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  • 1.
    Andersson, O.
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Operational geometric phase for mixed quantum states2013In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 15, p. 053006-Article in journal (Refereed)
    Abstract [en]

    The geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper, we introduce an operational geometric phase for mixed quantum states, based on spectral weighted traces of holonomies, and we prove that it generalizes the standard definition of the geometric phase for mixed states, which is based on quantum interferometry. We also introduce higher order geometric phases, and prove that under a fairly weak, generically satisfied, requirement, there is always a well-defined geometric phase of some order. Our approach applies to general unitary evolutions of both non-degenerate and degenerate mixed states. Moreover, since we provide an explicit formula for the geometric phase that can be easily implemented, it is particularly well suited for computations in quantum physics.

  • 2.
    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).

  • 3.
    Andersson, Ole
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Dynamic Distance Measure on Spaces of Isospectral Mixed Quantum States2013In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 15, no 9, p. 3688-3697Article in journal (Refereed)
    Abstract [en]

    Distance measures are used to quantify the extent to which information is preserved or altered by quantum processes, and thus are indispensable tools in quantum information and quantum computing. In this paper we propose a new distance measure for mixed quantum states, which we call the dynamic distance measure, and we show that it is a proper distance measure. The dynamic distance measure is defined in terms of a measurable quantity, which makes it suitable for applications. In a final section we compare the dynamic distance measure with the well-known Bures distance measure.

  • 4.
    Andersson, Ole
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Geometric uncertainty relation for mixed quantum states2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 4, p. 042110-Article in journal (Refereed)
    Abstract [en]

    In this paper we use symplectic reduction in an Uhlmann bundle to construct a principal fiber bundle over a general space of unitarily equivalent mixed quantum states. The bundle, which generalizes the Hopf bundle for pure states, gives in a canonical way rise to a Riemannian metric and a symplectic structure on the base space. With these we derive a geometric uncertainty relation for observables acting on quantum systems in mixed states. We also give a geometric proof of the classical Robertson-Schrodinger uncertainty relation, and we compare the two. They turn out not to be equivalent, because of the multiple dimensions of the gauge group for general mixed states. We give examples of observables for which the geometric relation provides a stronger estimate than that of Robertson and Schrodinger, and vice versa.

  • 5.
    Andersson, Ole
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Geometry of quantum evolution for mixed quantum states2014In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T160, p. 014004-Article in journal (Refereed)
    Abstract [en]

    The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this work we discuss a geometric formulation of mixed quantum states represented by density operators. Our formulation is based on principal fiber bundles and purifications of quantum states. In our construction, the Riemannian metric and symplectic form on the total space are induced from the real and imaginary parts of the Hilbert-Schmidt Hermitian inner product, and we define a mechanical connection in terms of a locked inertia tensor and moment map. We also discuss some applications of our geometric framework.

  • 6.
    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.

  • 7.
    Andersson, Ole
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Spectral weighted geometric phase for mixed quantum states2014In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T163, article id 014027Article in journal (Refereed)
    Abstract [en]

    Geometric phase has found a broad spectrum of applications in both classical and quantum physics. In this work we discuss a geometric phase for mixed quantum states based on traces of spectral weighted holonomies. Our approach applies to general unitary evolutions of both nondegenerate and degenerate mixed states, and it generalizes the standard definition of geometric phase for mixed states, which is based on quantum interferometry. We provide an explicit formula for the geometric phase that can be easily implemented for computations in quantum physics, and we discuss higher order analogs of the geometric phase that might be defined at points where the ordinary geometric phase is undefined.

  • 8.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    A class of quantum gate entanglers2010In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T140, p. 14048-Article in journal (Refereed)
    Abstract [en]

    We construct quantum gate entanglers for different classes of multipartite states based on the definition of W and GHZ concurrence classes. First, we review the basic construction of concurrence classes based on the orthogonal complement of a positive operator valued measure (POVM) on quantum phase. Then, we construct quantum gate entanglers for different classes of multi-qubit states. In particular, we show that these operators can entangle multipartite states if they satisfy some conditions for W and GHZ classes of states. Finally, we explicitly give the W class and GHZ classes of quantum gate entanglers for four-qubit states.

  • 9.
    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.

  • 10.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Construction of entanglement witnesses based on concurrence for multi-qubit states2008In: Quantum information & computation, ISSN 1533-7146, Vol. 8, no 09-aug, p. 791-796Article in journal (Refereed)
    Abstract [en]

    We establish a relation between concurrence and entanglement witnesses. In particular, we construct entanglement witnesses for three-qubit W and GHZ states in terms of concurrence. We also generalize our construction for multi-qubit states. This result gives the finest entanglement witnesses for a given class of state without any optimization.

  • 11.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Different classes of quantum gates entanglers2009In: International journal of quantum information, ISSN 0219-7499, Vol. 7, no 1, p. 279-285Article in journal (Refereed)
    Abstract [en]

    We construct quantum gates entanglers for different classes of multipartite states. In particular, we construct entangler operators for W and GHZ classes of multipartite states based on the construction of the concurrence classes. We also discuss in detail these two classes of the quantum gates entanglers for three-partite states.

  • 12.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Generalized controlled phase quantum gates entanglers2009In: International journal of quantum information, ISSN 0219-7499, Vol. 7, no 6, p. 1211-1216Article in journal (Refereed)
    Abstract [en]

    We construct a generalized controlled phased gate entangler for a multi-qubit state based on the geometrical structure of quantum systems. We also investigate the relation between the generalized controlled phase construction of a quantum gate entangler and graph state for two-qubit and three-qubit states.

  • 13.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Geometry and Structure of Quantum Phase Space2015In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 45, no 7, p. 851-857Article in journal (Refereed)
    Abstract [en]

    The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an important role in foundations of quantum mechanics and quantum information. In this work we discuss a geometric framework for mixed quantum states represented by density matrices, where the quantum phase space of density matrices is equipped with a symplectic structure, an almost complex structure, and a compatible Riemannian metric. This compatible triple allow us to investigate arbitrary quantum systems. We will also discuss some applications of the geometric framework.

  • 14.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Multipartite quantum systems and symplectic toric manifolds2011In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 10, no 2, p. 257-269Article in journal (Refereed)
    Abstract [en]

    In this paper we study the geometrical structures of multi-qubit states based on symplectic toric manifolds. After a short review of symplectic toric manifolds, we discuss the space of a single quantum state in terms of these manifolds. We also investigate entangled multipartite states based on moment map and Delzant's construction of toric manifolds and algebraic toric varieties.

  • 15.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Noncommutative Geometrical Structures of Multi-Qubit Entangled States2011In: International journal of theoretical physics, ISSN 0020-7748, E-ISSN 1572-9575, Vol. 50, no 5, p. 1486-1492Article in journal (Refereed)
    Abstract [en]

    We study the noncommutative geometrical structures of quantum entangled states. We show that the space of a pure entangled state is a noncommutative space. In particular we show that by rewriting the coordinate ring of a conifold or the Segre variety we can get a q-deformed relation in noncommutative geometry. We generalized our construction into a multi-qubit state. We also in detail discuss the noncommutative geometrical structure of a three-qubit state.

  • 16.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Phase Entanglers for Multi-Qubit States2010In: Journal of Computational and Theoretical Nanoscience, ISSN 1546-1955, Vol. 7, no 9, p. 1754-1758Article in journal (Refereed)
    Abstract [en]

    The emerging and innovative field of quantum computation and quantum information could bring new insight to our understanding of nature with many applications such as quantum cryptography, quantum secret sharing, quantum teleportation, and quantum computer. In conventional scheme, a quantum computer could be design by quantum gates and circuits. In this paper, we construct geometrical controlled phase quantum gate entanglers for multi-qubit states based on the complex projective Grassmann variety which is defined by the Plucker embedding of Grassmann space. We explicitly give an expression for a geometrical three-qubit quantum gate entangler. We also discuss in detail the construction of the gate entangler for four-qubit states. Moreover, We give illustrative examples of physical implementations of our quantum gate entangler for two- and multi-qubit systems.

  • 17.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Quantum Gate Entangler and Entangling Capacity of a General Multipartite Quantum System2008In: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 15, no 3, p. 213-222Article in journal (Refereed)
    Abstract [en]

    We construct quantum gate entangler for general multipartite states based on the construction of complex projective varieties. We also discuss in detail the construction of quantum gate entangler for higher dimensional bipartite and multipartite quantum systems. Moreover, we construct and discuss entangling capacity of general multipartite quantum systems.

  • 18.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Quantum relative phase, m-tangle, and multi-local Lorentz-group invariant2010In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 9, no 2, p. 233-238Article in journal (Refereed)
    Abstract [en]

    In this paper we define a family of hermitian operators by which to extract what we call quantum-relative-phase properties of a pure or mixed multipartite quantum state, and we relate these properties to known measures of entanglement, namely the m-tangle and the invariant S-(m)(2) of the multi-local Lorentz-group SL(2, C)(circle times m). Our construction is based on the orthogonal complement of a positive operator valued measure on quantum phase.

  • 19.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Quantum relative phase, m-tangle, and multi-local Lorentz-group invariant2009In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 9, no 2, p. 233-238Article in journal (Refereed)
    Abstract [en]

    In this paper we define a family of hermitian operators by which to extract what we call quantum-relative-phase properties of a pure or mixed multipartite quantum state, and we relate these properties to known measures of entanglement, namely the m-tangle and the invariant S(m)2S2(m) of the multi-local Lorentz-group SL(2, \mathbbC)ÄmSL(2C)m  . Our construction is based on the orthogonal complement of a positive operator valued measure on quantum phase

  • 20.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Selective Phase Rotation Quantum Gate Entangler2009In: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 16, no 4, p. 407-412Article in journal (Refereed)
    Abstract [en]

    We construct a quantum gate entangler for multi-qubit states based on a selective phase rotation transform. In particular, we establish a relation between the quantum integral transform and the quantum gate entangler in terms of universal controlled gates for multi-qubit states. Our result gives an effective way of constructing topological and geometrical quantum gate entanglers for multipartite quantum systems, which could also lead to a construction of geometrical quantum algorithms.

  • 21.
    Heydari, Hoshang
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Andersson, Ole
    Stockholm University, Faculty of Science, Department of Physics.
    Geometric uncertainty relation for quantum ensembles2015In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 90, no 2, article id 025102Article in journal (Refereed)
    Abstract [en]

    Geometrical structures of quantum mechanics provide us with new insightful results about the nature of quantum theory. In this work we consider mixed quantum states represented by finite rank density operators. We review our geometrical framework that provide the space of density operators with Riemannian and symplectic structures, and we derive a geometric uncertainty relation for observables acting on mixed quantum states. We also give an example that visualizes the geometric uncertainty relation for spin-1/2 particles.

  • 22. Lotfipour, H.
    et al.
    Allameh, Z.
    Roknizadeh, R.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Two schemes for characterization and detection of the squeezed light: dynamical Casimir effect and nonlinear materials2016In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455, Vol. 49, no 6, article id 065503Article in journal (Refereed)
    Abstract [en]

    Using two different schemes, a non-classical-squeezed state of light is detected and characterized. In the first scheme, in a one-dimensional cavity with a moving mirror (non-stationary Casimir effect) in the principal mode, we study the photon generation rate for two modes (squeezed and coherent state) of a driving field. Since the cavity with the moving mirror (similar to an optomechanical system) can be considered an analogue to a Kerr-like medium, in the second scheme, the probability amplitude for multi-photon absorption in a nonlinear (Kerr) medium will be quantum mechanically calculated. It is shown that because of the presence of nonlinear effects, the responses of these two systems to the squeezed versus coherent state are considerably distinguishable. The drastic difference between the results of these two states of light can be viewed as a proposal for detecting non-classical states.

  • 23. Roknizadeh, R.
    et al.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Complexifier Method for Generation of Coherent States of Nonlinear Harmonic Oscillator2015In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 45, no 7, p. 827-839Article in journal (Refereed)
    Abstract [en]

    In this work we present a construction of coherent states based on complexifier method for a special type of one dimensional nonlinear harmonic oscillator presented by Mathews and Lakshmanan (Q Appl Math 32:215, 1974). We will show the state quantization by using coherent states, or to build the Hilbert space according to a classical phase space, is equivalent to departure from real coordinates to complex ones.

  • 24.
    Roknizadeh, Rasoul
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    COMPLEXIFIER VERSUS FACTORIZATION AND DEFORMATION METHODS FOR GENERATION OF COHERENT STATES OF A 1D NLHO I. MATHEMATICAL CONSTRUCTION2013In: International Journal of Geometric Methods in Modern Physics (IJGMMP), ISSN 0219-8878, Vol. 10, no 10, p. 1350056-Article in journal (Refereed)
    Abstract [en]

    Three methods: complexifier, factorization and deformation, for construction of coherent states are presented for one-dimensional nonlinear harmonic oscillator (1D NLHO). Since by exploring the Jacobi polynomials P-n(a, b)' s, bridging the difference between them is possible, we give here also the exact solution of Schrodinger equation of 1D NLHO in terms of Jacobi polynomials.

  • 25.
    Sezer, Hasan Cavit
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    A representation of extra-special 2-group, entanglement, and Berry phase of two qubits in Yang-Baxter system2012In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 11, no 6, p. 1685-1694Article in journal (Refereed)
    Abstract [en]

    In this paper we show another representations of extra-special 2-groups. Based on this new representation, we infer a matrix which obeys the extra-special 2-groups algebra relations. We also derive a unitary matrix from the using the Yang-Baxterization process. A Hamiltonian for the two qubits is constructed from the unitary matrix. In this way, we study the Berry phase and entanglement of the two-qubit system. The results also establish relations between topological and holonomic quantum computation.

  • 26.
    Sharif, Puya
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    QUANTUM SOLUTION TO A THREE PLAYER KOLKATA RESTAURANT PROBLEM USING ENTANGLED QUTRITS2014In: Quantum information & computation, ISSN 1533-7146, Vol. 14, no 3-4, p. 295-305Article in journal (Refereed)
    Abstract [en]

    Three player quantum Kolkata restaurant problem is modelled using three entangled qutrits. This first use of three level quantum states in this context is a step towards a N-choice generalization of the N-player quantum minority game. It is shown that a better than classical payoff is achieved by a Nash equilibrium solution where the space of available strategies is spanned by subsets of SU(3) and the players share a tripartite entangled initial state.

  • 27.
    Tehrani, Mojtaba Taslimi
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Singularity avoidance of charged black holes in loop quantum gravity2012In: International journal of theoretical physics, ISSN 0020-7748, E-ISSN 1572-9575, Vol. 51, no 11, p. 3614-3626Article in journal (Refereed)
    Abstract [en]

    Based on spherically symmetric reduction of loop quantum gravity, quantization of the portion interior to the horizon of a Reissner-Nordstrom black hole is studied. Classical phase space variables of all regions of such a black hole are calculated for the physical case M (2)> Q (2). This calculation suggests a candidate for a classically unbounded function of which all divergent components of the curvature scalar are composed. The corresponding quantum operator is constructed and is shown explicitly to possess a bounded operator. Comparison of the obtained result with the one for the Schwarzschild case shows that the upper bound of the curvature operator of a charged black hole reduces to that of Schwarzschild at the limit Q -> 0. This local avoidance of singularity together with non-singular evolution equation indicates the role quantum geometry can play in treating classical singularity of such black holes.

1 - 27 of 27
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