| 1. |
- Andersson, Ole, et al.
(författare)
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Self-testing properties of Gisin's elegant Bell inequality
- 2017
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : American Physical Society. - 2469-9926 .- 2469-9934. ; 96:3
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 2. |
- Badziag, Piotr, et al.
(författare)
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Pentagrams and Paradoxes
- 2011
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Ingår i: FOUNDATIONS OF PHYSICS. - : Springer Science Business Media. - 0015-9018 .- 1572-9516. ; 41:3, s. 414-423
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Tidskriftsartikel (refereegranskat)abstract
- Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and then show how the pentagram underlies a number of other quantum "paradoxes", such as that of Hardy.
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| 3. |
- Bengtsson, Ingemar, et al.
(författare)
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A Kochen-Specker inequality for a SIC
- 2012
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Ingår i: Physics Letters A. - : Elsevier BV. - 0375-9601 .- 1873-2429. ; 376:4, s. 374-376
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Tidskriftsartikel (refereegranskat)abstract
- Yu and Oh (eprint) [1] have given a state-independent proof of the Kochen–Specker theorem in three dimensions using only 13 rays. The proof consists of showing that a non-contextual hidden variable theory necessarily leads to an inequality that is violated by quantum mechanics. We give a similar proof making use of 21 rays that constitute aSIC (symmetric informationally-complete positive operator-valued measure) and a complete set of MUB (mutually unbiased bases). A theory-independent inequality is also presented using the same 21 rays, as required for experimental tests of contextuality.
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| 4. |
- Bengtsson, Ingemar, et al.
(författare)
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Pentagrams and paradoxes
- 2011
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Ingår i: Foundations of Physics. ; 41, s. 414-
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Tidskriftsartikel (refereegranskat)
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| 5. |
- Bengtsson, Ingemar, et al.
(författare)
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Universality of State-Independent Violation of Correlation Inequalities for Non-Contextual Theories
- 2009
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 103:5, s. 050401-
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 6. |
- Cabello, Adan, et al.
(författare)
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Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality
- 2012
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 85:3, s. 032108-
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Tidskriftsartikel (refereegranskat)abstract
- Recent experiments have demonstrated ququart state-independent quantum contextuality and qutrit state-dependent quantum contextuality. So far, the most basic form of quantum contextuality pointed out by Kochen and Specker, and Bell, has eluded experimental confirmation. Here we present an experimentally feasible test to observe qutrit state-independent quantum contextuality using single photons in a three-path setup. In addition, we show that if the same measurements are performed on two entangled qutrits, rather than sequentially on the same qutrit, then the noncontextual inequality becomes a Bell inequality. We show that this connection also applies to other recently introduced noncontextual inequalities.
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