Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Comment on “Saturating quantum advantages in postselected metrology with the positive Kirkwood-Dirac distribution”

David R. M. Arvidsson-Shukur, C. H. W. Barnes, Hugo Vincent Lepage, Seth Lloyd, Noah Lupu-Gladstein, Wilfred Salmon, Flavio Salvati

Published Jun 21, 2024• 3 citations
Publisher

Abstract

In a recent paper [Das, Modak, and Bera, Phys. Rev. A 107, 042413 (2023)], Das et al. claim that Kirkwood-Dirac negativity is not required to achieve anomalous values of the quantum Fisher information encoded in postselected (filtered) particles. We argue that this claim is wrong. Further, we show that the quantum Fisher information in optimal postselected metrology is directly proportional to the total Kirkwood-Dirac nonclassicality.

DOI
10.1103/physreva.109.066401

Related papers

Reply to “Comment on ‘Saturating quantum advantages in postselected metrology with the positive Kirkwood-Dirac distribution' ”

Sourav Das, Subhrajit Modak, Manabendra Nath Bera

In Das et al. [Phys. Rev. A 107, 042413 (2023)], we showed that Kirkwood-Dirac negativity is not necessary to achieve anomalous quantum Fisher information. Arvidsson-Shukur et al. [preceding Comment, Phys. Rev. A (to be published)] claim that one of our conclusions is wrong. Here, we argue that the claim is unfounded and incorrect and conclusions in Das et al. stand correct when the standard form of the Kirkwood-Dirac distribution is investigated. The confusion arises due to the choice of the distribution under consideration. We clarify this issue along with an interpretation of nonclassicality attached to the positivity of Kirkwood-Dirac distribution.

Physical Review A•Jun 21, 2024•0 citations

Saturating quantum advantages in postselected metrology with the positive Kirkwood-Dirac distribution

Sourav Das, Subhrajit Modak, Manabendra Nath Bera

Weak amplification and other postselection-based metrological protocols can enhance precision while estimating small parameters, outperforming postselection-free protocols. In general, these enhancements are largely constrained because the protocols yielding higher precision are rarely obtained due to a lower probability of successful postselection. It is shown that this precision can further be improved with the help of quantum resources like entanglement and negativity in the quasiprobability distribution. However, these quantum advantages in attaining considerable success probability with large precision are bounded irrespective of any accessible quantum resources. The advantage is being considered only within the scope of postselected metrology. Here we derive a bound of these advantages in postselected metrology, establishing a connection with weak value optimization where the latter can be understood in terms of the geometric phase. We introduce a scheme that saturates the bound, yielding anomalously large precision. Moreover, we prove that these advantages can be achieved with positive quasiprobability distribution. We also provide an optimal metrological scheme using a three-level nondegenerate quantum system.

arXiv:2108.09220•Physical Review A•Apr 11, 2023•18 citations

Negative quasiprobabilities redistribute (and complex ones reduce) the information in unabsorbed photons

Jonte R. Hance

Negative Kirkwood--Dirac quasiprobabilities are credited with the quantum advantage of interaction-free measurement and postselected metrology. We test that claim on the task interaction-free measurement was designed for: learning about a sample letting it absorb as little light as possible. The Kirkwood--Dirac distribution of path and output gives the linear response to a weak sample: its real part responds to absorption, its imaginary part to a phase. For a pure single photon passing once through any interferometer, the Fisher information about transmittance per absorbed photon is the direct-transmission value minus a sum of squared imaginary parts: no interferometer or readout beats direct transmission. Negativity plays no role beyond concentrating information in weakly lit outputs. The imaginary parts of the Kirkwood-Dirac distribution depend on the output basis here, not on the sample, so a basis exists in which every term is real, which is optimal. A single photon gains information per absorbed photon only through a phase response, which for an optical line needs a thick or inhomogeneously broadened sample, or through many passes when absorptions go uncounted, as shown by a critically coupled resonator. For detecting a weak absorber, negativity gives a single-shot advantage that does not accumulate over multiple trials; advantage instead accumulates when there are outputs which are dark without the object, a case which needs no negativity.

quant-pharXiv:2610.00740•Oct 2, 2026•0 citations

Nonclassicality of the Kirkwood-Dirac quasiprobability distribution via quantum modification terms

Jiayu He, Shuangshuang Fu

The Kirkwood-Dirac (KD) quasiprobability is a quantum analog expression of the phase-space probability in classical statistical mechanics, yet it can behave nonclassically by taking negative or nonreal values. The nonclassicality of the KD quasiprobability distribution has lately been shown to provide advantages in some quantum information tasks and shed light on a number of aspects of quantum physics. Characterization and quantification of KD nonclassicality are crucial both theoretically and experimentally. Most of the existing measures of KD nonclassicality concentrate merely on the negative or/and imaginary part(s) of the KD distribution. Yet it is not clear whether these measures can account for all nonclassicality in the distribution. In this paper, we suggest a KD nonclassicality measure based on the two quantum modification terms in the quasiprobability distribution. The present paper is mainly motivated by the following two considerations: First, the two quantum modification terms are actually the sources of the negative and imaginary parts of the KD quasiprobability respectively. Secondly, these quantum modification terms deviate the KD quasiprobability from the classical joint probability distribution function of two successive projective measurements (termed as the Wigner formula), which can be obtained from the multiplication principle in classical probability theory. Our measure refines the quantification of KD nonclassicality in the sense that even for real and nonnegative KD distribution, its quantum modification terms can still exist, resulting in a nonvanishing KD nonclassicality. As an illustration, we analyze the KD nonclassicality of the positive KD distribution in the postselected metrology scheme [S. Das, S. Modak, and M. N. Bera, Phys. Rev. A 107, 042413 (2023)], which provides interpretation on the source of quantum advantages. We also give an upper bound on the KD nonclassicality measure and offer an easily verifiable sufficient condition for nonvanishing KD nonclassicality.

Physical Review A•Jan 22, 2024•15 citations

Bounding Kirkwood-Dirac negativity of Gaussian processes

Luca Bianchi, Carlo Marconi, Riccardo Cioli +1 more

The Kirkwood-Dirac quasiprobability provides an operational representation of a quantum state, whose negativity serves as a measure of nonclassicality. Despite its fundamental importance, the extremal values of the Kirkwood-Dirac negativity are still unknown in the general case. We investigate the Kirkwood-Dirac quasiprobability of an arbitrary quantum state under Gaussian processes. In this setting, we derive an upper bound on the negativity for any number of modes and measurements. For a single mode and two measurements, we show that the eigenstates of the quadrature operators saturate this upper bound, while a nontrivial minimum is reached by pure Gaussian states. As a consequence, our results indicate that Gaussian states are sufficient to achieve extreme values of nonclassicality.

quant-pharXiv:2607.11854•Jul 14, 2026•0 citations

Quantum advantage in postselected metrology

David R. M. Arvidsson-Shukur, Nicole Yunger Halpern, Hugo Vincent Lepage +3 more

In every parameter-estimation experiment, the final measurement or the postprocessing incurs a cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost. We show that this improvement stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, our quasiprobability distribution is real and nonnegative. In a quantum-mechanically noncommuting theory, nonclassicality manifests in negative or nonreal quasiprobabilities. Negative quasiprobabilities enable postselected experiments to outperform optimal postselection-free experiments: postselected quantum experiments can yield anomalously large information-cost rates. This advantage, we prove, is unrealizable in any classically commuting theory. Finally, we construct a preparation-and-postselection procedure that yields an arbitrarily large Fisher information. Our results establish the nonclassicality of a metrological advantage, leveraging our quasiprobability distribution as a mathematical tool.

arXiv:1903.02563•Nature Communications•Jul 29, 2020•141 citations
In a recent paper [Das, Modak, and Bera, Phys. Rev. A 107, 042413 (2023)], Das et al. claim that Kirkwood-Dirac negativity is not required to achieve anomalous values of the quantum Fisher information encoded in postselected (filtered) particles. We argue that this claim is wrong. Further, we show that the quantum Fisher information in optimal postselected metrology is directly proportional to the total Kirkwood-Dirac nonclassicality.
In Das et al. [Phys. Rev. A 107, 042413 (2023)], we showed that Kirkwood-Dirac negativity is not necessary to achieve anomalous quantum Fisher information. Arvidsson-Shukur et al. [preceding Comment, Phys. Rev. A (to be published)] claim that one of our conclusions is wrong. Here, we argue that the claim is unfounded and incorrect and conclusions in Das et al. stand correct when the standard form of the Kirkwood-Dirac distribution is investigated. The confusion arises due to the choice of the distribution under consideration. We clarify this issue along with an interpretation of nonclassicality attached to the positivity of Kirkwood-Dirac distribution.
Weak amplification and other postselection-based metrological protocols can enhance precision while estimating small parameters, outperforming postselection-free protocols. In general, these enhancements are largely constrained because the protocols yielding higher precision are rarely obtained due to a lower probability of successful postselection. It is shown that this precision can further be improved with the help of quantum resources like entanglement and negativity in the quasiprobability distribution. However, these quantum advantages in attaining considerable success probability with large precision are bounded irrespective of any accessible quantum resources. The advantage is being considered only within the scope of postselected metrology. Here we derive a bound of these advantages in postselected metrology, establishing a connection with weak value optimization where the latter can be understood in terms of the geometric phase. We introduce a scheme that saturates the bound, yielding anomalously large precision. Moreover, we prove that these advantages can be achieved with positive quasiprobability distribution. We also provide an optimal metrological scheme using a three-level nondegenerate quantum system.
Negative Kirkwood--Dirac quasiprobabilities are credited with the quantum advantage of interaction-free measurement and postselected metrology. We test that claim on the task interaction-free measurement was designed for: learning about a sample letting it absorb as little light as possible. The Kirkwood--Dirac distribution of path and output gives the linear response to a weak sample: its real part responds to absorption, its imaginary part to a phase. For a pure single photon passing once through any interferometer, the Fisher information about transmittance per absorbed photon is the direct-transmission value minus a sum of squared imaginary parts: no interferometer or readout beats direct transmission. Negativity plays no role beyond concentrating information in weakly lit outputs. The imaginary parts of the Kirkwood-Dirac distribution depend on the output basis here, not on the sample, so a basis exists in which every term is real, which is optimal. A single photon gains information per absorbed photon only through a phase response, which for an optical line needs a thick or inhomogeneously broadened sample, or through many passes when absorptions go uncounted, as shown by a critically coupled resonator. For detecting a weak absorber, negativity gives a single-shot advantage that does not accumulate over multiple trials; advantage instead accumulates when there are outputs which are dark without the object, a case which needs no negativity.
The Kirkwood-Dirac (KD) quasiprobability is a quantum analog expression of the phase-space probability in classical statistical mechanics, yet it can behave nonclassically by taking negative or nonreal values. The nonclassicality of the KD quasiprobability distribution has lately been shown to provide advantages in some quantum information tasks and shed light on a number of aspects of quantum physics. Characterization and quantification of KD nonclassicality are crucial both theoretically and experimentally. Most of the existing measures of KD nonclassicality concentrate merely on the negative or/and imaginary part(s) of the KD distribution. Yet it is not clear whether these measures can account for all nonclassicality in the distribution. In this paper, we suggest a KD nonclassicality measure based on the two quantum modification terms in the quasiprobability distribution. The present paper is mainly motivated by the following two considerations: First, the two quantum modification terms are actually the sources of the negative and imaginary parts of the KD quasiprobability respectively. Secondly, these quantum modification terms deviate the KD quasiprobability from the classical joint probability distribution function of two successive projective measurements (termed as the Wigner formula), which can be obtained from the multiplication principle in classical probability theory. Our measure refines the quantification of KD nonclassicality in the sense that even for real and nonnegative KD distribution, its quantum modification terms can still exist, resulting in a nonvanishing KD nonclassicality. As an illustration, we analyze the KD nonclassicality of the positive KD distribution in the postselected metrology scheme [S. Das, S. Modak, and M. N. Bera, Phys. Rev. A 107, 042413 (2023)], which provides interpretation on the source of quantum advantages. We also give an upper bound on the KD nonclassicality measure and offer an easily verifiable sufficient condition for nonvanishing KD nonclassicality.
The Kirkwood-Dirac quasiprobability provides an operational representation of a quantum state, whose negativity serves as a measure of nonclassicality. Despite its fundamental importance, the extremal values of the Kirkwood-Dirac negativity are still unknown in the general case. We investigate the Kirkwood-Dirac quasiprobability of an arbitrary quantum state under Gaussian processes. In this setting, we derive an upper bound on the negativity for any number of modes and measurements. For a single mode and two measurements, we show that the eigenstates of the quadrature operators saturate this upper bound, while a nontrivial minimum is reached by pure Gaussian states. As a consequence, our results indicate that Gaussian states are sufficient to achieve extreme values of nonclassicality.
In every parameter-estimation experiment, the final measurement or the postprocessing incurs a cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost. We show that this improvement stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, our quasiprobability distribution is real and nonnegative. In a quantum-mechanically noncommuting theory, nonclassicality manifests in negative or nonreal quasiprobabilities. Negative quasiprobabilities enable postselected experiments to outperform optimal postselection-free experiments: postselected quantum experiments can yield anomalously large information-cost rates. This advantage, we prove, is unrealizable in any classically commuting theory. Finally, we construct a preparation-and-postselection procedure that yields an arbitrarily large Fisher information. Our results establish the nonclassicality of a metrological advantage, leveraging our quasiprobability distribution as a mathematical tool.