves the left-moving conformal symmetry, while breaking locality on the right-moving side. Operators in the J (T) over bar -deformed CFT are naturally labeled by the left-moving position and right-moving momentum and transform in representations of the one-dimensional extended conformal group. We derive an all-orders formula for the spectrum of conformal dimensions and charges of the deformed CFT, which we cross-check at leading order using conformal perturbation theory. We also compute the linear corrections to the one-dimensional OPE coefficients and comment on the extent to which the correlation functions in J (T) over bar -deformed CFTs can be obtained from field-dependent coordinate transformations.

  • 25.
    Guica, Monica
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). CEA Saclay, France; Uppsala University, Sweden.
    Levkovich Maslyuk, Fedor
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Zarembo, Konstantin
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Uppsala University, Sweden.
    Integrability in dipole-deformed N=4 super Yang-Mills2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 39, article id 394001Article in journal (Refereed)
    Abstract [en]

    We study the null dipole deformation of N = 4 super Yang-Mills theory, which is an example of a potentially solvable 'dipole CFT': a theory that is non-local along a null direction, has non-relativistic conformal invariance along the remaining ones, and is holographically dual to a Schrodinger space-time. We initiate the field-theoretical study of the spectrum in this model by using integrability inherited from the parent theory. The dipole deformation corresponds to a nondiagonal Drinfeld-Reshetikhin twist in the spin chain picture, which renders the traditional Bethe ansatz inapplicable from the very beginning. We use instead the Baxter equation supplemented with nontrivial asymptotics, which gives the full 1-loop spectrum in the sl(2) sector. We show that anomalous dimensions of long gauge theory operators perfectly match the string theory prediction, providing a quantitative test of Schrodinger holography.

  • 26. Harland, Derek
    et al.
    Jäykkä, Juha
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Shnir, Yakov
    Speight, Martin
    Isospinning hopfions2013In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 22, p. 225402-Article in journal (Refereed)
    Abstract [en]

    The problem of constructing internally rotating solitons of fixed angular frequency omega in the Faddeev-Skyrme model is reformulated as a variational problem for an energy-like functional, called pseudoenergy, which depends parametrically on omega. This problem is solved numerically using a gradient descent method, without imposing any spatial symmetries on the solitons, and the dependence of the solitons' energy on omega, and on their conserved total isospin J, studied. It is found that, generically, the shape of a soliton is independent of omega, and that its size grows monotonically with omega. A simple elastic rod model of time-dependent hopfions is developed which, despite having only one free parameter, accounts well for most of the numerical results.

  • 27.
    Hertz, John A.
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Copenhagen, Denmark.
    Roudi, Yasser
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Kavli Institute for Systems Neuroscience and Centre for Neural Computation, NTNU, Norway; Institute for Advanced Study, Princeton, NJ, USA.
    Sollich, Peter
    Path integral methods for the dynamics of stochastic and disordered systems2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 3, article id 033001Article, review/survey (Refereed)
    Abstract [en]

    We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose/Janssen-De Dominicis-Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models.

  • 28.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    A geometric framework for mixed quantum states based on a Kahler structure2015In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, no 25, article id 255301Article in journal (Refereed)
    Abstract [en]

    In this paper we introduce a geometric framework for mixed quantum states based on a Kahler structure. The geometric framework includes a symplectic form, an almost complex structure, and a Riemannian metric that characterize the space of mixed quantum states. We argue that the almost complex structure is integrable. We also in detail discuss a visualizing application of this geometric framework by deriving a geometric uncertainty relation for mixed quantum states. The framework is computationally effective and it provides us with a better understanding of general quantum mechanical systems.

  • 29.
    Kate, Blanchfield
    Stockholm University, Faculty of Science, Department of Physics.
    Orbits of mutually unbiased bases2014In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 47, no 13, p. 135303-Article in journal (Refereed)
    Abstract [en]

    We express Alltop's construction of mutually unbiased bases as orbits under the Weyl–Heisenberg group in prime dimensions and find a related construction in dimensions 2 and 4. We reproduce Alltop's mutually unbiased bases using abelian subgroups of the Clifford group in prime dimensions, in direct analogy to the well-known construction of mutually unbiased bases using abelian subgroups of the Weyl–Heisenberg group. Finally, we prove three theorems relating to the distances and linear dependencies among different sets of mutually unbiased bases.

  • 30.
    Krishnamurthy, Supriya
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Smith, Eric
    Solving moment hierarchies for chemical reaction networks2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 42, article id 425002Article in journal (Refereed)
    Abstract [en]

    The study of chemical reaction networks (CRN's) is a very active field. Earlier well-known results (Feinberg 1987 Chem. Enc. Sci. 42 2229, Anderson et al 2010 Bull. Math. Biol. 72 1947) identify a topological quantity called deficiency, for any CRN, which, when exactly equal to zero, leads to a unique factorized steady-state for these networks. No results exist however for the steady states of non-zero-deficiency networks. In this paper, we show how to write the full moment-hierarchy for any non-zero-deficiency CRN obeying mass-action kinetics, in terms of equations for the factorial moments. Using these, we can recursively predict values for lower moments from higher moments, reversing the procedure usually used to solve moment hierarchies. We show, for non-trivial examples, that in this manner we can predict any moment of interest, for CRN's with non-zero deficiency and non-factorizable steady states.

  • 31.
    Kurasov, Pavel
    Stockholm University.
    Response to "Comment on 'On the Coulomb potential in one dimension' " by W.Fisher, H.Leschke and P.Muller1997In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121Article in journal (Refereed)
  • 32.
    Kurasov, Pavel
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Malenova, G.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Naboko, S.
    Spectral gap for quantum graphs and their edge connectivity2013In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 27, p. 275309-Article in journal (Refereed)
    Abstract [en]

    The spectral gap for Laplace operators on metric graphs and the relation between the graph's edge connectivity is investigated, in particular what happens to the gap if an edge is added to (or deleted from) a graph. It is shown that, in contrast to discrete graphs, the connection between the connectivity and the spectral gap is not one-to-one. The size of the spectral gap depends not only on the topology of the metric graph but on its geometric properties as well. It is shown that adding sufficiently large edges as well as cutting away sufficiently small edges leads to a decrease of the spectral gap. Corresponding explicit criteria are given.

  • 33.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Nowaczyk, Marlena
    Lunds universitet.
    Inverse spectral problem for quantum graphs2005In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121Article in journal (Refereed)
  • 34.
    Kurasov, Pavel
    et al.
    Stockholm University.
    Stenberg, Fredrik
    On the inverse scattering problem on branching graphs2002In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121Article in journal (Refereed)
  • 35.
    Larson, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Irish, Elinor K.
    Some remarks on 'superradiant' phase transitions in light-matter systems2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 17, article id 174002Article in journal (Refereed)
    Abstract [en]

    In this paper we analyze properties of the phase transition that appears in a set of quantum optical models; Dicke, Tavis-Cummings, quantum Rabi, and finally the Jaynes-Cummings model. As the light-matter coupling is increased into the deep strong coupling regime, the ground state turns from vacuum to become a superradiant state characterized by both atomic and photonic excitations. It is pointed out that all four transitions are of the mean-field type, that quantum fluctuations are negligible, and hence these fluctuations cannot be responsible for the corresponding vacuum instability. In this respect, these are not quantum phase transitions. In the case of the Tavis-Cummings and Jaynes-Cummings models, the continuous symmetry of these models implies that quantum fluctuations are not only negligible, but strictly zero. However, all models possess a non-analyticity in the ground state in agreement with a continuous quantum phase transition. As such, it is a matter of taste whether the transitions should be termed quantum or not. In addition, we also consider the modifications of the transitions when photon losses are present. For the Dicke and Rabi models these non-equilibrium steady states remain critical, while the criticality for the open Tavis-Cummings and Jaynes-Cummings models is completely lost, i. e. in realistic settings one cannot expect a true critical behaviour for the two last models.

  • 36. Mahdifar, Ali
    et al.
    Mirza, Behrouz
    Roknizadeh, Rasoul
    Stockholm University, Faculty of Science, Department of Physics.
    Two-dimensional isotropic harmonic oscillator on a time-dependent sphere2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 46, p. 465301-Article in journal (Refereed)
    Abstract [en]

    In this paper, we investigate a two-dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a fluctuating background, transition probabilities per unit time are obtained. Transitions are possible if the energy eigenvalues of the oscillator E-i and frequencies of the fluctuating background omega(n) satisfy the following two simple relations: E-j similar or equal to E-i - (h) over bar omega(n) (stimulated emission) and E-j similar or equal to E-i + (h) over bar omega(n) (absorption). This indicates that a background fluctuating at a frequency of omega(n) interacts with the oscillator as a quantum field of the same frequency. We believe this result is also applicable for an arbitrary quantum system defined on a fluctuating maximally symmetric background.

  • 37.
    Majidzadeh Garjani, Babak
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Faculty of Science, Department of Mathematics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Ardonne, Eddy
    Stockholm University, Faculty of Science, Department of Physics.
    Anyon chains with pairing terms2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 13, article id 135201Article in journal (Refereed)
    Abstract [en]

    In this paper we introduce a one-dimensional model of $su(2)_k$ anyons in which the number of anyons can uctuate by means of a pairing term. The model can be tuned to a point at which one can determine the exact zero-energy ground states, in close analogy to the spin-1 AKLT model. We also determine the points at which the model is integrable and determine the behavior of the model at these integrable points. 

  • 38.
    Majidzadeh Garjani, Babak
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Estienne, B.
    Ardonne, Eddy
    Stockholm University, Faculty of Science, Department of Physics.
    On the particle entanglement spectrum of the Laughlin states2015In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, no 28, article id 285205Article in journal (Refereed)
    Abstract [en]

    The study of the entanglement entropy and entanglement spectrum has proven to be very fruitful in identifying topological phases of matter. Typically, one performs numerical studies of finite-size systems. However, there are few rigorous results in this regard. We revisit the problem of determining the rank of the 'particle entanglement spectrum' (PES) of the Laughlin states. We reformulate the problem into a problem concerning the ideal of symmetric polynomials that vanish under the formation of several clusters of particles. We introduce an explicit generating set of this ideal, and we prove that polynomials in this ideal have a total degree that is bounded from below. We discuss the difficulty in proving the same bound on the degree of any of the variables, which is necessary to determine the rank of the PES.

  • 39.
    Manikandan, Sreekanth K.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Krishnamurthy, Supriya
    Stockholm University, Faculty of Science, Department of Physics.
    Exact results for the finite time thermodynamic uncertainty relation2018In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 51, no 11, article id 11LT01Article in journal (Refereed)
    Abstract [en]

    We obtain exact results for the recently discovered finite-time thermodynamic uncertainty relation, for the dissipated work W-d, in a stochastically driven system with non-Gaussian work statistics, both in the steady state and transient regimes, by obtaining exact expressions for any moment of W-d at arbitrary times. The uncertainty function (the Fano factor of W-d) is bounded from below by 2k(B)T as expected, for all times tau, in both steady state and transient regimes. The lower bound is reached at tau = 0 as well as when certain system parameters vanish (corresponding to an equilibrium state). Surprisingly, we find that the uncertainty function also reaches a constant value at large tau for all the cases we have looked at. For a system starting and remaining in steady state, the uncertainty function increases monotonically, as a function of tau as well as other system parameters, implying that the large t value is also an upper bound. For the same system in the transient regime, however, we find that the uncertainty function can have a local minimum at an accessible time tau(m), for a range of parameter values. The large tau value for the uncertainty function is hence not a bound in this case. The non-monotonicity suggests, rather counter-intuitively, that there might be an optimal time for the working of microscopic machines, as well as an optimal configuration in the phase space of parameter values. Our solutions show that the ratios of higher moments of the dissipated work are also bounded from below by 2k(B)T. For another model, also solvable by our methods, which never reaches a steady state, the uncertainty function, is in some cases, bounded from below by a value less than 2k(B)T.

  • 40. Nissinen, Jaakko
    et al.
    Ardonne, Eddy
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Local height probabilities in a composite Andrews-Baxter-Forrester model2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 43, p. 435001-Article in journal (Refereed)
    Abstract [en]

    We study the local height probabilities in a composite height model, derived from the restricted solid-on-solid model introduced by Andrews, Baxter and Forrester, and their connection with conformal field theory characters. The obtained conformal field theories also describe the critical behavior of the model at two different critical points. In addition, at criticality, the model is equivalent to a one-dimensional chain of anyons, subject to competing two-and three-body interactions. The anyonic-chain interpretation provided the original motivation to introduce the composite height model, and by obtaining the critical behavior of the composite height model, the critical behavior of the anyonic chains is established as well. Depending on the overall sign of the Hamiltonian, this critical behavior is described by a diagonal coset-model, generalizing the minimal models for one sign, and by Fateev-Zamolodchikov parafermions for the other.

  • 41.
    Rakityansky, S. A.
    et al.
    Univ Pretoria, Dept Phys, Pretoria, South Africa.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Analytic structure and power series expansion of the Jost function for the two-dimensional problem2012In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 45, no 13, p. 135209-Article in journal (Refereed)
    Abstract [en]

    For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multi-valued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots.

  • 42. Rakityansky, S. A.
    et al.
    Elander, Nils
    Stockholm University, Faculty of Science, Department of Physics.
    Multi-channel analog of the effective-range expansion2011In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 44, no 11, p. 115303-Article in journal (Refereed)
    Abstract [en]

    Similar to the standard effective-range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jost-matrix that can be done near an arbitrary point on the Riemann surface of the energy within the domain of its analyticity. In order to do this, we analytically factorize its momentum dependences at all the branching points on the Riemann surface. The remaining single-valued matrix functions of the energy are then expanded in the power series near an arbitrary point in the domain of the complex energy plane where it is analytic. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This means that near an arbitrary point in the domain of physically interesting complex energies it is possible to obtain a semi-analytic expression for the Jost-matrix (and therefore for the S-matrix) and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles.

  • 43.
    Rakityansky, S. A.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Elander, Nils O
    Stockholm University, Faculty of Science, Department of Physics.
    Generalized effective-range expansion2009In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 42, no 22, p. 225302-Article in journal (Refereed)
    Abstract [en]

    A systematic and accurate procedure has been developed for calculating the coefficients phi((in/out))(ln) of the series expansion f(l)((in/out))(k) = Sigma(infinity)(n=0)(k-k(0))(n) phi((in/out))(ln) of the Jost functions in the vicinity of an arbitrary point k(0) in the complex momentum plane. This makes it possible to obtain an analytic expression for the S-matrix s(l)(k) = f(l)((out))(k)/f(l)((in))(k) around k(0) and locate its possible poles. In the particular case of l = 0 and k(0) = 0, any number of the parameters of the standard effective-range expansion k cot delta(0) = -1/a + r(0)k(2)/2 - ... are easily obtained using the corresponding coefficients phi((in/out))(ln). Numerical examples demonstrate the stability and accuracy of the proposed method.

  • 44.
    Rohleder, Jonathan
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Kühn, Christian
    Visibility of quantum graph spectrum from the vertices2018In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 51, no 9, article id 095204Article in journal (Refereed)
    Abstract [en]

    We investigate the relation between the eigenvalues of the Laplacian with Kirchhoff vertex conditions on a finite metric graph and a corresponding Titchmarsh–Weyl function (a parameter-dependent Neumann-to-Dirichlet map). We give a complete description of all real resonances, including multiplicities, in terms of the edge lengths and the connectivity of the graph, and apply it to characterize all eigenvalues which are visible for the Titchmarsh–Weyl function.

  • 45.
    Sarbicki, Gniewomir
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Nicolaus Copernicus University, Poland.
    Bengtsson, Ingemar
    Stockholm University, Faculty of Science, Department of Physics.
    Dissecting the qutrit2013In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 3, article id 035306Article in journal (Refereed)
    Abstract [en]

    To visualize a higher dimensional object it is convenient to consider its two-dimensional cross-sections. The set of quantum states for a three level system has eight dimensions. We supplement a recent paper by Goyal et al (arXiv: 1111.4427) by considering the set of all possible two-dimensional cross-sections of the qutrit. Each such cross-section is bounded by a plane cubic curve.

  • 46.
    Sarbicki, Gniewomir
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Nicolaus Copernicus University, Poland.
    Chruściński, Dariusz
    A class of exposed indecomposable positive maps2013In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 1, article id 015306Article in journal (Refereed)
    Abstract [en]

    Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a class of indecomposable positive maps in the algebra of 2n x 2n complex matrices with n >= 2. It is shown that these maps are exposed and hence define the strongest tool in entanglement theory to discriminate between separable and entangled states.

  • 47.
    Shapiro, Boris
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Zarembo, Konstantin
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Uppsala University, Sweden.
    Level crossing in random matrices: I. Random perturbation of a fixed matrix2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 4, article id 045201Article in journal (Refereed)
    Abstract [en]

    We consider level crossing in a matrix family H = H-0 + lambda V where H-0 is a fixed N x N matrix and V belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing points in the complex plane of lambda, for which we obtain a number of exact, asymptotic and approximate formulas.

  • 48.
    Tavakoli, Armin
    Stockholm University, Faculty of Science, Department of Physics. ICFO-Institut de Ciencies Fotoniques, Spain; University of California, USA.
    Quantum correlations in connected multipartite Bell experiments2016In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 49, no 14, article id 145304Article in journal (Refereed)
    Abstract [en]

    Bell experiments measure correlations between outcomes of a number of observers measuring on a shared physical state emitted from a single source. Quantum correlations arising in such Bell experiments have been intensively studied over the last decades. Much less is known about the nature of quantum correlations arising in network structures beyond Bell experiments. Such networks can involve many independent sources emitting states to observers in accordance with the network configuration. Here, we will study classical and quantum correlations in a family of networks which can be regarded as compositions of several independent multipartite Bell experiments connected together through a central node. For such networks we present tight Bell-type inequalities which are satisfied by all classical correlations. We study properties of the violations of our inequalities by probability distributions arising in quantum theory.

  • 49.
    Tavakoli, Armin
    et al.
    Stockholm University, Faculty of Science, Department of Physics. Uniwersytet Gdański, Poland.
    Zohren, Stefan
    Pawlowski, Marcin
    Maximal non-classicality in multi-setting Bell inequalities2016In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 49, no 14, article id 145301Article in journal (Refereed)
    Abstract [en]

    The discrepancy between maximally entangled states and maximally non-classical quantum correlations is well-known but still not well understood. We aim to investigate the relation between quantum correlations and entanglement in a family of Bell inequalities with N-settings and d outcomes. Using analytical as well as numerical techniques, we derive both maximal quantum violations and violations obtained from maximally entangled states. Furthermore, we study the most non-classical quantum states in terms of their entanglement entropy for large values of d and many measurement settings. Interestingly, we find that the entanglement entropy behaves very differently depending on whether N = 2 or N > 2: when N = 2 the entanglement entropy is a monotone function of d and the most non-classical state is far from maximally entangled, whereas when N > 2 the entanglement entropy is a non-monotone function of d and converges to that of the maximally entangled state in the limit of large d.

  • 50.
    Zarembo, Konstantin
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Uppsala University, Sweden.
    Localization and AdS/CFT correspondence2017In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 50, no 44, article id 443011Article, review/survey (Refereed)
    Abstract [en]

    An interplay between localization and holography is reviewed with the emphasis on the AdS5/CFT4 correspondence.

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