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Kirkwood-Dirac classical pure states
Quantum Physics · Submitted 6 Oct 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this paper, we provide some characterizations for the general structure of KD classical pure states.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Kirkwood-Dirac (KD) distribution is a representation of quantum states. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | Recently, KD distribution has been employed in many scenarios such as quantum metrology, quantum chaos and foundations of quantum theory. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s2 | KD distribution is a quasiprobability distribution, and negative or nonreal elements may signify quantum advantages in certain tasks. | background 0.96 | 0.06 | 0.02 | hedged possibility 0.98 |
| s3 | A quantum state is called KD classical if its KD distribution is a probability distribution. | background 1.00 | 0.08 | 0.05 | asserted 1.00 |
| s4 | 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. | background 0.72 | 0.07 | 0.04 | asserted 0.98 |
| s5 | In this paper, we provide some characterizations for the general structure of KD classical pure states. | contribution 1.00 | 0.95 | 0.41 | asserted 0.99 |
| s6 | 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. | result 0.75 | 0.90 | 0.39 | asserted 1.00 |
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The paper
Original 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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How the literature uses it
4 arXiv papers cite this in 4 sentences
Papers citing it · 3 sentences without a confident label
Cites it as background 1 paper
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More information about $$, when the transition matrix is a Hadamard matrix ($|a_ib_j|^2 = 1/d =$ for all $i,j$), appears in [ref] .
Properties and Applications of the Kirkwood-Dirac Distribution · Characterising the set of KD-positive states · 0.83
What it cites · 2 sentences without a confident label
Cites as background 2 papers
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In recent years, KD distribution has been found significant applications in several areas of quantum mechanics, such as in weak-value amplification [ref] , tomographic reconstruction of a quantum state [ref] , quantum chaos [ref] , quantum metrology [ref] , quantum thermodynamics [ref] , and the foundations of quantum mechanics [ref] , see [ref] for an extensive review and references therein.
1907.02432 · Introduction · 0.98
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In recent years, KD distribution has been found significant applications in several areas of quantum mechanics, such as in weak-value amplification [ref] , tomographic reconstruction of a quantum state [ref] , quantum chaos [ref] , quantum metrology [ref] , quantum thermodynamics [ref] , and the foundations of quantum mechanics [ref] , see [ref] for an extensive review and references therein.
Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables · Introduction · 0.98
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