Incompatibility probability of random quantum measurements

Abstract

Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum uncertainty relations, and quantum steering. We study the necessary and sufficient conditions of quantum compatibility for a given collection of $n$ measurements in $d$-dimensional space. From the compatibility criterion for two-qubit measurements, we compute the incompatibility probability of a pair of independent random measurements. For a pair of unbiased random qubit measurements, we derive that the incompatibility probability is exactly $\frac{3}{5}$. Detailed results are also presented in figures for pairs of general qubit measurements.

arXiv comment8 pages, 3 figures, LaTex

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Cited by in corpus (5)

• Incompatible measurements in quantum information science
• Dirac Delta Function of Matrix Argument
• Random positive operator valued measures
• Classification of incompatibility for two orthonormal bases
• Uncertainty regions of observables and state-independent uncertainty relations