DeepAI AI Chat
Log In Sign Up

Resource theory of asymmetric distinguishability for quantum channels

by   Xin Wang, et al.

This paper develops the resource theory of asymmetric distinguishability for quantum channels, generalizing the related resource theory for states [arXiv:1006.0302, arXiv:1905.11629]. The key constituents of the channel resource theory are quantum channel boxes, consisting of a pair of quantum channels, which can be manipulated for free by means of an arbitrary quantum superchannel (the most general physical transformation of a quantum channel). One main question of the resource theory is the approximate channel box transformation problem, in which the goal is to transform an initial channel box (or boxes) to a final channel box (or boxes), while allowing for an asymmetric error in the transformation. The channel resource theory is richer than its counterpart for states because there is a wider variety of ways in which this question can be framed, either in the one-shot or n-shot regimes, with the latter having parallel and sequential variants. As in [arXiv:1905.11629], we consider two special cases of the general channel box transformation problem, known as distinguishability distillation and dilution. For the one-shot case, we find that the optimal values of the various tasks are equal to the non-smooth or smooth channel min- or max-relative entropies, thus endowing all of these quantities with operational interpretations. In the asymptotic sequential setting, we prove that the exact distinguishability cost is equal to channel max-relative entropy and the distillable distinguishability is equal to the amortized channel relative entropy of [arXiv:1808.01498]. This latter result can also be understood as a solution to Stein's lemma for quantum channels in the sequential setting. Finally, the theory simplifies significantly for environment-seizable and classical--quantum channel boxes.


page 1

page 2

page 36

page 37

page 38


Resource theory of asymmetric distinguishability

This paper systematically develops the resource theory of asymmetric dis...

Symmetric distinguishability as a quantum resource

We develop a resource theory of symmetric distinguishability, the fundam...

Relative Entropy and Catalytic Relative Majorization

Given two pairs of quantum states, a fundamental question in the resourc...

Entropy of a quantum channel

The von Neumann entropy of a quantum state is a central concept in physi...

An information-theoretic treatment of quantum dichotomies

Given two pairs of quantum states, we want to decide if there exists a q...

Efficiently computable bounds for magic state distillation

Magic state manipulation is a crucial component in the leading approache...

Partially smoothed information measures

Smooth entropies are a tool for quantifying resource trade-offs in (quan...