Incompatibility probability of random quantum measurements

Lin Zhang, Hua Xiang, Xianqing Li-Jost, and Shao-Ming Fei

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Submission date: 28. Dec. 2019
Pages: 10
published in: Physical review / E, 100 (2019) 6, art-no. 062139 
DOI number (of the published article): 10.1103/PhysRevE.100.062139
Bibtex
Keywords and phrases: random quantum measurement, incompatibility probability, joint measurement
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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 35 . Detailed results are also presented in figures for pairs of general qubit measurements.