A coherence monotone from Kirkwood-Dirac nonclassicality with respect to mutually unbiased bases

TL;DR

This paper introduces a new coherence monotone based on Kirkwood-Dirac nonclassicality relative to mutually unbiased bases, linking quantum coherence to weak values and classicality in prime-dimensional Hilbert spaces.

Contribution

It defines a novel coherence monotone from Kirkwood-Dirac nonclassicality and relates it to weak values, advancing understanding of quantum coherence and classicality in quantum states.

Findings

Quantum states are Kirkwood-Dirac classical for two MUB sets iff they are incoherent in one basis.

The coherence monotone can be expressed via weak values.

Quantum coherence can be used to detect anomalous weak values.

Abstract

The Kirkwood-Dirac distribution, serving as an informationally complete representation of a quantum state, has recently garnered increasing attention. We investigate the Kirkwood-Dirac classicality with respect to mutually unbiased bases. For prime dimensional Hilbert spaces, {we demonstrate that a quantum state exhibits Kirkwood-Dirac classicality for two distinct sets of mutually unbiased bases $(A,B)$ and $(A,B')$ if and only if it is incoherent with respect to $A$}. We subsequently introduce a coherence monotone based on Kirkwood-Dirac nonclassicality with respect to mutually unbiased bases. Additionally, we establish that this coherence monotone can be expressed through weak values, suggesting that quantum coherence can be utilized to detect anomalous weak values.