Self-testing of any pure entangled state with minimal number of measurements and optimal randomness certification in one-sided device-independent scenario

Abstract

Certification of quantum systems and their properties has become a field of intensive studies. Here, taking advantage of the one-sided device-independent scenario (known also as quantum steering scenario), we propose a self-testing scheme for all bipartite entangled states using a single family of steering inequalities with the minimal number of two measurements per party. Building on this scheme we then show how to certify all rank-one extremal measurements, including non-projective $d^2$-outcome measurements, which in turn can be used for certification of the maximal amount of randomness from every entangled bipartite state of local dimension $d$, that is, $2{\log }_{2}d$ bits. Finally, in a particular case of $d=3$, we extend our self-testing results to the fully device-independent setting.

arXiv commentCorrected and improved version. Comments are welcome!

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• All Real Projective Measurements Can be Self-tested
• Certification of unbounded randomness with arbitrary noise
• Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
• Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios
• Constant-sized self-tests for maximally entangled states and single projective measurements
• Witnessing network steerability of every bipartite entangled state without inputs
• Quantum bounds and device-independent security with rank-one qubit measurements
• Almost device-independent certification of GME states with minimal measurements
• Topologically noise robust network steering without inputs
• Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering
• Any gate of a quantum computer can be certified device-independently
• Communication scenario enables robust self-testing of n-party Greenberger-Horne-Zeilinger basis measurements