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

Tavakoli, Armin; Rosset, Denis; Renou, Marc-Olivier

doi:10.1103/physrevlett.122.070501

Cited by 54 publications

(57 citation statements)

References 70 publications

(137 reference statements)

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“…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. In a similar fashion in [TRR19] the authors provide a self-test of d-dimensional SIC POVM (whenever it exists). To prove the ideal self-testing all works use the same idea; if there is one outcome of a measurement that never occurs for a given preparation, it follows that the corresponding POVM element must be opposite to the preparation 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

239

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

confidence: 99%

Self-testing of quantum systems: a review

Šupić

Bowles

2020

Quantum

239

166

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“…Consider a prepare-and-measure scenario in which Alice has a random input x ∈ achieves its quantum maximum when both S and the above sum individually are maximal. The optimal quantum value obeys [26] max Q S 1 2…”

Section: Appendix B: Certification and Falsification Of Sic Compoundsmentioning

confidence: 99%

“…Nevertheless, semidefinite relaxations can be evaluated by employing the symmetrization techniques of Ref. [26]. For instance, we consider the (trivial) case of deciding the existence of three orthogonal SICs for d = 2.…”

Section: Appendix B: Certification and Falsification Of Sic Compoundsmentioning

confidence: 99%

“…SIC POVMs are key tools for quantum state tomography [11][12][13], which has motivated their experimental realization in highdimensional Hilbert spaces [14][15][16]. Generally, SICs and SIC POVMs are used in a range of protocols: quantum key distribution (QKD) [17][18][19], entanglement detection [20][21][22], device-independent random number generation [23,24], dimension witnessing [25], and characterization of quantum devices [26][27][28][29][30]. Moreover, SICs have been studied in the context of quantum nonlocality [24,[31][32][33] and they have an interesting foundational role in QBism [34].…”

Section: Introductionmentioning

confidence: 99%

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Compounds of symmetric informationally complete measurements and their application in quantum key distribution

Tavakoli

Bengtsson

Gisin

et al. 2020

Phys. Rev. Research

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Symmetric informationally complete measurements (SICs) are elegant, celebrated, and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC compound is defined to be a collection of d 3 vectors in d-dimensional Hilbert space that can be partitioned in two different ways: into d SICs and into d 2 orthonormal bases. While a priori their existence may appear unlikely when d > 2, we surprisingly find an explicit construction for d = 4. Remarkably this SIC compound admits a close relation to mutually unbiased bases, as is revealed through quantum state discrimination. Going beyond fundamental considerations, we leverage these exotic properties to construct a protocol for quantum key distribution and analyze its security under general eavesdropping attacks. We show that SIC compounds enable secure key generation in the presence of errors that are large enough to prevent the success of the generalization of the six-state protocol.

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“…To obtain tight bounds, one may need a reasonably high hi-erarchy level which can be efficiently implemented using the methods of Ref. [39].…”

Section: Certification Methods For Non-projective Measurementsmentioning

confidence: 99%

Self-testing nonprojective quantum measurements in prepare-and-measure experiments

et al. 2020

Self Cite

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Self-testing represents the strongest form of certification of a quantum system. Here we investigate theoretically and experimentally the question of self-testing non-projective quantum measurements. That is, how can one certify, from observed data only, that an uncharacterised measurement device implements a desired non-projective positive-operator-valued-measure (POVM). We consider a prepare-and-measure scenario with a bound on the Hilbert space dimension, which we argue is natural for this problem since any measurement can be made projective by artificially increasing the Hilbert space dimension. We develop methods for (i) robustly self-testing extremal qubit POVMs (which feature either three or four outcomes), and (ii) certify that an uncharacterised qubit measurement is non-projective, or even a genuine four-outcome POVM. Our methods are robust to noise and thus applicable in practice, as we demonstrate in a photonic experiment. Specifically, we show that our experimental data implies that the implemented measurements are very close to certain ideal three and four outcome qubit POVMs, and hence non-projective. In the latter case, the data certifies a genuine four-outcome qubit POVM. Our results open interesting perspective for strong "black-box" certification of quantum devices.

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

Cited by 54 publications

References 70 publications

Self-testing of quantum systems: a review

Self-testing of quantum systems: a review

Compounds of symmetric informationally complete measurements and their application in quantum key distribution

Self-testing nonprojective quantum measurements in prepare-and-measure experiments

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