| 1. |
- Budroni, Costantino, et al.
(author)
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Kochen-Specker contextuality
- 2022
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In: Reviews of Modern Physics. - : AMER PHYSICAL SOC. - 0034-6861 .- 1539-0756. ; 94:4
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Research review (peer-reviewed)abstract
- A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here compatible measurements are those that can be implemented simultaneously or, more generally, those that are jointly measurable. This conflict is generically called quantum contextuality. In this review, an introduction to this subject and its current status is presented. Several proofs of the Kochen-Specker theorem and different notions of contextuality are reviewed. How to experimentally test some of these notions is explained, and connections between contextuality and nonlocality or graph theory are discussed. Finally, some applications of contextuality in quantum information processing are reviewed.
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| 2. |
- Cabello, Adan, et al.
(author)
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Thermodynamical cost of some interpretations of quantum theory
- 2016
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In: PHYSICAL REVIEW A. - : AMER PHYSICAL SOC. - 2469-9926. ; 94:5
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Journal article (peer-reviewed)abstract
- The interpretation of quantum theory is one of the longest-standing debates in physics. Type I interpretations see quantum probabilities as determined by intrinsic properties of the observed system. Type II see them as relational experiences between an observer and the system. It is usually believed that a decision between these two options cannot be made simply on purely physical grounds but requires an act of metaphysical judgment. Here we show that, under some assumptions, the problem is decidable using thermodynamics. We prove that type I interpretations are incompatible with the following assumptions: (i) The choice of which measurement is performed can be made randomly and independently of the system under observation, (ii) the system has limited memory, and (iii) Landauers erasure principle holds.
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| 3. |
- Guehne, Otfried, et al.
(author)
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Bounding the quantum dimension with contextuality
- 2014
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In: Physical Review A. Atomic, Molecular, and Optical Physics. - : American Physical Society. - 1050-2947 .- 1094-1622. ; 89:6
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Journal article (peer-reviewed)abstract
- We show that the phenomenon of quantum contextuality can be used to certify lower bounds on the dimension accessed by the measurement devices. To prove this, we derive bounds for different dimensions and scenarios of the simplest noncontextuality inequalities. Some of the resulting dimension witnesses work independently of the prepared quantum state. Our constructions are robust against noise and imperfections, and we show that a recent experiment can be viewed as an implementation of a state-independent quantum dimension witness.
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| 4. |
- Guehne, Otfried, et al.
(author)
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Compatibility and noncontextuality for sequential measurements
- 2010
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In: PHYSICAL REVIEW A. - 1050-2947. ; 81:2, s. 022121-
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Journal article (peer-reviewed)abstract
- A basic assumption behind the inequalities used for testing noncontextual hidden variable models is that the observables measured on the same individual system are perfectly compatible. However, compatibility is not perfect in actual experiments using sequential measurements. We discuss the resulting "compatibility loophole" and present several methods to rule out certain hidden variable models that obey a kind of extended noncontextuality. Finally, we present a detailed analysis of experimental imperfections in a recent trapped-ion experiment and apply our analysis to that case.
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| 5. |
- Kleinmann, Matthias, et al.
(author)
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Memory cost of quantum contextuality
- 2011
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In: New Journal of Physics. - : Institute of Physics. - 1367-2630. ; 13:113011
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Journal article (peer-reviewed)abstract
- The simulation of quantum effects requires certain classical resources, and quantifying them is an important step to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of state-independent quantum contextuality, we show that the minimum amount of memory used by the simulation is the critical resource. We derive optimal simulation strategies for important cases and prove that reproducing the results of sequential measurements on a two-qubit system requires more memory than the information-carrying capacity of the system.
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| 6. |
- Kleinmann, Matthias, et al.
(author)
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Optimal Inequalities for State-Independent Contextuality
- 2012
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In: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 109:25, s. 250402-
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Journal article (peer-reviewed)abstract
- Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the contextual behavior is independent of the quantum state. We show that the quest for an optimal inequality separating quantum from classical noncontextual correlations in a state-independent manner admits an exact solution, as it can be formulated as a linear program. We introduce the noncontextuality polytope as a generalization of the locality polytope and apply our method to identify two different tight optimal inequalities for the most fundamental quantum scenario with state-independent contextuality.
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| 7. |
- Larsson, Jan-Åke, et al.
(author)
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Maximal violation of state-independent contextuality inequalities
- 2012
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In: Quantum Theory: Reconsideration of Foundations - 6. - : American Institute of Physics (AIP). - 9780735411265 ; , s. 265-274
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Conference paper (peer-reviewed)abstract
- The discussion on noncontextual hidden variable models as an underlying description for the quantum-mechanical predictions started in ernest with 1967 paper by Kochen and Specker. There, it was shown that no noncontextual hidden-variable model can give these predictions. The proof used in that paper is complicated, but recently, a paper by Yu and Oh [PRL, 2012] proposes a simpler statistical proof that can also be the basis of an experimental test. Here we report on a sharper version of that statistical proof, and also explain why the algebraic upper bound to the expressions used are not reachable, even with a reasonable contextual hidden variable model. Specifically, we show that the quantum mechanical predictions reach the maximal possible value for a contextual model that keeps the expectation value of the measurement outcomes constant.
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