On the Clustering of Conditional Mutual Information via Dissipative Dynamics

• URL: http://arxiv.org/abs/2504.02235v1
• Date: Thu, 03 Apr 2025 03:06:55 GMT
• Title: On the Clustering of Conditional Mutual Information via Dissipative Dynamics
• Abstract summary: Conditional mutual information (CMI) has attracted significant attention as a key quantity for characterizing quantum correlations in many-body systems.<n>It is conjectured that CMI decays rapidly in finite-temperature Gibbs states.<n>Previous work addressed this problem in the high-temperature regime using cluster expansion techniques.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conditional mutual information (CMI) has recently attracted significant attention as a key quantity for characterizing quantum correlations in many-body systems. While it is conjectured that CMI decays rapidly in finite-temperature Gibbs states, a complete and general proof remains elusive. Previous work addressed this problem in the high-temperature regime using cluster expansion techniques [T. Kuwahara, K. Kato, F.G.S.L. Brand\~ao, Phys. Rev. Lett. 124, 220601 (2020)]; however, flaws in the proof have been pointed out, and the method does not provide a uniformly convergent expansion at arbitrarily high temperatures. In this work, we demonstrate that the cluster expansion approach indeed fails to converge absolutely, even at any high-temperatures. To overcome this limitation, we propose a new approach to proving the spatial decay of CMI. Our method leverages the connection between CMI and quantum recovery maps, specifically utilizing the Fawzi-Renner theorem. We show that such recovery maps can be realized through dissipative dynamics, and by analyzing the locality properties of these dynamics, we establish the exponential decay of CMI in high-temperature regimes. As a technical contribution, we also present a new result on the perturbative stability of quasi-local Liouvillian dynamics. Our results indicate that, contrary to common intuition, high-temperature Gibbs states can exhibit nontrivial mathematical structure, particularly when multipartite correlations such as CMI are considered.

Related papers

• A rigorous quasipolynomial-time classical algorithm for SYK thermal expectations [51.660331450043806]
  Estimating local observables in Gibbs states is a central problem in quantum simulation.<n>We give a proof of a quasipolynomial-time classical algorithm that estimates SYK local thermal expectations at sufficiently high constant temperature.<n>Our result introduces a new Wick-pair expansion that we expect to be broadly useful for quantum many-body systems.
  arXiv  Detail & Related papers  (2026-04-22T21:14:04Z)
• Belief Propagation and Tensor Network Expansions for Many-Body Quantum Systems: Rigorous Results and Fundamental Limits [0.005389965299678531]
  Belief propagation (BP) provides a scalable for contracting tensor networks on loopy graphs.<n>We rigorously study the applicability of BP to many-body quantum systems.<n>We show that loop-decay" emphnecessarily implies exponential decay of connected correlations.
  arXiv  Detail & Related papers  (2026-04-03T17:59:09Z)
• Grand Canonical-like Thermalization of Quantum Many-body Scars [2.4244302965852387]
  Quantum many-body scar (QMBS) in kinetically constrained quantum systems challenges the conventional eigenstate thermalization hypothesis (ETH)<n>We develop an open-system description for constrained dynamics and introduce the definition of quasiparticle number in the system.<n>Our framework shows that the anomalous fluctuations and quasi-periodic dynamics of scar states arise naturally from low-DOS regions.
  arXiv  Detail & Related papers  (2026-03-06T09:26:51Z)
• Clustering of quantum correlations at low temperature [0.0]
  Identifying conditions for clustering of correlations in thermal states is a central problem in quantum many-body physics.<n>We present a direct proof that the thermal state satisfies exponential decay of correlations at low temperature, with a correlation length that stays uniformly bounded as $Tto0$.
  arXiv  Detail & Related papers  (2025-08-21T18:10:13Z)
• Thermal state preparation by repeated interactions at and beyond the Lindblad limit [41.94295877935867]
  We study the nature of thermalization dynamics and the associated preparation (simulation) time under the repeated interaction protocol.<n>We observe a Mpemba-like effect: Starting from a maximally mixed state, thermalization to an intermediate-temperature state takes longer than to a lower-temperature one.
  arXiv  Detail & Related papers  (2025-06-13T18:34:49Z)
• Quantum Gibbs states are locally Markovian [1.9643748953805944]
  We show that for any Hamiltonian with a bounded interaction degree, the quantum Gibbs state is locally Markov at arbitrary temperature. We introduce a regularization scheme for imaginary-time-evolved operators at arbitrarily low temperatures.
  arXiv  Detail & Related papers  (2025-04-03T01:54:42Z)
• Conditional Mutual Information and Information-Theoretic Phases of Decohered Gibbs States [5.062448779099901]
  Adding local dissipation to a Markov network turns it into a emphhidden Markov network.<n>We show that low-temperature hidden Markov networks can sustain long-range CMI.
  arXiv  Detail & Related papers  (2025-02-18T19:00:02Z)
• Crosscap Quenches and Entanglement Evolution [0.0]
  We propose a novel quench protocol, termed the "crosscap quench"<n>We analyze conformal field theories (CFTs) and derive universal features in the time evolution of the entanglement entropy.<n>We validate these findings through numerical simulations in both nonintegrable and integrable quantum spin systems.
  arXiv  Detail & Related papers  (2024-12-24T18:59:58Z)
• Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics [1.5999407512883517]
  We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension.<n>We prove that any such Gibbs state which satisfies a clustering condition that we coin decay of matrix-valued quantum conditional mutual information can be quasi-optimally prepared on a quantum computer.
  arXiv  Detail & Related papers  (2024-12-02T17:25:24Z)
• Gapless Floquet topology [40.2428948628001]
  We study the existence of topological edge zero- and pi-modes despite the lack of bulk gaps in the quasienergy spectrum. We numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's Golden Rule.
  arXiv  Detail & Related papers  (2024-11-04T19:05:28Z)
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures [0.0]
  Recent investigations have unveiled exotic quantum phases that elude characterization by simple bipartite correlation functions. In these phases, long-range entanglement arising from tripartite correlations plays a central role. Our findings unveil that, even at low temperatures, a broad class of tripartite entanglement cannot manifest in the long-range regime.
  arXiv  Detail & Related papers  (2024-07-08T11:30:12Z)
• Many-Body Localization in the Age of Classical Computing [0.0]
  This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase.<n>The drifts are related to tendencies towards thermalization and non-vanishing transport observed in the dynamics of many-body systems.<n>Questions about thermalization and its failure in disordered many-body systems remain captivating area open for further explorations.
  arXiv  Detail & Related papers  (2024-03-11T19:00:06Z)
• Neural-network quantum states for ultra-cold Fermi gases [49.725105678823915]
  This work introduces a novel Pfaffian-Jastrow neural-network quantum state that includes backflow transformation based on message-passing architecture. We observe the emergence of strong pairing correlations through the opposite-spin pair distribution functions. Our findings suggest that neural-network quantum states provide a promising strategy for studying ultra-cold Fermi gases.
  arXiv  Detail & Related papers  (2023-05-15T17:46:09Z)
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition [62.997667081978825]
  We analyze the role of boundary conditions in the statistics of topological defects. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
  arXiv  Detail & Related papers  (2022-07-08T09:55:05Z)
• Genuine Multipartite Correlations in a Boundary Time Crystal [56.967919268256786]
  We study genuine multipartite correlations (GMC's) in a boundary time crystal (BTC) We analyze both (i) the structure (orders) of GMC's among the subsystems, as well as (ii) their build-up dynamics for an initially uncorrelated state.
  arXiv  Detail & Related papers  (2021-12-21T20:25:02Z)
• Fast Thermalization from the Eigenstate Thermalization Hypothesis [69.68937033275746]
  Eigenstate Thermalization Hypothesis (ETH) has played a major role in understanding thermodynamic phenomena in closed quantum systems. This paper establishes a rigorous link between ETH and fast thermalization to the global Gibbs state. Our results explain finite-time thermalization in chaotic open quantum systems.
  arXiv  Detail & Related papers  (2021-12-14T18:48:31Z)
• Out-of-time-order correlations and the fine structure of eigenstate thermalisation [58.720142291102135]
  Out-of-time-orderors (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalisation. We show explicitly that the OTOC is indeed a precise tool to explore the fine details of the Eigenstate Thermalisation Hypothesis (ETH) We provide an estimation of the finite-size scaling of $omega_textrmGOE$ for the general class of observables composed of sums of local operators in the infinite-temperature regime.
  arXiv  Detail & Related papers  (2021-03-01T17:51:46Z)
• Exact many-body scars and their stability in constrained quantum chains [55.41644538483948]
  Quantum scars are non-thermal eigenstates characterized by low entanglement entropy. We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size.
  arXiv  Detail & Related papers  (2020-11-16T19:05:50Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)

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.