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Kirkwood discovered in 1933, and Dirac discovered in 1945, a representation of quantum states that has undergone a renaissance recently. The Kirkwood-Dirac (KD) distribution has been employed to study nonclassicality across quantum physics,…

A central problem in quantum information is determining quantum-classical boundaries. A useful notion of classicality is provided by the quasiprobability formulation of quantum theory. In this framework, a state is called classical if it is…

Kirkwood-Dirac (KD) quasiprobability is a quantum analog of classical phase space probability. It offers an informationally complete representation of quantum state wherein the quantumness associated with quantum noncommutativity manifests…

Quantum Physics · Physics 2024-12-17 Agung Budiyono

The Kirkwood-Dirac (KD) quasiprobability distribution can describe any quantum state with respect to the eigenbases of two observables $A$ and $B$. KD distributions behave similarly to classical joint probability distributions but can…

Quantum Physics · Physics 2024-08-02 Christopher Langrenez , David R. M. Arvidsson-Shukur , Stephan De Bièvre

Kirkwood-Dirac (KD) quasiprobability is a quantum analog of phase space probability of classical statistical mechanics, allowing negative or/and nonreal values. It gives an informationally complete representation of a quantum state. Recent…

Quantum Physics · Physics 2023-09-19 Agung Budiyono , Hermawan K. Dipojono

We provide an in-depth study of the recently introduced notion of completely incompatible observables and its links to the support uncertainty and to the Kirkwood-Dirac nonclassicality of pure quantum states. The latter notion has recently…

Quantum Physics · Physics 2023-04-04 Stephan De Bievre

Just a few years after the inception of quantum mechanics, there has been a research program using the nonclassical values of some quasiprobability distributions to delineate the nonclassical aspects of quantum phenomena. In particular, in…

Quantum Physics · Physics 2024-05-24 Agung Budiyono , Joel F. Sumbowo , Mohammad K. Agusta , Bagus E. B. Nurhandoko

Given two observables $A$ and $B$, one can associate to every quantum state a Kirkwood-Dirac (KD) quasiprobability distribution. KD distributions are like joint classical probabilities except that they can have negative or nonreal values,…

Quantum Physics · Physics 2025-06-30 Christopher Langrenez , Stephan De Bièvre , David R. M. Arvidsson-Shukur

Recent years have seen the Kirkwood-Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be…

The Kirkwood-Dirac (KD) quasiprobability distribution is a fundamental representation for quantum states and has been widely applied in quantum metrology, quantum chaos, weak values in recent years. A quantum state is KD-classical if its…

Quantum Physics · Physics 2026-03-17 Lin-Yan Cai , Ying-Hui Yang , Zhu-Jun Zheng

We show that a Kirkwood-Dirac type quasiprobability distribution is sufficient to reveal any arbitrary quantum resource. This is achieved by demonstrating that it is always possible to identify a set of incompatible measurements that…

Quantum Physics · Physics 2024-01-09 Kok Chuan Tan , Souradeep Sasmal

Classical computers can simulate models of quantum computation with restricted input states. The identification of such states can sharpen the boundary between quantum and classical computations. Previous works describe simulable states of…

We uncover new features of generalized contextuality by connecting it to the Kirkwood-Dirac (KD) quasiprobability distribution. Quantum states can be represented by KD distributions, which take values in the complex unit disc. Only for…

Kirkwood-Dirac (KD) distribution is a representation of quantum states. Recently, KD distribution has been employed in many scenarios such as quantum metrology, quantum chaos and foundations of quantum theory. KD distribution is a…

Quantum Physics · Physics 2024-04-30 Jianwei Xu

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.…

Quantum Physics · Physics 2025-06-11 Yan Liu , Zhihua Guo , Zhihao Ma , Shao-Ming Fei

Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to properly account for non-classical features in the context of condensed matter physics (scrambling, dynamical phase transitions)…

We propose a characterization and a quantification of general quantum correlation which is exhibited even by a separable (unentangled) mixed bipartite state in terms of the nonclassical values of the associated Kirkwood-Dirac (KD)…

Quantum Physics · Physics 2024-05-15 Agung Budiyono , Bobby E. Gunara , Bagus E. B. Nurhandoko , Hermawan K. Dipojono

The Kirkwood-Dirac (KD) distribution has recently emerged as a powerful quasiprobability framework with wide-ranging applications in quantum information processing tasks. In this work, we introduce an experimentally motivated criterion for…

Quantum Physics · Physics 2026-03-27 Sudip Chakrabarty , Bivas Mallick , Saheli Mukherjee , Ananda G. Maity

The Kirkwood-Dirac (KD) quasiprobability describes measurement statistics of joint quantum observables, and has generated great interest as prominent indicators of non-classical features in various quantum information processing tasks. It…

Quantum Physics · Physics 2025-04-15 Lijun Liu , Shuming Cheng

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…

Quantum Physics · Physics 2024-04-01 Shun Umekawa , Jaeha Lee , Naomichi Hatano
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