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Physica A Statistical Mechanics and its Applications

Quantum simultaneous measurement of non-commuting observables based on K -means clustering

Wei Cui, Yang Yang

Published Nov 1, 2021• 3 citations
Publisher
DOI
10.1016/j.physa.2021.126559

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Quantum simultaneous measurement of non-commuting observables based on K-means clustering

Cui, Wei, Yang, Yang

Simultaneous measurement of non-commuting observables deepens the understanding of Heisenberg’s uncertainty principle and has significant applications to quantum feedback control theory. Here we use techniques from machine learning to define a measure for the degree of non-commuting behavior of quantum measurements coming from the initial and final states of the measurements. Both the measurement strength effect and the angle effect between two observables have been constructed by using the K-means clustering method to reflect the defined non-commutativity measure. The rationality of the measure is demonstrated and its application in obtaining the measurement limitation that physically realizable is presented. Our work helps to advance the understanding of quantum non-commuting measurement and quantum control theory.

•Jan 1, 2022•0 citations
Simultaneous measurement of non-commuting observables deepens the understanding of Heisenberg’s uncertainty principle and has significant applications to quantum feedback control theory. Here we use techniques from machine learning to define a measure for the degree of non-commuting behavior of quantum measurements coming from the initial and final states of the measurements. Both the measurement strength effect and the angle effect between two observables have been constructed by using the K-means clustering method to reflect the defined non-commutativity measure. The rationality of the measure is demonstrated and its application in obtaining the measurement limitation that physically realizable is presented. Our work helps to advance the understanding of quantum non-commuting measurement and quantum control theory.