Constant-sized robust self-tests for states and measurements of unbounded dimension

Mančinska, Laura; Prakash, J.; Schafhauser, Christopher

doi:10.48550/arxiv.2103.01729

Cited by 10 publications

(9 citation statements)

References 28 publications

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“…This property is a crucial requirement for establishing theorem 1.1 via lemma 5.1. We remark that a similar property to being δ-ATP arose in the work of [12] while investigating robust self-testing with finite-dimensional algebras.…”

Section: Approximate Representations Of Game Algebras From ǫ-Optimal ...mentioning

confidence: 62%

Rounding near-optimal quantum strategies for nonlocal games to strategies using maximally entangled states

Paul-Paddock¹

2022

Preprint

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For the classes of synchronous, binary constraint systems, and XOR nonlocal games, we show that near-optimal finitedimensional quantum strategies with arbitrary states are approximate representations of their affiliated nonlocal game algebra. We also show that finite-dimensional approximate representations of these nonlocal game algebras are close to near-optimal strategies where the players employ a maximally entangled state. As a corollary, we show that near-optimal quantum strategies are close to a near-optimal quantum strategy that uses a maximally entangled state.

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Section: Approximate Representations Of Game Algebras From ǫ-Optimal ...mentioning

confidence: 62%

Rounding near-optimal quantum strategies for nonlocal games to strategies using maximally entangled states

Paul-Paddock¹

2022

Preprint

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“…where the first equality is by definition, the second uses (6) together with the fact that for a PME strategy the reduced density of |ψ on either system is proportional to the identity, hence commutes with any operator, the third equality uses that all A x a are projections and the last that they sum to identity. We reproduce a definition from [MPS21]. 6 Definition 2.4 (Local (ε, ν)-dilation).…”

Section: Definition 23 (Pme Strategies) a Strategy S = (|ψmentioning

confidence: 99%

Almost synchronous quantum correlations

Vidick

2022

Journal of Mathematical Physics

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The study of quantum correlation sets initiated by Tsirelson in the 1980s and originally motivated by questions in the foundations of quantum mechanics has more recently been tied to questions in quantum cryptography, complexity theory, operator space theory, group theory, and more. Synchronous correlation sets introduced by Paulsen et al. [J. Funct. Anal. 270, 2188–2222 (2016)] are a subclass of correlations that has proven particularly useful to study and arises naturally in applications. We show that any correlation that is almost synchronous, in a natural ℓ1 sense, arises from a state and measurement operators that are well-approximated by a convex combination of projective measurements on a maximally entangled state. This extends a result of Paulsen et al. [J. Funct. Anal. 270, 2188–2222 (2016)] that applies to exactly synchronous correlations. Crucially, the quality of approximation is independent of the dimension of the Hilbert spaces or of the size of the correlation. Our result allows one to reduce the analysis of many classes of nonlocal games, including rigidity properties, to the case of strategies using maximally entangled states that are generally easier to manipulate.

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“…We now formally introduce the notion of self-testing. We recall the definition of a local dilation from [MPS21].…”

Section: Preliminariesmentioning

confidence: 99%

Glued magic games self-test maximally entangled states

Mančinska,

Nielsen,

Prakash

2021

Preprint

Self Cite

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Self-testing results allow us to infer the underlying quantum mechanical description of states and measurements from classical outputs produced by non-communicating parties. The standard definition of self-testing does not apply in situations when there are two or more inequivalent optimal strategies. To address this, we introduce the notion of self-testing convex combinations of reference strategies, which is a generalisation of self-testing to multiple strategies. We show that the Glued Magic Square game [Cui+20] self-tests a convex combination of two inequivalent strategies. As a corollary, we obtain that the Glued Magic square game self-tests two EPR pairs thus answering an open question from [Cui+20]. Our self-test is robust and extends to natural generalisations of the Glued Magic Square game.

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Constant-sized robust self-tests for states and measurements of unbounded dimension

Cited by 10 publications

References 28 publications

Rounding near-optimal quantum strategies for nonlocal games to strategies using maximally entangled states

Rounding near-optimal quantum strategies for nonlocal games to strategies using maximally entangled states

Almost synchronous quantum correlations

Glued magic games self-test maximally entangled states

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