Time-inhomogeneous Quantum Markov Chains with Decoherence on Finite State Spaces

• URL: http://arxiv.org/abs/2012.05449v1
• Date: Thu, 10 Dec 2020 04:23:18 GMT
• Title: Time-inhomogeneous Quantum Markov Chains with Decoherence on Finite State Spaces
• Authors: Chia-Han Chou and Wei-Shih Yang
• Abstract summary: We study time-inhomogeneous quantum Markov chains with parameter $zeta ge 0$ and decoherence parameter $0 leq p leq 1$ on finite spaces.
• Score: 0.2538209532048866
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce and study time-inhomogeneous quantum Markov chains with parameter $\zeta \ge 0$ and decoherence parameter $0 \leq p \leq 1$ on finite spaces and their large scale equilibrium properties. Here $\zeta$ resembles the inverse temperature in the annealing random process and $p$ is the decoherence strength of the quantum system. Numerical evaluations show that if $ \zeta$ is small, then quantum Markov chain is ergodic for all $0 < p \le 1$ and if $ \zeta $ is large, then it has multiple limiting distributions for all $0 < p \le 1$. In this paper, we prove the ergodic property in the high temperature region $0 \le \zeta \le 1$. We expect that the phase transition occurs at the critical point $\zeta_c=1$. For coherence case $p=0$, a critical behavior of periodicity also appears at critical point $\zeta_o=2$.

Related papers

• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. Even with sublinear barriers, we use Feynman-Kac techniques to lift classical to quantum ones establishing tight lower bound $T_mathrmmix = 2Omega(nalpha)$.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• High-Temperature Gibbs States are Unentangled and Efficiently Preparable [22.397920564324973]
  We show that thermal states of local Hamiltonians are separable above a constant temperature. This sudden death of thermal entanglement upends conventional wisdom about the presence of short-range quantum correlations in Gibbs states.
  arXiv  Detail & Related papers  (2024-03-25T15:11:26Z)
• Dimension Independent Disentanglers from Unentanglement and Applications [55.86191108738564]
  We construct a dimension-independent k-partite disentangler (like) channel from bipartite unentangled input. We show that to capture NEXP, it suffices to have unentangled proofs of the form $| psi rangle = sqrta | sqrt1-a | psi_+ rangle where $| psi_+ rangle has non-negative amplitudes.
  arXiv  Detail & Related papers  (2024-02-23T12:22:03Z)
• Universal contributions to charge fluctuations in spin chains at finite temperature [5.174839433707792]
  We show that $gamma(theta)$ only takes non-zero values at isolated points of $theta$, which is $theta=pi$ for all our examples. In two exemplary lattice systems we show that $gamma(pi)$ takes quantized values when the U(1) symmetry exhibits a specific type of 't Hooft anomaly with other symmetries.
  arXiv  Detail & Related papers  (2024-01-17T19:05:07Z)
• Quantum connection, charges and virtual particles [65.268245109828]
  A quantum bundle $L_hbar$ is endowed with a connection $A_hbar$ and its sections are standard wave functions $psi$ obeying the Schr"odinger equation. We will lift the bundles $L_Cpm$ and connection $A_hbar$ on them to the relativistic phase space $T*R3,1$ and couple them to the Dirac spinor bundle describing both particles and antiparticles.
  arXiv  Detail & Related papers  (2023-10-10T10:27:09Z)
• Measurement-induced phase transition for free fermions above one dimension [46.176861415532095]
  Theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. Critical point separates a gapless phase with $elld-1 ln ell$ scaling of the second cumulant of the particle number and of the entanglement entropy.
  arXiv  Detail & Related papers  (2023-09-21T18:11:04Z)
• Beyond the Berry Phase: Extrinsic Geometry of Quantum States [77.34726150561087]
  We show how all properties of a quantum manifold of states are fully described by a gauge-invariant Bargmann. We show how our results have immediate applications to the modern theory of polarization.
  arXiv  Detail & Related papers  (2022-05-30T18:01:34Z)
• Fidelity and entanglement entropy for infinite-order phase transitions [4.453923176362749]
  We study the fidelity and the entanglement entropy for the ground states of quantum systems that have infinite-order quantum phase transitions. In particular, we consider the quantum O(2) model with a spin-$S$ truncation, where there is an infinite-order Gaussian (IOG) transition for $S = 1$. We show that the height of the peak in the fidelity susceptibility ($chi_F$) converges to a finite thermodynamic value as a power law of $1/L$ for the IOG transition and as $1/ln(L)$ for BKT transitions.
  arXiv  Detail & Related papers  (2021-08-23T06:28:50Z)
• Stochastic behavior of outcome of Schur-Weyl duality measurement [45.41082277680607]
  We focus on the measurement defined by the decomposition based on Schur-Weyl duality on $n$ qubits. We derive various types of distribution including a kind of central limit when $n$ goes to infinity.
  arXiv  Detail & Related papers  (2021-04-26T15:03:08Z)
• Statistical properties of the localization measure of chaotic eigenstates and the spectral statistics in a mixed-type billiard [0.0]
  We study the quantum localization in the chaotic eigenstates of a billiard with mixed-type phase space. We show that the level repulsion exponent $beta$ is empirically a rational function of $alpha$, and the mean $langle A rangle$ as a function of $alpha$ is also well approximated by a rational function.
  arXiv  Detail & Related papers  (2021-04-23T15:33:26Z)
• Truncation effects in the charge representation of the O(2) model [3.770141864638074]
  We study the quantum phase transition in the charge representation with a truncation to spin $S$. The exponential convergence of the phase-transition point is studied in both Lagrangian and Hamiltonian formulations.
  arXiv  Detail & Related papers  (2021-04-13T16:37:21Z)

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.