A Quantum EL Theorem

TL;DR

This paper proves a quantum version of the EL Theorem, showing that large-rank non-exotic projections lead to simple quantum states, impacting quantum communication by limiting the complexity of states used for sources with high von Neumann entropy.

Contribution

It introduces a quantum EL Theorem, extending classical results to quantum projections and their implications for quantum state complexity and communication.

Findings

Large-rank non-exotic projections have simple quantum states in their images

Quantum sources with high von Neumann entropy cannot be communicated without simple states

The theorem constrains the complexity of quantum states used in high-entropy sources

Abstract

In this paper, we prove a quantum version of the EL Theorem. It states that non-exotic projections of large rank must have simple quantum states in their images. A consequence to this is there is no way to communicate a quantum source with corresponding large enough von Neumann entropy without using simple quantum states.