Parity Oblivious d-Level Random Access Codes and Class of Noncontextuality Inequalities

Ambainis, Andris; Banik, Manik; Chaturvedi, Anubhav; Kravchenko, Dmitry V.; Rai, Ashutosh

doi:10.48550/arxiv.1607.05490

Cited by 8 publications

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“…must be satisfied for any s q and c q arising in a noncontextual model that reproduces the data in Table I and respects the operational equivalence of Eq. (12). While the proof provided in the main text uses an intuitive argument that is native to the task of state discrimination, the argument in this section abstracts away from the specific problem at hand, and as such extends naturally to the more general method required for proving Eq.…”

Section: Future Directionsmentioning

confidence: 99%

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Contextual Advantage for State Discrimination

2018

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Finding quantitative aspects of quantum phenomena which cannot be explained by any classical model has foundational importance for understanding the boundary between classical and quantum theory. It also has practical significance for identifying information processing tasks for which those phenomena provide a quantum advantage. Using the framework of generalized noncontextuality as our notion of classicality, we find one such nonclassical feature within the phenomenology of quantum minimum error state discrimination. Namely, we identify quantitative limits on the success probability for minimum error state discrimination in any experiment described by a noncontextual ontological model. These constraints constitute noncontextuality inequalities that are violated by quantum theory, and this violation implies a quantum advantage for state discrimination relative to noncontextual models. Furthermore, our noncontextuality inequalities are robust to noise and are operationally formulated, so that any experimental violation of the inequalities is a witness of contextuality, independently of the validity of quantum theory. Along the way, we introduce new methods for analyzing noncontextuality scenarios, and demonstrate a tight connection between our minimum error state discrimination scenario and a Bell scenario.1 Such models are ψ-epistemic, in the terminology of Ref. [17].

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Section: Future Directionsmentioning

confidence: 99%

“…For example, violations of Bell inequalities have been shown to be a resource for device-independent key distribution [7], certified randomness [8], and communication complexity [9]. The failure of noncontextuality has also been shown to be a resource, leading to advantages for cryptography [10][11][12] and computation [13][14][15].…”

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confidence: 99%

Contextual Advantage for State Discrimination

2018

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“…Furthermore, using this strong connection between preparation contextuality and Bell inequality violations in quantum theory, we can qualitatively and quantitatively explain the degree of preparation contextuality observed in Refs. [10,11], and also solve an open problem in this field; namely demonstrating the preparation contextuality of the maximally mixed quantum state in any dimension.…”

Section: Introductionmentioning

confidence: 98%

“…Interestingly, examples of communication games are known in which the better-than-classical performance in the game constitutes a certificate of the system exhibiting preparation contextuality [10,11]. Preparation noncontextuality is the assumption that, for a given operational theory, if two preparations of a system cannot be distinguished by any measurement allowed in that theory, then the respective hidden variables which determine the ontic states of the two systems must have the same distribution [12].…”

Section: Introductionmentioning

confidence: 99%

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Quantum communication games manifest preparation contextuality

Tavakoli

2016

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Communication games are collaborative information processing tasks involving a number of players with limited communication. Such games are useful tools for studying physical theories. A physical theory exhibits preparation contextuality whenever observed behaviour cannot be explained by a preparation noncontextual model. Here we show that there is a fundamental connection between the performance in communication games and the degree of preparation (non)contextuality. For this purpose, we present a general framework that allows us to construct communication games such that the game performance corresponds to a measure of preparation (non)contextuality. We illustrate the power of this framework by, 1) deriving many examples of tests of preparation contextuality, 2) showing that quantum violations of Bell inequalities can be derived from quantum violations of preparation noncontextuality, 3) qualitatively and quantitatively explaining related previous results on preparation contextuality in quantum communication games, and 4) solving the open problem of revealing the preparation contextuality of the maximally mixed quantum state in any dimension.

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Deriving robust noncontextuality inequalities from algebraic proofs of the Kochen–Specker theorem: the Peres–Mermin square

2017

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When a measurement is compatible with each of two other measurements that are incompatible with one another, these define distinct contexts for the given measurement. The Kochen-Specker theorem rules out models of quantum theory that satisfy a particular assumption of context-independence: that sharp measurements are assigned outcomes both deterministically and independently of their context. This notion of noncontextuality is not suited to a direct experimental test because realistic measurements always have some degree of unsharpness due to noise. However, a generalized notion of noncontextuality has been proposed that is applicable to any experimental procedure, including unsharp measurements, but also preparations as well, and for which a quantum no-go result still holds. According to this notion, the model need only specify a probability distribution over the outcomes of a measurement in a context-independent way, rather than specifying a particular outcome. It also implies novel constraints of context-independence for the representation of preparations. In this article, we describe a general technique for translating proofs of the Kochen-Specker theorem into inequality constraints on realistic experimental statistics, the violation of which witnesses the impossibility of a noncontextual model. We focus on algebraic state-independent proofs, using the Peres-Mermin square as our illustrative example. Our technique yields the necessary and sufficient conditions for a particular set of correlations (between the preparations and the measurements) to admit a noncontextual model. The inequalities thus derived are demonstrably robust to noise. We specify how experimental data must be processed in order to achieve a test of these inequalities. We also provide a criticism of prior proposals for experimental tests of noncontextuality based on the Peres-Mermin square.

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Parity Oblivious d-Level Random Access Codes and Class of Noncontextuality Inequalities

Cited by 8 publications

References 0 publications

Contextual Advantage for State Discrimination

Contextual Advantage for State Discrimination

Quantum communication games manifest preparation contextuality

Deriving robust noncontextuality inequalities from algebraic proofs of the Kochen–Specker theorem: the Peres–Mermin square

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