Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems

• URL: http://arxiv.org/abs/2309.06836v1
• Date: Wed, 13 Sep 2023 09:35:42 GMT
• Title: Advantages of the Kirkwood-Dirac distribution among general quasi-probabilities for finite-state quantum systems
• Authors: Shun Umekawa, Jaeha Lee, Naomichi Hatano
• Abstract summary: We investigate features of the quasi-joint-probability distribution for finite-state quantum systems. We show that the Kirkwood-Dirac distribution behaves nicely for the finite-state quantum systems.
• Score: 0.8024120666398408
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate features of the quasi-joint-probability distribution for finite-state quantum systems, especially the two-state and three-state quantum systems, comparing different types of quasi-joint-probability distributions based on the general framework of quasi-classicalization. We show from two perspectives that the Kirkwood-Dirac distribution is the quasi-joint-probability distribution that behaves nicely for the finite-state quantum systems. One is the similarity to the genuine probability and the other is the information that we can obtain from the quasi-probability. By introducing the concept of the possible values of observables, we show for the finite-state quantum systems that the Kirkwood-Dirac distribution behaves more similarly to the genuine probability distribution in contrast to most of the other quasi-probabilities including the Wigner function. We also prove that the states of the two-state and three-state quantum systems can be completely distinguished by the Kirkwood-Dirac distribution of only two directions of the spin and point out for the two-state system that the imaginary part of the quasi-probability is essential for the distinguishability of the state.

Related papers

• Non-Gaussian generalized two-mode squeezing: applications to two-ensemble spin squeezing and beyond [0.0]
  We show that the basic structure of these states can be generalized to arbitrary bipartite quantum systems. We show that these general states can always be stabilized by a relatively simple Markovian dissipative process.
  arXiv  Detail & Related papers  (2024-06-30T15:03:29Z)
• One-Shot Min-Entropy Calculation And Its Application To Quantum Cryptography [21.823963925581868]
  We develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state. It gives an alternative tight finite-data analysis for the well-known BB84 quantum key distribution protocol. It provides a security proof for a novel source-independent continuous-variable quantum random number generation protocol.
  arXiv  Detail & Related papers  (2024-06-21T15:11:26Z)
• 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)
• Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement [41.94295877935867]
  We introduce and develop the framework of Gibbs-preserving local operations and classical communication. We focus on systems with fully degenerate local Hamiltonians, where local cooling aligns with the extraction of local purity. Our findings open doors to various practical applications, including techniques for entanglement detection and estimation.
  arXiv  Detail & Related papers  (2023-11-20T14:58:31Z)
• Quantification of Entanglement and Coherence with Purity Detection [16.01598003770752]
  Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence. Our research offers an efficient means of verifying large-scale quantum information processing.
  arXiv  Detail & Related papers  (2023-08-14T11:03:40Z)
• Interacting bosons in a triple well: Preface of many-body quantum chaos [0.0]
  We investigate the onset of quantum chaos in a triple-well model that moves away from integrability as its potential gets tilted. Even in its deepest chaotic regime, the system presents features reminiscent of integrability.
  arXiv  Detail & Related papers  (2021-11-26T19:00:03Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Determination of All Unknown Pure Quantum States with Two Observables [3.19428095493284]
  Efficiently extracting information from pure quantum states using minimal observables on the main system is a longstanding and fundamental issue in quantum information theory. We show that two orthogonal bases are capable of effectively filtering up to $2d-1$ finite candidates by disregarding a measure-zero set. We also show that almost all pure qudits can be uniquely determined by adaptively incorporating a POVM in the middle, followed by measuring the complementary observable.
  arXiv  Detail & Related papers  (2021-08-12T13:46:14Z)
• Improving application performance with biased distributions of quantum states [0.0]
  We analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert--Schmidt distributions. We demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert--Schmidt distributions results in measurable performance advantages.
  arXiv  Detail & Related papers  (2021-07-15T23:29:10Z)
• Symmetric distinguishability as a quantum resource [21.071072991369824]
  We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources. We study the resource theory for two different classes of free operations: $(i)$ $rmCPTP_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doubly (CDS) maps acting on $XA$.
  arXiv  Detail & Related papers  (2021-02-24T19:05:02Z)
• Genuine Network Multipartite Entanglement [62.997667081978825]
  We argue that a source capable of distributing bipartite entanglement can, by itself, generate genuine $k$-partite entangled states for any $k$. We provide analytic and numerical witnesses of genuine network entanglement, and we reinterpret many past quantum experiments as demonstrations of this feature.
  arXiv  Detail & Related papers  (2020-02-07T13:26:00Z)

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.