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  • 1.
    Ahrens, Johan
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Badziag, Piotr
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Cabello, Adan
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. University of Sevilla, Spain.
    Bourennane, Mohamed
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Experimental device independent tests of classical and quantum dimensions2012Inngår i: Nature Physics, ISSN 1745-2473, E-ISSN 1745-2481, Vol. 8, nr 8, s. 592-595Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A fundamental resource in any communication and computation task is the amount of information that can be transmitted and processed. The classical information encoded in a set of states is limited by the number of distinguishable states or classical dimension d(c) of the set. The sets used in quantum communication and information processing contain states that are neither identical nor distinguishable, and the quantum dimension d(q) of the set is the dimension of the Hilbert space spanned by these states. An important challenge is to assess the (classical or quantum) dimension of a set of states in a device-independent way, that is, without referring to the internal working of the device generating the states. Here we experimentally test dimension witnesses designed to efficiently determine the minimum dimension of sets of (three or four) photonic states from the correlations originated from measurements on them, and distinguish between classical and quantum sets of states.

  • 2.
    Andersson, Ole
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Badziag, Piotr
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Bengtsson, Ingemar
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Dumitru, Irina
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Cabello, Adan
    Self-testing properties of Gisin's elegant Bell inequality2017Inngår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information, ISSN 2469-9926, E-ISSN 2469-9934, Vol. 96, nr 3, artikkel-id 032119Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An experiment in which the Clauser-Horne-Shimony-Holt inequality is maximally violated is self-testing (i.e., it certifies in a device-independent way both the state and the measurements). We prove that an experiment maximally violating Gisin's elegant Bell inequality is not similarly self-testing. The reason can be traced back to the problem of distinguishing an operator from its complex conjugate. We provide a complete and explicit characterization of all scenarios in which the elegant Bell inequality is maximally violated. This enables us to see exactly how the problem plays out.

  • 3.
    Badziag, Piotr
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Brukner, Caslav
    Laskowski, Wieslaw
    Paterek, Tomasz
    Zukowski, Marek
    Experimentally friendly geometrical criteria for entanglement2008Inngår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 100, nr 14, s. 140403-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A simple geometrical criterion gives experimentally friendly sufficient conditions for entanglement. Its generalization gives a necessary and sufficient condition. It is linked with a family of entanglement identifiers, which is strictly richer than the family of entanglement witnesses.

  • 4.
    Badziag, Piotr
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Horodecki, Pawel
    Horodecki, Ryszard
    Augusiak, Remigiusz
    Separability in terms of a single entanglement witness2013Inngår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 88, nr 1, s. 010301-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The separability problem is formulated in terms of a characterization of a single entanglement witness. More specifically, we show that any (in general multipartite) state rho is separable if and only if a specially constructed entanglement witness W-rho is weakly optimal, i.e., its expectation value vanishes on at least one product vector. Interestingly, the witness can always be chosen to be decomposable. Our result changes the conceptual aspect of the separability problem and raises some questions about the properties of positive maps.

  • 5.
    Bengtsson, Ingemar
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Badziag, Piotr
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Cabello, Adan
    Pitowsky, Itamar
    Universality of State-Independent Violation of Correlation Inequalities for Non-Contextual Theories2009Inngår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 103, nr 5, s. 050401-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We show that the state-independent violation of inequalities for noncontextual hidden variable theories introduced in [Phys. Rev. Lett. 101, 210401 (2008)] is universal, i.e., occurs for any quantum mechanical system in which noncontextuality is meaningful. We describe a method to obtain state-independent violations for any system of dimension d >= 3. This universality proves that, according to quantum mechanics, there are no "classical'' states.

  • 6. Cabello, Adan
    et al.
    Badziag, Piotr
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Cunha, Marcelo Terra
    Bourennane, Mohamed
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Simple Hardy-Like Proof of Quantum Contextuality2013Inngår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 111, nr 18, s. 180404-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Contextuality and nonlocality are two fundamental properties of nature. Hardy's proof is considered the simplest proof of nonlocality and can also be seen as a particular violation of the simplest Bell inequality. A fundamental question is: Which is the simplest proof of contextuality? We show that there is a Hardy-like proof of contextuality that can also be seen as a particular violation of the simplest noncontextuality inequality. Interestingly, this new proof connects this inequality with the proof of the Kochen-Specker theorem, providing the missing link between these two fundamental results, and can be extended to an arbitrary odd number n of settings, an extension that can be seen as a particular violation of the n-cycle inequality.

  • 7.
    Sadiq, Muhammad
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Badziag, Piotr
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Bourennane, Mohamed
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Cabello, Adán
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum. Universidad de Sevilla, Spain.
    Bell inequalities for the simplest exclusivity graph2013Inngår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 87, nr 1, artikkel-id 012128Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Which is the simplest logical structure for which there is quantum nonlocality? We show that there are only three bipartite Bell inequalities with quantum violation associated with the simplest graph of relationships of exclusivitywith a quantum-classical gap. These are the most elementary logical Bell inequalities. We showthat the quantum violation of some well-known Bell inequalities is related to them. We test the three Bell inequalities with pairs of polarization-entangled photons and report violations in good agreement with the quantum predictions. Unlike other experiments testing noncontextuality inequalities with pentagonal exclusivity, the ones reported here are free of the compatibility loophole. DOI: 10.1103/PhysRevA.87.012128

  • 8. Wu, Yu-Chun
    et al.
    Badziag, Piotr
    Stockholms universitet.
    Wiesniak, Marcin
    Zukowski, Marek
    Stockholms universitet.
    Extending Bell inequalities to more parties2008Inngår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 77, nr 3, s. 32105-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We describe a method of extending Bell inequalities from n to n+ 1 parties and formulate sufficient conditions for our method to produce tight inequalities from tight inequalities. The method is nontrivial in the sense that the inequalities produced by it, when applied to entangled quantum states may be violated stronger than the original inequalities. In other words, the method is capable of generating inequalities which are more powerful indicators of nonclassical correlations than the original inequalities.

  • 9. Wu, Yu-Chun
    et al.
    Badziag, Piotr
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Zukowski, Marek
    Stockholms universitet, Naturvetenskapliga fakulteten, Fysikum.
    Clauser-Horne-Shimony-Holt-type Bell inequalities involving a party with two or three local binary settings2009Inngår i: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 79, nr 2, s. 22110-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We construct a simple algorithm to generate any Clauser-Horne-Shimony-Holt- (CHSH-) type Bell inequality involving a party with two local binary measurements from two CHSH-type inequalities without this party. The algorithm readily generalizes to situations where the additional observer uses three measurement settings. There, each inequality involving the additional party is constructed from three inequalities with this party excluded. With this generalization at hand, we construct and analyze a class of symmetric inequalities for four observers and three experimental settings per observer.

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