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

¹ School of Mathematics and Statistics, Shaanxi Normal University - Xi'an 710119, China
² School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University - Shanghai 200240, China
³ Shanghai Seres Information Technology Co., Ltd - Shanghai 200040, China
⁴ Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology Shenzhen 518055, China
⁵ School of Mathematical Sciences, Capital Normal University - Beijing 100048, China

Received: 25 March 2025
Accepted: 13 May 2025

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 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.