Fundamental limitations on distillation of quantum channel resources

TL;DR

This paper establishes fundamental no-go theorems and bounds on the processing and distillation of quantum channels, impacting quantum computation and communication by defining limits on resource manipulation.

Contribution

It introduces universal limitations and quantitative bounds for quantum channel distillation, including error restrictions and overhead lower bounds, applicable to various quantum information tasks.

Findings

Derived lower bounds for magic state distillation overhead

Established no-go theorems for quantum channel processing

Provided bounds for quantum channel capacity in communication

Abstract

Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Focusing on the class of distillation tasks -- which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels -- we develop fundamental restrictions on the error incurred in such transformations and comprehensive lower bounds for the overhead of any distillation protocol. In the asymptotic setting, our results yield broadly applicable bounds for rates of distillation. We demonstrate our results through applications to fault-tolerant quantum computation, where we obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication, where we recover a number of strong converse bounds for quantum channel capacity.