Entangled inputs cannot make imperfect quantum channels perfect

TL;DR

This paper proves that entangled inputs cannot transform imperfect quantum channels into perfect ones, establishing fundamental limits on quantum channel capacities and providing practical bounds related to entanglement measures.

Contribution

It demonstrates that entangled inputs cannot maximize quantum channel capacity, offering simple computable bounds and applying these results to specific channels like the qubit amplitude damping.

Findings

Entangled inputs cannot make noisy channels perfect.

Provides practical bounds for quantum channel capacities.

First meaningful bound for the classical capacity of amplitude damping channels.

Abstract

Entangled inputs can enhance the capacity of quantum channels, this being one of the consequences of the celebrated result showing the non-additivity of several quantities relevant for quantum information science. In this work, we answer the converse question (whether entangled inputs can ever render noisy quantum channels have maximum capacity) to the negative: No sophisticated entangled input of any quantum channel can ever enhance the capacity to the maximum possible value; a result that holds true for all channels both for the classical as well as the quantum capacity. This result can hence be seen as a bound as to how "non-additive quantum information can be". As a main result, we find first practical and remarkably simple computable single-shot bounds to capacities, related to entanglement measures. As examples, we discuss the qubit amplitude damping and identify the first meaningful bound for its classical capacity.