What exactly does Bekenstein bound?

TL;DR

This paper investigates the Bekenstein bound's implications for quantum and classical communication capacities, demonstrating that while some capacities are constrained, others like zero-bits can exceed these limits under certain conditions.

Contribution

The study provides a rigorous analysis of the Bekenstein bound in the context of quantum channels, revealing conditions under which it constrains or does not constrain information transmission.

Findings

Classical and quantum capacities obey the Bekenstein bound.

Zero-bits can be transmitted beyond the Bekenstein bound.

Channel capacity constraints depend on encoder and decoder restrictions.

Abstract

The Bekenstein bound posits a maximum entropy for matter with finite energy confined to a spatial region. It is often interpreted as a fundamental limit on the information that can be stored by physical objects. In this work, we test this interpretation by asking whether the Bekenstein bound imposes constraints on a channel's communication capacity, a context in which information can be given a mathematically rigorous and operationally meaningful definition. We study specifically the \emph{Unruh channel} that describes a stationary Alice exciting different species of free scalar fields to send information to an accelerating Bob, who is confined to a Rindler wedge and exposed to the noise of Unruh radiation. We show that the classical and quantum capacities of the Unruh channel obey the Bekenstein bound that pertains to the decoder Bob. In contrast, even at high temperatures, the Unruh channel can transmit a significant number of \emph{zero-bits}, which are quantum communication resources that can be used for quantum identification and many other primitive protocols. Therefore, unlike classical bits and qubits, zero-bits and their associated information processing capability are generally not constrained by the Bekenstein bound. However, we further show that when both the encoder and the decoder are restricted, the Bekenstein bound does constrain the channel capacities, including the zero-bit capacity.