Bounds on Quantum Information Storage and Retrieval

Abstract

We present certain universal bounds on the capacity of quantum information storage and on the time scale of its retrieval for a generic quantum field theoretic system. The capacity, quantified by the microstate entropy, is bounded from above by the surface area of the object measured in units of a Goldstone decay constant. The Goldstone bosons are universally present due to the spontaneous breaking of Poincare and internal symmetries by the information-storing object. Applied to a black hole, the bound reproduces the Bekenstein-Hawking entropy. However, the relation goes beyond gravity. The minimal time-scale required for retrieving the quantum information from a system is equal to its volume measured in units of the same Goldstone scale. For a black hole this reproduces the Page time as well as the quantum break-time. The same expression for the information retrieval time is shared by non-gravitational saturated states in gauge theories, including QCD. The saturated objects exhibit some universal signatures such as the emission of ultra-soft radiation. Similar bounds apply to non-relativistic many-body systems.