Mean-State Entropy Hierarchies and Classical Communication through Quantum Convolutions

• URL: http://arxiv.org/abs/2607.16653v2
• Date: Tue, 21 Jul 2026 04:39:48 GMT
• Title: Mean-State Entropy Hierarchies and Classical Communication through Quantum Convolutions
• Abstract summary: Quantum convolution provides a discrete-variable analogue of classical convolution.<n>We establish a finite-step entropy hierarchy generated by compatible stabilizer dephasings.<n>For quantum convolutional channels, Weyl covariance reduces the one-shot classical communication problem to minimal output entropy.
• Score: 10.599996939957501
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum convolution provides a discrete-variable analogue of classical convolution, with the mean state capturing the stabilizer structure preserved under repeated convolution. We establish a finite-step entropy hierarchy generated by compatible stabilizer dephasings. Along every compatible isotropic flag, the entropy increases toward the mean-state entropy ceiling, while the relative-entropy distance to the mean state decomposes exactly into successive coherence losses and a terminal classical nonuniformity. Optimizing over compatible subspaces yields an intrinsic entropy profile of the state. For quantum convolutional channels, Weyl covariance reduces the one-shot classical communication problem to minimal output entropy. A spectral-transfer argument shows that suitable stabilizer inputs reproduce stabilizer-measurement distributions of the environment as channel-output spectra. This gives a computable Holevo lower bound over all complete stabilizer measurements; its compatible restriction is characterized by the entropy hierarchy and refines the previous mean-state bound of Bu, Gu, and Jaffe. The bound is exact for stabilizer-diagonal environments, for which the Holevo capacity is strongly additive, and yields a single-letter formula for a nonstabilizer qutrit family. The same family also exhibits a coexistence region with simultaneously positive classical and quantum communication rates

Related papers

• Floquet-Resolved Dissipation Selects Entanglement Beyond Population Spectroscopy [41.99844472131922]
  We show that two dissipative descriptions of the same parametrically coupled qubits can yield closely similar period-averaged populations.<n>Both retain the complete periodically driven Hamiltonian, the same microscopic bath couplings, and the same physical observables.
  arXiv  Detail & Related papers  (2026-08-12T15:33:26Z)
• A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Łojasiewicz condition [39.146761527401424]
  This work introduces a proximal subgradient method for minimizing the sum of an expected cost.<n>We use the Kurdyka-Lojasiewicz (KL) property to guarantee convergence of the whole trajectory to a single stationary point.
  arXiv  Detail & Related papers  (2026-08-05T23:07:27Z)
• Stochastic Counterdiabatic Driving via Biorthogonal Liouvillian Eigenmodes [42.668742604089324]
  Escorted free energy simulations address the non-adiabatic lag by engineering control fields $mathbfu$ that eliminate the lag.<n>We construct a complementary numerical framework based on gauge-type transforms instead of generalized coordinate transforms.<n>We show that the counterdiabatic condition is satisfied to machine precision, with the non-adiabatic lag suppressed by roughly twelve orders of magnitude.
  arXiv  Detail & Related papers  (2026-07-27T13:08:14Z)
• Universal Crossovers of Stabilizer Entropy Beyond Criticality [0.0]
  We show that stabilizer entropy contains universal critical data and boundary-sensitive terms.<n>We derive exact finite-size formulas for both full periodic chains and finite intervals of the infinite chain.<n>Our results provide an exact lattice benchmark for the emerging QFT description of stabilizer entropy beyond isolated conformal points.
  arXiv  Detail & Related papers  (2026-06-11T18:27:11Z)
• Anomalous Mixed-State Floquet Topology in One-Dimensional Open Quantum Systems [41.99844472131922]
  We investigate the non-equilibrium topology of a periodically driven, dissipative Su-Schrieffer-Heeger chain.<n>We show that the steady state can be characterised by a Hermitian purity spectrum.<n>We identify a pair of topological invariants $(0_mathrmEGP, _mathrmEGP)$, revealing a structure consistent with a $mathbbZtimesmathbbZ$ classification known from isolated Floquet SSH systems.
  arXiv  Detail & Related papers  (2026-04-28T05:54:40Z)
• A Periodic Orbit Trace Formula for Quantum Scrambling: The Role of the Normally Hyperbolic Invariant Manifold [0.0]
  We derive a leading-order semiclassical expansion for the local microcanonical OTOC in systems with an index-1 saddle point.<n>We extend periodic-orbit trace methods to scrambling observables, yielding a local instability exponent (J) governing the leading semiclassical growth window.
  arXiv  Detail & Related papers  (2026-04-14T06:58:23Z)
• Stabilizer-Shannon Renyi Equivalence: Exact Results for Quantum Critical Chains [0.0]
  Shannon-Renyi and stabilizer entropies are key diagnostics of structure, non-stabilizerness, phase transitions, and in quantum many-body states.<n>Specializing to the transverse-field Ising (TFI) chain, the TFI ground state stabilizer entropies maps to the Shannon-Renyi entropies of the XX-chain ground state of length $2L$.<n>Building on this correspondence, together with other exact identities we prove, closed expressions for the stabilizer entropy at indices $alpha=frac12,2,4$ for a broad class of critical
  arXiv  Detail & Related papers  (2025-09-12T21:32:10Z)
• Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavity [4.604003661048267]
  This is the first work addressing this second-order quantitative stability estimate in general unbounded settings.<n>We deduce exponential convergence rates for gradient and Hessian of Sinkhorns along Sinkhorn's algorithm.
  arXiv  Detail & Related papers  (2025-04-15T12:34:09Z)
• 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)
• Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
  Signatures of localization have been observed in condensed matter and cold atomic systems. We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths. We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
  arXiv  Detail & Related papers  (2023-03-13T12:45:25Z)
• Spectral stabilizability [0.0]
  We develop conditions for stabilizability based on the target state's eigendecomposition. We use the spectral approach to derive upper bounds on stabilizability for a number of exemplary open system scenarios.
  arXiv  Detail & Related papers  (2022-12-23T10:38:31Z)

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.