Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems
arxiv(2023)
摘要
We investigate features of the quasi-joint-probability distribution for
finite-state quantum systems, especially the two-state and three-state quantum
systems, comparing different types of quasi-joint-probability distributions
based on the general framework of quasi-classicalization. We show from two
perspectives that the Kirkwood-Dirac distribution is the
quasi-joint-probability distribution that behaves nicely for the finite-state
quantum systems. One is the similarity to the genuine probability and the other
is the information that we can obtain from the quasi-probability. By
introducing the concept of the possible values of observables, we show for the
finite-state quantum systems that the Kirkwood-Dirac distribution behaves more
similarly to the genuine probability distribution in contrast to most of the
other quasi-probabilities including the Wigner function. We also prove that the
states of the two-state and three-state quantum systems can be completely
distinguished by the Kirkwood-Dirac distribution of only two directions of the
spin and point out for the two-state system that the imaginary part of the
quasi-probability is essential for the distinguishability of the state.
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