Certification of incompatible measurements using quantum steering

Abstract

In this letter we consider the problem of certification of quantum measurements with an arbitrary number of outcomes. We propose a simple scheme for certifying any set of $d$-outcome projective measurements which do not share any common invariant proper subspace, termed here genuinely incompatible, and the maximally entangled state of two qudits. For our purpose, we focus on a simpler scenario, termed as one-sided device-independent scenario where the resource employed for certification is quantum steering. We also study robustness of our self-testing statements for a certain class of genuinely incompatible measurements including mutually unbiased bases which are essential for several quantum information-theoretic tasks such as quantum cryptography.

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Cited by in corpus (15)

• Measurement incompatibility and quantum advantage in communication
• Self-testing of any pure entangled state with minimal number of measurements and optimal randomness certification in one-sided device-independent scenario
• Robust certification of arbitrary outcome quantum measurements from temporal correlations
• Distrustful quantum steering
• Certification of the maximally entangled state using non-projective measurements
• Network quantum steering enables randomness certification without seed randomness
• All Real Projective Measurements Can be Self-tested
• 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
• Almost device-independent certification of GME states with minimal measurements
• Witnessing network steerability of every bipartite entangled state without inputs
• Multi-object operational tasks for measurement incompatibility
• Topologically noise robust network steering without inputs
• Certifying classes of $d$-outcome measurements with quantum steering
• Communication scenario enables robust self-testing of n-party Greenberger-Horne-Zeilinger basis measurements