Resource theory of contextuality

Amaral, Bárbara

doi:10.1098/rsta.2019.0010

Cited by 24 publications

(23 citation statements)

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“…This is why the noncontextual inequalities are fundamentally different. In the wake of the quantification of contextuality that is nowadays underway, it seems that they can not only serve to rule out other (meta)physical theories, but that, by highlighting the private area of quantum mechanics, they provide a material resource theory [173].…”

Section: A Setting a Protocol To Derive Experimentally Robust Inequal...mentioning

confidence: 99%

“…Several publications have shown the relations between the sheaf-theoretic approach of contextuality and phenomena such as relational database theory, robust constraint satisfaction, natural language semantics and logical paradoxes, a general theory of which, called contextual semantics, is given in [205]. Finally, the deeper and more general work in that direction is the formalisation of contextuality as a ressource by Duarte and Amaral [173,206].…”

Section: Quantum Computation Advantage and A Little Bit Morementioning

confidence: 99%

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From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality

Masse

2021

Preprint

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J. A tale of contextuality... K. ...and its logical implications III. Mathematical proofs of contextuality A. The Kochen-Specker Bell theorem B. KCBS inequality C. Peres-Mermin Square IV. The graph-theoretic approach of Cabello, Severini and Winter (CSW) A. General definitions B. The case of KCBS as a paradigmatic example C. Generalisation D. Link with Bell inequalities V. A sheaf-category theoretic approach to contextuality A. Pictorial representation 1. Probabilistic contextuality 2. Logical contextuality 3. Strong contextuality B. A brief presentation of the mathematical frameworks of the model 1. Correlation experiments in sheaf-theoretic approach 2. Compatibility of marginals 3. Hierarchy of contextuality C. New questions D. An illustration of contextuality VI. A hypergrah approach to contextuality VII. An operational version of contextuality A. A toy model B. An operational theory of contextuality C. Application to quantum mechanics D. Reinterpretation of the Kochen-Specker results VIII. Contextuality-by-Default A.

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Section: A Setting a Protocol To Derive Experimentally Robust Inequal...mentioning

confidence: 99%

Section: Quantum Computation Advantage and A Little Bit Morementioning

confidence: 99%

From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality

Masse

2021

Preprint

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“…There are two ways in which these deterministic simulations are weaker than one would want in a general resource theory of contextuality: first of all, one might want to allow the usage of auxiliary (non-contextual) randomness, so that the dependence of measurements and their outcomes of T on those of S is stochastic. The usage of auxiliary randomness is captured in [45] and discussed further in [46], and in our terms could be defined by allowing probabilistic mixtures of transformations. However, this viewpoint leaves out another important generalization-namely the possibility that a single measurement in T can depend on a joint measurement of S as in [47] or more generally on a measurement protocol on S that chooses which joint measurement to perform adaptively.…”

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confidence: 99%

Neither Contextuality nor Nonlocality Admits Catalysts

Karvonen

2021

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We show that the resource theory of contextuality does not admit catalysts. As a corollary, we observe that the same holds for non-locality. This adds a further example to the list of "anomalies of entanglement", showing that non-locality and entanglement behave differently as resources. We also show that catalysis remains impossible even if instead of classical randomness we allow some more powerful behaviors to be used freely in the free transformations of the resource theory. Introduction. Contextuality [1] and non-locality [2, 3] play a prominent role in a wide variety of applications of quantum mechanics, with non-locality being used for example in quantum key-distribution [4], certified randomness [5] and randomness expansion [6].Similarly, contextuality powers quantum computation in some computational models [7][8][9][10][11][12] and even increases expressive power in quantum machine learning [13]. Consequently, it is vital to understand how non-locality and contextuality behave as resources.In this Letter, we show that neither contextuality nor non-locality admit catalysts: that is, there are no correlations that can be used to enable an otherwise impossible conversion between correlations and still recovered afterwards. To state this slightly more precisely, let us write d, e, f . . . for various correlations (whether classical or not), d ⊗ e for having independent instances of d and e, and d e (read as "d simulates e") for the existence of a conversion d → e. Then our results state that, in suitably formalized resource theories of contextuality and non-locality, whenever d ⊗ e d ⊗ f , then e f already. This gives a strong indication that contextuality (and non-locality) are resources that get spent when you use them: there is no way of using a correlation d to achieve a task you could not do otherwise while keeping d intact. As entanglement theory famously allows for catalysts [14],this can be seen as yet another "anomaly of non-locality" [15] and thus further testament to the fact that non-locality and entanglement are different resources. [16] We do this by working in precisely defined resource theories of contextuality and nonlocality. These are not strictly speaking quantum resource theories [17], but resource theories in a more general sense [18, 19], as we allow resources such as PR-boxes [20] that are not quantum realizable. The kinds of conversions between correlations we have in mind capture the intuitive idea of using one system to simulate another one, and have been studied in earlier literature [21][22][23][24][25][26][27][28][29]. These roughly correspond to the local operations and shared randomness-paradigm ((LOSR)) or to wirings and prior-to-input classical communication

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“…Since contextuality is a central concept in quantum foundations as well as a fundamental resource in quantum technologies [92,104], including quantum computation [105][106][107][108][109], quantum cryptography [110,111], random number generation [112,113], and so on, we believe that the investigation presented in this master's thesis is justified, as well as possible continuations. Possible future works may include investigations on bounds for "Hardy's probabilities" in the same fashion of Ref.…”

Section: Final Remarksmentioning

confidence: 96%

“…It is possible to demonstrate that the this number is equal to one only for SC [17,91]. Furthermore, such a contextuality measure plays a very important role in resource theories for contextuality, due to the fact that it is a monotone under all linear operations that preserve the NC set [92].…”

Section: Theoremmentioning

confidence: 98%

On Quantum Possibilistic Paradoxes and Logical Contextuality

Santos¹

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First of all I thank my family for everything; my uncle José, Elaine, Bruno, and Neuza (in memorian) for the comfortable hosting during part of this Master's; and my advisor, Prof. Bárbara Amaral, for accepting me into your group, guiding me through these two years, and for all contributions you have made in my academic life and beyond. I also thank all the professors I have had since the beginning of my undergrad studies, in particular I highlight Profs. Gabriel Landi, Márcio Bortoloti, Jorge Anderson, and Ivanor Nunes (in memorian). I thank the friends that Physics gave me, among which I highlight the "derivators": Emmanuel, Erison, and Pablo; Thiago and his cosmo-collegues; and also my group colleagues: Alisson, Ari, Daniel, Giulio, Gustavo, Marina, Rafael, Silvio, and Tiago. I also leave a thank to my non-academic friends, in particular: Shirley for the beers and chats, my crazy Colombian friend Karol for nothing (I only mentioned you because I like you), and Gabrielle for the long chats, English helps, and for all the ABBA songs we listen to. Finally, thanks to everyone who kept the correlations with me as strong as possible despite the space-like separation. A special ¬thank to COVID-19 (and its collaborators).

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Resource theory of contextuality

Cited by 24 publications

References 46 publications

From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality

From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality

Neither Contextuality nor Nonlocality Admits Catalysts

On Quantum Possibilistic Paradoxes and Logical Contextuality

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