The quantum non-Markovianity for a special class of generalized Weyl channel

• URL: http://arxiv.org/abs/2503.10338v1
• Date: Thu, 13 Mar 2025 13:16:32 GMT
• Title: The quantum non-Markovianity for a special class of generalized Weyl channel
• Authors: Wen Xu, Mao-Sheng Li, Bo Li, Gui-Mei Jiao, Zhu-Jun Zheng,
• Abstract summary: We study a special class of generalized Weyl channel where the Kraus operators are proportional to the Weyl diagonal and the rest are vanishing.<n>We identify the non-Markovianity based on the methods of CP divisibility and distinguishability.
• Score: 5.728415959563255
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A quantum channel is usually represented as a sum of Kraus operators. The recent study [Phys. Rev. A 98, 032328 (2018)] has shown that applying a perturbation to the Kraus operators in qubit Pauli channels, the dynamical maps exhibit interesting properties, such as non-Markovianity, singularity. This has sparked our interest in studying the properties of other quantum channels. In this work, we study a special class of generalized Weyl channel where the Kraus operators are proportional to the Weyl diagonal matrices and the rest are vanishing. We use the Choi matrix of intermediate map to study quantum non-Markovianity. The crossover point of the eigenvalues of Choi matrix is a singularity of the decoherence rates in the canonical form of the master equation. Moreover, we identify the non-Markovianity based on the methods of CP divisibility and distinguishability. We also quantify the non-Markovianity in terms of the Hall-Cresser-Li-Andersson (HCLA) measure and the Breuer-Laine-Piilo (BLP) measure, respectively. In particular, we choose mutually unbiased bases as a pair of orthogonal initial states to quantify the non-Markovianity based on the BLP measure.

Related papers

• An unbiased measure over the matrix product state manifold [0.05524804393257919]
  We show that the usual ensemble of sequentially generated random matrix product states (RMPS) using local Haar random unitaries is not uniform when viewed as a restriction of the full Hilbert space. As a result, the entanglement across the chain exhibits an anomalous asymmetry under spatial asymmetry. Some properties of this new ensemble are investigated both analytically and numerically.
  arXiv  Detail & Related papers  (2025-04-30T18:00:02Z)
• Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition [49.1574468325115]
  "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems. We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors. We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
  arXiv  Detail & Related papers  (2025-04-29T13:14:15Z)
• Non-Markovian Ensemble Propagation [41.94295877935867]
  We introduce the Non-Markovian Ensemble Propagation (NMEP) method, which extends the Monte Carlo Wave-Function (MCWF) method to the non-Markovian case.<n>We demonstrate its accuracy and effectiveness in a selection of examples, and compare the results with either analytic expressions or direct numerical integration of the master equation.
  arXiv  Detail & Related papers  (2024-10-16T06:59:44Z)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Non-Markovian quantum dynamics from symmetric measurements [0.0]
  We use symmetric measurement operators to construct quantum channels that provide a further generalization of generalized Pauli channels. We analyze their important properties, such as complete positivity and the ability to break quantum entanglement.
  arXiv  Detail & Related papers  (2024-02-06T21:26:22Z)
• Bootstrapping entanglement in quantum spin systems [0.06554326244334867]
  We employ the bootstrap method to determine the expectation values in quantum many-body systems. We then use these values to assess the entanglement content of the system. We show that this approach offers not only a new computational methodology but also a comprehensive view of both bipartite and multipartite entanglement properties.
  arXiv  Detail & Related papers  (2023-10-25T09:45:17Z)
• Learning the eigenstructure of quantum dynamics using classical shadows [6.12834448484556]
  We show that for moderate size Hilbert spaces, low Kraus rank of the channel, and short time steps, the eigenvalues of the Choi matrix corresponding to the channel have a special structure. We use tools from random matrix theory to understand the effect of estimation noise in the eigenspectrum of the estimated Choi matrix.
  arXiv  Detail & Related papers  (2023-09-22T05:56:58Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Three-fold way of entanglement dynamics in monitored quantum circuits [68.8204255655161]
  We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles. We obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements.
  arXiv  Detail & Related papers  (2022-01-28T17:21:15Z)
• Preserving quantum correlations and coherence with non-Markovianity [50.591267188664666]
  We demonstrate the usefulness of non-Markovianity for preserving correlations and coherence in quantum systems. For covariant qubit evolutions, we show that non-Markovianity can be used to preserve quantum coherence at all times.
  arXiv  Detail & Related papers  (2021-06-25T11:52:51Z)
• Isospectral twirling and quantum chaos [0.0]
  We show that the most important measures of quantum chaos like frame potentials, scrambling, Loschmidt echo, and out-of-time correlators (OTOCs) can be described by the unified framework of the isospectral twirling. We show that, by exploiting random matrix theory, these measures of quantum chaos clearly distinguish the finite time profiles of probes to quantum chaos.
  arXiv  Detail & Related papers  (2020-11-11T19:01:08Z)
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain [21.24186888129542]
  We study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves.
  arXiv  Detail & Related papers  (2020-10-14T16:46:11Z)
• Generalization of Pauli channels through mutually unbiased measurements [0.0]
  We introduce a new generalization of the Pauli channels using the mutually unbiased measurement operators. We analyze the channel properties, such as complete positivity, entanglement breaking, and multiplicativity of maximal output purity.
  arXiv  Detail & Related papers  (2020-03-26T22:27:56Z)

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.