All the self-testings of the singlet for two binary measurements

Abstract

Self-testing refers to the possibility of characterizing uniquely (up to local isometries) the state and measurements contained in quantum devices, based only on the observed input-output statistics. Already in the basic case of the two-qubit singlet, self-testing is not unique: the two known criteria (the maximal violation of the CHSH inequality and the Mayers-Yao correlations) are not equivalent. It is unknown how many criteria there are. In this paper, we find the whole set of criteria for the ideal self-testing of singlet with two measurements and two outcomes on each side: it coincides with all the extremal points of the quantum set that can be obtained by measuring the singlet.

14 pages, 5 figures, 24 references

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Cited by in corpus (48)

• Self-testing of quantum systems: a review
• All Pure Bipartite Entangled States can be Self-Tested
• Geometry of the set of quantum correlations
• Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
• Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
• Self-testing of binary observables based on commutation
• Self-testing mutually unbiased bases in the prepare-and-measure scenario
• Self-testing protocols based on the chained Bell inequalities
• Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems
• Quantum Correlations in the Minimal Scenario
• Robust self-testing of two-qubit states
• Experimental robust self-testing of the state generated by a quantum network
• Device-independent quantum key distribution with arbitrarily small nonlocality
• Device-independent tests of quantum channels
• Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory
• A weak form of self-testing
• Self-testing of multipartite GHZ states of arbitrary local dimension with arbitrary number of measurements per party
• Certification of incompatible measurements using quantum steering
• Self-testing quantum states via nonmaximal violation in Hardy's test of nonlocality
• Device-independent certification of tensor products of quantum states using single-copy self-testing protocols
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios
• Custom Bell inequalities from formal sums of squares
• Quantum correlations on the no-signaling boundary: self-testing and more
• Robust certification of arbitrary outcome quantum measurements from temporal correlations
• Necessary and sufficient criterion for extremal quantum correlations in the simplest Bell scenario
• Structure of the set of quantum correlators via semidefinite programming
• Non-local games and optimal steering at the boundary of the quantum set
• Certification of the maximally entangled state using non-projective measurements
• Self-testing two-qubit maximally entangled states from generalized CHSH tests
• Quantifying the intrinsic randomness in sequential measurements
• Geometrical self-testing of partially entangled two-qubit states
• Cryptographic Quantum Bound on Nonlocality
• Self-testing quantum systems of arbitrary local dimension with minimal number of measurements
• Self-testing of different entanglement resources via fixed measurement settings
• A universal scheme to self-test any quantum state or measurement
• Model-independent inference of quantum interaction from statistics
• All two-party facet Bell inequalities are violated by Almost Quantum correlations
• Self-testing composite measurements and bound entangled state in a single quantum network
• Robust one-sided self-testing of two-qubit states via quantum steering
• Seedless extractors for device-independent quantum cryptography
• Parallel remote state preparation for fully device-independent verifiable blind quantum computation
• (Almost-)Quantum Bell Inequalities and Device-Independent Applications
• Composable framework for device-independent state certification
• Topologically noise robust network steering without inputs
• Any gate of a quantum computer can be certified device-independently
• Self-testing of symmetric three-qubit states
• Certifying classes of $d$-outcome measurements with quantum steering
• Device-independent secure correlations in sequential quantum scenarios