Computational distinguishability of degradable and antidegradable channels

TL;DR

This paper proves that distinguishing degradable and antidegradable quantum channels remains computationally hard (PSPACE-complete), even when restricted to these classes, using embeddings that relate general channels to these special classes.

Contribution

It demonstrates the PSPACE-completeness of the channel distinguishability problem within degradable and antidegradable classes, extending prior complexity results.

Findings

Distinguishing degradable channels is PSPACE-complete.

Distinguishing antidegradable channels is PSPACE-complete.

Embedding constructions relate general channels to these classes.

Abstract

A channel is degradable if there exists a second channel that maps the output state of the channel to the environment state. These channels satisfy the property that the output state contains more information about the input than the environment does. A complementary class of channels is the antidegradable channels, which admit channels that map the environment state to the output state of the channel. In this paper we show that the computational problem of distinguishing two channels remains PSPACE-complete when restricted to these classes of channels. This is shown using a construction of Cubitt, Ruskai, and Smith that embeds any channel into a degradable channel, and a related construction for the case of antidegradable channels.