Bounds on Quantum Information Storage and Retrieval

TL;DR

This paper establishes universal bounds on quantum information storage capacity and retrieval time in various systems, linking them to symmetry breaking and Goldstone modes, with implications for black holes and gauge theories.

Contribution

It introduces bounds on quantum information capacity and retrieval times based on symmetry breaking and Goldstone bosons, extending beyond gravity to gauge theories and many-body systems.

Findings

Capacity bounded by surface area in Goldstone units.

Retrieval time proportional to system volume in Goldstone units.

Universal signatures like ultra-soft radiation emission.

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.