Quantum Memory from Rare Thermal Boundaries

Thermal equilibrium can suppress the configurations through which stored quantum information changes. The challenge is to turn that equilibrium statement into protection of an unknown input after it has been written into a memory. This paper proves two storage criteria under the exact joint system–bath Hamiltonian dynamics. When all three logical Pauli commutators are supported on a common projection of Gibbs probability p, ideal logical subsystem replacement gives a deterministic channel-error bound proportional to p times the holding time. A protocol using a classical Pauli frame gives a sharper thermal correlation bound. Both estimates preserve arbitrary entanglement with an external reference and retain the full exponential coefficient of any separately established rare-boundary estimate. The argument separates a relative-entropy control of rare events from a general Bell–Weyl correlation-to-channel theorem. The latter applies to arbitrary fixed correlated resources and joint quantum channels, with an algebraic extension for infinite baths. Further results give sufficient conditions for imperfect writing, a normalized-sector formulation, and explicit obstructions showing why initial logical accuracy or domination by one thermal resource need not characterize a useful memory. The results are abstract storage criteria. They assume an accessible exact logical algebra and a specified joint resource; they do not supply a new three-dimensional code, efficient Gibbs-state preparation, or a generic noisy-writing threshold. A separate collective-symmetry application retains its exact coupling and energy-scale assumptions. Established correlation, entropy, channel-randomization and noiseless-subsystem machinery is credited throughout.