Geometry of the set of quantum correlations

Goh, Koon Tong; Kaniewski, Jędrzej; Wolfe, Elie; Vértesi, Tamás; Wu, Xingyao; Cai, Yu; Liang, Yeong-Cherng; Scarani, Valerio

doi:10.1103/physreva.97.022104

Cited by 103 publications

(113 citation statements)

References 79 publications

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“…1. Any such 2-dimensional slice is spanned by three affinely-independent correlations in this space (see, e.g., [40]). In our case, the chosen slice is spanned by the uniform (white-noise) distribution ℘ 0 ℘ 0 (ab|xy) = 1 4 , ∀ a, b, x, y, (S. 14) an extreme point of the LF polytope: In our plot, we have chosen the left-hand side of Eq.…”

Section: S3 Maximal Quantum Violations Of the Genuine Lf Inequalitiesmentioning

confidence: 99%

Testing the reality of Wigner's friend's experience

Bong

Utreras-Alarcón

Ghafari

et al. 2019

AOS Australian Conference on Optical Fibre Technology (ACOFT) and Australian Conference on Optics, Lasers, and Spectroscopy (AC

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Does quantum theory apply to observers? A resurgence of interest in the long-standing Wigner's friend paradox has shed new light on this fundamental question. Brukner introduced a scenario with two separated but entangled "friends". Here, building on that work, we rigorously prove that if quantum evolution is controllable on the scale of an observer, then one of the following three assumptions must be false: "freedom of choice", "locality", or "observer-independent facts" (i.e. that every observed event exists absolutely, not relatively). We show that although the violation of Bell-type inequalities in such scenarios is not in general sufficient to demonstrate the contradiction between those assumptions, new inequalities can be derived, in a theory-independent manner, which are violated by quantum correlations. We demonstrate this in a proof-of-principle experiment where a photon's path is deemed an observer. We discuss how this new theorem places strictly stronger constraints on quantum reality than Bell's theorem.

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Section: S3 Maximal Quantum Violations Of the Genuine Lf Inequalitiesmentioning

confidence: 99%

Testing the reality of Wigner's friend's experience

Bong

Utreras-Alarcón

Ghafari

et al. 2019

AOS Australian Conference on Optical Fibre Technology (ACOFT) and Australian Conference on Optics, Lasers, and Spectroscopy (AC

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“…The set of quantum correlations Q forms a convex set satisfying L ⊂ Q ⊂ N . It is, however, not a polytope [11] (see also [45]). When necessary, we will use Q n to denote the set of quantum correlations arising in an n-partite Bell scenario.…”

Section: A Bell Scenariomentioning

confidence: 99%

“…In other words, the set of quantum maximizers of any input-lifted Bell inequality define a flat region of the boundary of the quantum set of correlations, cf. [45]. In particular, it could lead to completely flat boundaries of Q on specific two-dimensional slices in the correlation space (see Fig.…”

Section: A More Inputsmentioning

confidence: 99%

“…As we illustrate in this work, the maximizers of lifted Bell inequalities are not unique. There is thus no hope (see, e.g., [45]) of providing a complete selftesting of the employed quantum device using a lifted Bell inequality. Nonetheless, we provide numerical evidence suggesting that lifted Bell inequalities provide the same level of robustness for self-testing the relevant parts of the devices.…”

Section: Introductionmentioning

confidence: 99%

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Maximal violation of a broad class of Bell inequalities and its implication on self-testing

Jebarathinam

Hung

Chen

et al. 2019

Phys. Rev. Research

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In quantum information, lifting is a systematic procedure that can be used to derive-when provided with a seed Bell inequality-other Bell inequalities applicable in more complicated Bell scenarios. It is known that the procedure of lifting introduced by Pironio [J. Math. Phys. A 46, 062112 (2005)] preserves the facet-defining property of a Bell inequality. Lifted Bell inequalities therefore represent a broad class of Bell inequalities that can be found in all Bell scenarios. Here, we show that the maximal value of any lifted Bell inequality is preserved for both the set of nonsignaling correlations and quantum correlations. Despite the degeneracy in the maximizers of such inequalities, we show that the ability to self-test a quantum state is preserved under these lifting operations. In addition, except for outcome-lifting, local measurements that are self-testable using the original Bell inequality-despite the degeneracy-can also be self-tested using any lifted Bell inequality derived therefrom. While it is not possible to self-test all the positive-operator-valued measure elements using an outcome-lifted Bell inequality, we show that partial, but robust self-testing statements on the underlying measurements can nonetheless be made from the quantum violation of these lifted inequalities. We also highlight the implication of our observations on the usefulness of using lifted Bell-like inequalities as a device-independent witnesses for entanglement depth. The impact of the aforementioned degeneracy on the geometry of the quantum set of correlations is briefly discussed.

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“…When a realization is a unique maximizer of a Bell inequality, the realized correlation is a self-testable extremal point. Although there exist non-exposed extremal points that cannot be a unique maximizer of any Bell inequality, a correlation is extremal when the realization is self-testable [8]. In this way, self-testability and extremality are intimately connected.…”

Section: Introductionmentioning

confidence: 99%

Geometrical self-testing of partially entangled two-qubit states

Ishizaka

2020

New J. Phys.

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Quantum nonlocality has recently been intensively studied in connection to device-independent quantum information processing, where the extremal points of the set of quantum correlations play a crucial role through self-testing. In most protocols, the proofs for self-testing rely on the maximal violation of the Bell inequalities, but there is another known proof based on the geometry of state vectors to self-test a maximally entangled state. We present a geometrical proof in the case of partially entangled states. We show that, when a set of correlators in the simplest Bell scenario satisfies a condition, the geometry of the state vectors is uniquely determined. The realization becomes selftestable when another unitary observable exists on the geometry. Applying this proven fact, we propose self-testing protocols by intentionally adding one more measurement. This geometrical scheme for self-testing is superior in that, by using this as a building block and repeatedly adding measurements, a realization with an arbitrary number of measurements can be self-tested. Besides the application, we also attempt to describe nonlocal correlations by guessing probabilities of distant measurement outcomes. In this description, the quantum set is also convex, and a large class of extremal points is identified by the uniqueness of the geometry.

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Geometry of the set of quantum correlations

Cited by 103 publications

References 79 publications

Testing the reality of Wigner's friend's experience

Testing the reality of Wigner's friend's experience

Maximal violation of a broad class of Bell inequalities and its implication on self-testing

Geometrical self-testing of partially entangled two-qubit states

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