On the strong converses for the quantum channel capacity theorems

TL;DR

This paper develops a unified framework to establish strong converse theorems for quantum channel capacities, providing explicit bounds and error exponents, and confirming the strong converse for quantum information transfer in specific channels.

Contribution

It introduces a unified approach to prove strong converses for quantum channel capacities, including explicit bounds and error exponents, addressing longstanding open problems.

Findings

Established strong converse theorems for quantum channel capacities.

Derived explicit upper bounds on fidelity measures.

Proved the strong converse for quantum information transfer over erasure channels.

Abstract

A unified approach to prove the converses for the quantum channel capacity theorems is presented. These converses include the strong converse theorems for classical or quantum information transfer with error exponents and novel explicit upper bounds on the fidelity measures reminiscent of the Wolfowitz strong converse for the classical channel capacity theorems. We provide a new proof for the error exponents for the classical information transfer. A long standing problem in quantum information theory has been to find out the strong converse for the channel capacity theorem when quantum information is sent across the channel. We give the quantum error exponent thereby giving a one-shot exponential upper bound on the fidelity. We then apply our results to show that the strong converse holds for the quantum information transfer across an erasure channel for maximally entangled channel inputs.