Lipschitz continuity of quantum-classical conditional entropies with respect to angular distance and related properties

• URL: http://arxiv.org/abs/2210.04874v2
• Date: Wed, 22 Mar 2023 23:12:25 GMT
• Title: Lipschitz continuity of quantum-classical conditional entropies with respect to angular distance and related properties
• Abstract summary: Lipschitz continuity bound for quantum-classical conditional entropies with respect to angular distance. We study the characterization of states which saturate the Fuchs--van de Graaf inequality and thus have angular distance approximately equal to trace distance. For the noninvertible case, we show that the situation appears to be significantly more elaborate, and seems to be strongly connected to the question of characterizing the set of fidelity-preserving measurements.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive a Lipschitz continuity bound for quantum-classical conditional entropies with respect to angular distance, with a Lipschitz constant that is independent of the dimension of the conditioning system. This bound is sharper in some situations than previous continuity bounds, which were either based on trace distance (where Lipschitz continuity is not possible), or based on angular distance but did not include a conditioning system. However, we find that the bound does not directly generalize to fully quantum conditional entropies. To investigate possible counterexamples in that setting, we study the characterization of states which saturate the Fuchs--van de Graaf inequality and thus have angular distance approximately equal to trace distance. We give an exact characterization of such states in the invertible case. For the noninvertible case, we show that the situation appears to be significantly more elaborate, and seems to be strongly connected to the question of characterizing the set of fidelity-preserving measurements.

Related papers

• Ghost Degrees of Freedom Without Quantum Runaway: Exact Moment Bounds from an Operator Conservation Law [0.0]
  We prove a rigorous, state-independent upper bound on the mean squared phase-space radius for all time and every quantum state with initial second moments.<n>The interaction is bounded and vanishes at large separations, the generic situation in effective field theory.<n>The absence of confining potential means the proof is silent on spectral discreteness and the existence of a finite ground state.
  arXiv  Detail & Related papers  (2026-04-23T07:06:58Z)
• Tight any-shot quantum decoupling [23.729027844524893]
  We prove a novel one-shot decoupling theorem formulated in terms of quantum entropy relative distance.<n>We show that this bound is ensemble-tight in quantum relative entropy distance.
  arXiv  Detail & Related papers  (2026-02-19T15:01:26Z)
• Stability of Maximum-Entropy Inference in Finite Dimensions [0.0]
  We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints.<n>We prove that convergence of moments and entropy implies convergence of states in trace norm.
  arXiv  Detail & Related papers  (2025-10-24T02:13:48Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Powering a quantum clock with a non-equilibrium steady state [50.24983453990065]
  We propose powering a quantum clock with the non-thermal resources offered by the stationary state of an integrable quantum spin chain. Using experimentally relevant examples of quantum spin chains, we suggest crossing a phase transition point is crucial for optimal performance.
  arXiv  Detail & Related papers  (2024-12-17T17:25:11Z)
• Continuity of entropies via integral representations [16.044444452278064]
  We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. We obtain a number of results: (1) a tight continuity relation for the conditional entropy in the case where the two states have equal marginals on the conditioning system, resolving a conjecture by Wilde in this special case; (2) a stronger version of the Fannes-Audenaert inequality on quantum entropy; and (3) better estimates on the quantum capacity of approximately degradable channels.
  arXiv  Detail & Related papers  (2024-08-27T17:44:52Z)
• Proposal of an optical Bell's experiment to test the boundary between determinism and indeterminism in Quantum Mechanics [41.94295877935867]
  It was recently noted the existence of an apparently discontinuous boundary between determinism and indeterminism in Quantum Mechanics. We propose to explore this boundary by recording the distribution of outcomes of a given parity interrupted by outcomes of the other parity. The features of these distributions for small rotations of the angle settings near critical points may indicate whether the underlying process is in-deterministic or not.
  arXiv  Detail & Related papers  (2024-08-20T14:48:08Z)
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution [18.47824812164327]
  We introduce the concept of imaginary-time Lindbladian evolution as an alternative framework. This new approach defines gapped quantum phases in open systems through the spectrum properties of the imaginary-Liouville superoperator.
  arXiv  Detail & Related papers  (2024-08-06T14:53:40Z)
• Tightening continuity bounds on entropies and bounds on quantum capacities [15.2292571922932]
  We prove a tight uniform continuity bound for the Shannon entropy in terms of both the local- and total variation distances. We also obtain a uniform continuity bound for the von Neumann entropy in terms of both the operator norm- and trace distances.
  arXiv  Detail & Related papers  (2023-10-26T11:50:01Z)
• Continuity bounds on observational entropy and measured relative entropies [0.0]
  We derive a measurement-independent continuity bound on the observational entropy for general POVM measurements. The same insight is used to obtain continuity bounds for other entropic quantities, including the measured relative entropy distance to a convex a set of states under a general set of measurements.
  arXiv  Detail & Related papers  (2023-02-01T12:25:53Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware [62.997667081978825]
  We observe partial and infinite-temperature thermalization on a quantum superconducting processor. We show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis.
  arXiv  Detail & Related papers  (2022-11-14T15:18:11Z)
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme [8.37609145576126]
  The relative entropy of entanglement $E_Rite is defined as the distance of a multi-part quantum entanglement from the set of separable states as measured by the quantum relative entropy. We show that this state is always achieved, i.e. any state admits a closest separable state, even in dimensions; also, $E_Rite is everywhere lower semi-negative $lambda_$quasi-probability distribution.
  arXiv  Detail & Related papers  (2021-05-17T18:03:02Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)

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.