Kirkwood-Dirac classical pure states

• URL: http://arxiv.org/abs/2210.02876v2
• Date: Thu, 18 Jan 2024 04:04:17 GMT
• Title: Kirkwood-Dirac classical pure states
• Authors: Jianwei Xu
• Abstract summary: A quantum state is called KD classical if its KD distribution is a probability distribution. We provide some characterizations for the general structure of KD classical pure states.
• Score: 0.32634122554914
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Bi\`{e}vre [Phys. Rev. Lett. 127, 190404 (2021)] which finds out all KD classical pure states for discrete Fourier transformation.

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