Entanglement-assisted zero-error capacity is upper bounded by the Lovasz theta function

TL;DR

This paper proves that the Lovasz theta function remains an upper bound on the zero-error capacity of classical channels even when the sender and receiver share entanglement, extending classical bounds to quantum-assisted scenarios.

Contribution

It demonstrates that entanglement does not increase the zero-error capacity beyond the Lovasz theta function, providing a key theoretical limit in quantum information theory.

Findings

Lovasz theta function bounds entanglement-assisted zero-error capacity

Entanglement does not improve zero-error capacity beyond classical bounds

Extends classical graph theory bounds to quantum-assisted communication

Abstract

The zero-error capacity of a classical channel is expressed in terms of the independence number of some graph and its tensor powers. This quantity is hard to compute even for small graphs such as the cycle of length seven, so upper bounds such as the Lovasz theta function play an important role in zero-error communication. In this paper, we show that the Lovasz theta function is an upper bound on the zero-error capacity even in the presence of entanglement between the sender and receiver.