Kirkwood-Dirac classical pure states
arXiv:2210.02876 · doi:10.1016/j.physleta.2024.129529
Abstract
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 quasiprobability distribution, and negative or nonreal elements may signify quantum advantages in certain tasks. A quantum state is called KD classical if its KD distribution is a probability distribution. Since most quantum information processings use pure states as ideal resources, then a key problem is to determine whether a quantum pure state is KD classical. In this paper, we provide some characterizations for the general structure of KD classical pure states. As an application of our results, we prove a conjecture raised by De Bièvre [Phys. Rev. Lett. 127, 190404 (2021)] which finds out all KD classical pure states for discrete Fourier transformation.
11 pages, 5 figures. Comments are welcome!
References in corpus (19)
- Complex weak values in quantum measurement
- Anomalous Weak Values Are Proofs of Contextuality
- Optimizing the Signal to Noise Ratio of a Beam Deflection Measurement with Interferometric Weak Values
- Jarzynski-like equality for the out-of-time-ordered correlator
- Quantum theory of successive projective measurements
- Negative quasiprobabilities enhance phase estimation in quantum-optics experiment
- Quantifying quantum coherence via nonreal Kirkwood-Dirac quasiprobability
- Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
- Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra
- Kirkwood-Dirac nonclassicality, support uncertainty and complete incompatibility
- Conditions tighter than noncommutation needed for nonclassicality
- Weak Measurement of Superconducting Qubit Reconciles Incompatible Operators
- Classical versus quantum completeness
- Quantum coherence as asymmetry from complex weak values
- Post-Selection and Counterfactual Communication
- Bounding Quantum Advantages in Postselected Metrology
- Classification of incompatibility for two orthonormal bases
- General quantum correlation from nonreal values of Kirkwood-Dirac quasiprobability over orthonormal product bases
- On Kirkwood--Dirac quasiprobabilities and unravelings of quantum channel assigned to a tight frame
Cited by in corpus (7)
- Kirkwood-Dirac representations beyond quantum states (and their relation to noncontextuality)
- Characterizing the geometry of the Kirkwood-Dirac positive states
- Convex roofs witnessing Kirkwood-Dirac nonpositivity
- Geometry of Kirkwood-Dirac classical states: A case study based on discrete Fourier transform
- The Kirkwood-Dirac representation associated to the Fourier transform for finite abelian groups: positivity
- Almost no experiments have classical Kirkwood-Dirac representations
- Hermitian Kirkwood-Dirac real operators for discrete Fourier transformations