Compatibility of Generalized Noisy Qubit Measurements

Abstract

It is a crucial feature of quantum mechanics that not all measurements are compatible with each other. However, if measurements suffer from noise they may lose their incompatibility. Here, we consider the effect of white noise and determine the critical visibility such that all qubit measurements, i.e. all positive operator-valued measures (POVMs), become compatible, i.e. jointly measurable. In addition, we apply our methods to quantum steering and Bell nonlocality. We obtain a tight local hidden state model for two-qubit Werner states of visibility $1/2$. This determines the exact steering bound for two-qubit Werner states and also provides a local hidden variable model that improves on previously known models. Interestingly, this proves that POVMs are not more powerful than projective measurements to demonstrate quantum steering for these states.

5+9 pages, 5 figures, close to published version

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Cited by in corpus (10)

• Exact Steering Bound for Two-Qubit Werner States
• Semidefinite relaxations for high-dimensional entanglement in the steering scenario
• Thermodynamic Approach to Quantifying Incompatible Instruments
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Constrained Measurement Incompatibility from Generalised Contextuality of Steered Preparation
• Cost of Simulating Entanglement in Steering Scenario
• Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality
• Catalytic Activation of Bell Nonlocality
• Witness High-Dimensional Quantum Steering via Majorization Lattice
• On compatibility of binary qubit measurements