Minimum Energy-Surface Required by Quantum Memory Devices

TL;DR

This paper establishes a fundamental lower bound on the combined energy and spatial resources needed for quantum memory devices to store classical information, independent of thermodynamic bounds.

Contribution

It derives a nonzero lower bound on the product of energy and spatial extent for quantum memory systems based on mass, degrees of freedom, and information content.

Findings

Lower bound on P proportional to d^2/m (exp(S/d)-1)^2

Bound applies to non-relativistic quantum systems storing classical info

Result is independent of thermodynamic entropy bounds

Abstract

We address the question what physical resources are required and sufficient to store classical information. While there is no lower bound on the required energy or space to store information, we find that there is a nonzero lower bound for the product (P = <E> <r^2>) of these two resources. Specifically, we prove that any physical system of mass m and d degrees of freedom that stores S bits of information will have lower bound on the product P that is proportional to d^2/m (exp(S/d)-1)^2. This result is obtained in a non-relativistic, quantum mechanical setting and it is independent from earlier thermodynamical results such as the Bekenstein bound on the entropy of black holes.