Experimentally feasible semi-device-independent certification of four-outcome positive-operator-valued measurements

Mironowicz, Piotr; Pawłowski, Marcin

doi:10.1103/physreva.100.030301

Cited by 47 publications

(39 citation statements)

References 28 publications

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“…These lower bounds were verified to be achieved with projective measurements up to machine precision. The results show that the obtained upper bounds are either optimal or close to optimal, depending on d. In analogy with previous works [32][33][34][35][36], we find that the gap between optimal quantum correlations and those obtained under projective measurements is small.…”

supporting

confidence: 85%

“…To this end, we introduce a family of CCPs, prove that they enable self-tests of d-dimensional symmetric informationally complete (SIC) POVMs, then use symmetrised semidefinite relaxations to bound the correlations attainable under projective measurements. This allows us to go beyond previously studied qubit systems [32][33][34][35][36] and robustly certify the nonprojectiveness of SIC-POVMs subject to imperfections.…”

mentioning

confidence: 95%

“…Non-projective measurements have diverse applications in quantum theory [32,[40][41][42][43][44][45][46]. This has motivated interest in their blackbox certification [32][33][34][35][36]. Using semidefinite relaxations (whose complexity scale quickly with dimension) as a primary tool, these works limit themselves to qubits.…”

mentioning

confidence: 99%

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Enabling Computation of Correlation Bounds for Finite-Dimensional Quantum Systems via Symmetrization

2019

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We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finitedimensional Hilbert spaces. The technique, which we make publicly available through a user-friendly software package, relies on the exploitation of symmetries present in the optimisation problem to reduce the number of variables and the block sizes in semidefinite relaxations. It is widely applicable in problems encountered in quantum information theory and enables computations that were previously too demanding. We demonstrate its advantages and general applicability in several physical problems. In particular, we use it to robustly certify the non-projectiveness of high-dimensional measurements in a black-box scenario based on self-tests of d-dimensional symmetric informationally complete POVMs.

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confidence: 85%

mentioning

confidence: 95%

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Enabling Computation of Correlation Bounds for Finite-Dimensional Quantum Systems via Symmetrization

2019

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“…In [MP19] the authors start from the 3 2 → 1 RAC to develop a self-test of the extremal 'tetrahedral' qubit POVM. In [TSV + 20], a general method is given to self-test any extremal qubit POVM, given a self-test of a set of preparations with opposite Bloch vectors to the POVM on the Bloch sphere.…”

Section: One Sided Device-independent Self-testing (Epr Steering)mentioning

confidence: 99%

Self-testing of quantum systems: a review

Šupić

Bowles

2020

Quantum

259

166

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Self-testing is a method to infer the underlying physics of a quantum experiment in a black box scenario. As such it represents the strongest form of certification for quantum systems. In recent years a considerable self-testing literature has developed, leading to progress in related device-independent quantum information protocols and deepening our understanding of quantum correlations. In this work we give a thorough and self-contained introduction and review of self-testing and its application to other areas of quantum information.

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“…Self-testing is an active research field and a particularly interesting direction is to explore its powers and limitations by deriving new types of self-testing statements or impossibility results. For instance we have recently learned that one can self-test quantum channels [49], entangled measurements [50,51], and quantum instruments [52], or that one can extend the concept of self-testing to prepare-and-measure scenarios [53][54][55][56][57][58]. In this work we derive a new type of self-testing statement which allows us to certify the state but not the measurements.…”

Section: Discussionmentioning

confidence: 99%

Weak form of self-testing

Kaniewski

2020

Phys. Rev. Research

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The concept of self-testing (or rigidity) refers to the fact that for certain Bell inequalities the maximal violation can be achieved in an essentially unique manner. In this work we present a family of Bell inequalities which are maximally violated by multiple inequivalent quantum realizations. We completely characterize the quantum realizations achieving the maximal violation and we show that each of them requires a maximally entangled state of two qubits. This implies the existence of a new, weak form of self-testing in which the maximal violation allows us to identify the state, but does not fully determine the measurements. From the geometric point of view the set of probability points that saturate the quantum bound is a line segment. We then focus on a particular member of the family and show that the self-testing statement is robust, i.e., that observing a nonmaximal violation allows us to make a quantitative statement about the unknown state. To achieve this we present a new construction of extraction channels and analyze their performance. For completeness we provide two independent approaches: analytical and numerical. The noise robustness, i.e., the amount of white noise at which the bound becomes trivial, of the analytical bound is rather small (≈0.06%), but the numerical method takes us into an experimentally relevant regime (≈5%). We conclude by investigating the amount of randomness that can be certified using these Bell violations. Perhaps surprisingly, we find that the qualitative behavior resembles the behavior of rigid inequalities such as the Clauser-Horne-Shimony-Holt inequality. This shows that rigidity is not strictly necessary for device-independent applications.

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Experimentally feasible semi-device-independent certification of four-outcome positive-operator-valued measurements

Abstract: In this paper we construct a semi-device-independent protocol able to certify the presence of the generalized measurements. We show robustness of the protocol and conclude that it allows for experimental realisations using current technology.

Cited by 47 publications

References 28 publications

Enabling Computation of Correlation Bounds for Finite-Dimensional Quantum Systems via Symmetrization

Enabling Computation of Correlation Bounds for Finite-Dimensional Quantum Systems via Symmetrization

Self-testing of quantum systems: a review

Weak form of self-testing

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