The boundary of Kirkwood-Dirac quasiprobability

• URL: http://arxiv.org/abs/2504.09238v1
• Date: Sat, 12 Apr 2025 14:23:36 GMT
• Title: The boundary of Kirkwood-Dirac quasiprobability
• Authors: Lijun Liu, Shuming Cheng,
• Abstract summary: The Kirkwood-Dirac quasiprobability describes measurement statistics of joint quantum observables.<n>We introduce the postquantum quasiprobability under mild assumptions to provide an outer boundary for KD quasiprobability.<n>Surprisingly, we are able to derive some nontrivial bounds valid for both classical probability and KD quasiprobability.
• Score: 0.759660604072964
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 relaxes the Kolmogorov axioms of probability by allowing for negative and even imaginary probabilities, and thus incorporates the classical probability theory as its inner boundary. In this work, we introduce the postquantum quasiprobability under mild assumptions to provide an outer boundary for KD quasiprobability. Specifically, we present qualitative and quantitative evidence to show that the classical, KD, and postquantum quasiprobabilities form a strict hierarchy, in the sense that joint probability distributions are a strict subset of KD quasiprobability distributions that are a strict subset of postquantum ones. Surprisingly, we are able to derive some nontrivial bounds valid for both classical probability and KD quasiprobability, and even valid for the KD quasiprobability generated by an arbitrary number of measurements. Finally, other interesting bounds are obtained, and their implications are noted. Our work solves the fundamental problems of what and how to bound the KD quasiprobability, and hence provides a deeper understanding of utilizing it in quantum information processing.

Related papers

• To Believe or Not to Believe Your LLM [51.2579827761899]
  We explore uncertainty quantification in large language models (LLMs) We derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large. We conduct a series of experiments which demonstrate the advantage of our formulation.
  arXiv  Detail & Related papers  (2024-06-04T17:58:18Z)
• Sufficient conditions, lower bounds and trade-off relations for quantumness in Kirkwood-Dirac quasiprobability [0.0]
  Kirkwood-Dirac (KD) quasiprobability is a quantum analog of classical phase space probability. It offers an informationally complete representation of quantum state. How does such form of quantumness comply with the uncertainty principle which also arise from quantum noncommutativity?
  arXiv  Detail & Related papers  (2024-05-14T05:44:07Z)
• Testing trajectory-based determinism via time probability distributions [44.99833362998488]
  Bohmian mechanics (BM) has inherited more predictive power than quantum mechanics (QM) We introduce a prescription for constructing a flight-time probability distribution within generic trajectory-equipped theories. We derive probability distributions that are unreachable by QM.
  arXiv  Detail & Related papers  (2024-04-15T11:36:38Z)
• Properties and Applications of the Kirkwood-Dirac Distribution [0.0]
  The KD distribution can represent a quantum state in terms of arbitrary observables.<n>This paper reviews the KD distribution, in three parts.<n>We emphasise connections between operational quantum advantages and negative or non-real KD quasi-probabilities.
  arXiv  Detail & Related papers  (2024-03-27T18:00:02Z)
• Kirkwood-Dirac Type Quasiprobabilities as Universal Identifiers of Nonclassical Quantum Resources [0.0]
  We show that a Kirkwood-Dirac type quasiprobability distribution is sufficient to reveal any arbitrary quantum resource. The quasiprobability reveals a resourceful quantum state by having at least one quasiprobability outcome with a strictly negative numerical value.
  arXiv  Detail & Related papers  (2024-01-07T14:56:32Z)
• Quantum coherence from Kirkwood-Dirac nonclassicality, some bounds, and operational interpretation [0.0]
  We develop a faithful quantifier of quantum coherence based on the KD nonclassicality. The KD-nonclassicality coherence captures simultaneously the nonreality and the negativity of the KD quasiprobability.
  arXiv  Detail & Related papers  (2023-09-17T05:29:49Z)
• Quantifying quantum coherence via nonreal Kirkwood-Dirac quasiprobability [0.0]
  Kirkwood-Dirac (KD) quasiprobability is a quantum analog of phase space probability of classical statistical mechanics. Recent works have revealed the important roles played by the KD quasiprobability in the broad fields of quantum science and quantum technology.
  arXiv  Detail & Related papers  (2023-09-17T04:34:57Z)
• Work statistics, quantum signatures and enhanced work extraction in quadratic fermionic models [62.997667081978825]
  In quadratic fermionic models we determine a quantum correction to the work statistics after a sudden and a time-dependent driving. Such a correction lies in the non-commutativity of the initial quantum state and the time-dependent Hamiltonian. Thanks to the latter, one can assess the onset of non-classical signatures in the KDQ distribution of work.
  arXiv  Detail & Related papers  (2023-02-27T13:42:40Z)
• Controlling Moments with Kernel Stein Discrepancies [74.82363458321939]
  Kernel Stein discrepancies (KSDs) measure the quality of a distributional approximation.<n>We first show that standard KSDs used for weak convergence control fail to control moment convergence.<n>We then provide sufficient conditions under which alternative diffusion KSDs control both moment and weak convergence.
  arXiv  Detail & Related papers  (2022-11-10T08:24:52Z)
• Probabilities of Causation: Role of Observational Data [20.750773939911685]
  We discuss the conditions that observational data are worth considering to improve the quality of the bounds. We also apply the proposed theorems to the unit selection problem defined by Li and Pearl.
  arXiv  Detail & Related papers  (2022-10-17T09:10:11Z)
• Probabilities of Causation with Nonbinary Treatment and Effect [20.750773939911685]
  Tian and Pearl derived sharp bounds for the probability of necessity and sufficiency. We provide theoretical bounds for all types of probabilities of causation to multivalued treatments and effects.
  arXiv  Detail & Related papers  (2022-08-19T23:54:47Z)
• Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality [69.62715388742298]
  We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs) We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
  arXiv  Detail & Related papers  (2022-03-08T14:47:39Z)
• Distribution Regression with Sliced Wasserstein Kernels [45.916342378789174]
  We propose the first OT-based estimator for distribution regression. We study the theoretical properties of a kernel ridge regression estimator based on such representation.
  arXiv  Detail & Related papers  (2022-02-08T15:21:56Z)
• A Unified Joint Maximum Mean Discrepancy for Domain Adaptation [73.44809425486767]
  This paper theoretically derives a unified form of JMMD that is easy to optimize. From the revealed unified JMMD, we illustrate that JMMD degrades the feature-label dependence that benefits to classification. We propose a novel MMD matrix to promote the dependence, and devise a novel label kernel that is robust to label distribution shift.
  arXiv  Detail & Related papers  (2021-01-25T09:46:14Z)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.