Incompatibility probability of random quantum measurements
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Updated: Dec 30, 2025

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source
Published on: April 4, 2017
Lin Zhang1,2, Hua Xiang3, Xianqing Li-Jost2
1Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, People's Republic of China.
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 3/5. Detailed results are also presented in figures for pairs of general qubit measurements.
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