Ultimate limits of approximate unambiguous discrimination

TL;DR

This paper establishes the fundamental limits of approximate unambiguous discrimination for quantum states and channels, providing bounds that apply broadly and identifying cases where these bounds are achievable with specific strategies.

Contribution

It introduces the first formulation of approximate unambiguous discrimination for quantum channels and derives universal performance bounds, including for adaptive protocols and teleportation-covariant channels.

Findings

Lower bounds on inconclusive probability for quantum channels with adaptive protocols.

Achievability of bounds using entangled inputs for teleportation-covariant channels.

Extension of ultimate discrimination limits from states to channels.

Abstract

Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an unambiguous discrimination strategy, an inconclusive decision (abstention) is allowed to vanish any possibility of errors when a conclusive result is obtained. In both scenarios, the testing between quantum states are relatively well-understood, for example, the ultimate limits of the performance are established decades ago; however, the testing between quantum channels is less understood. Although the ultimate limit of minimum error discrimination between channels has been explored recently, the corresponding limit of unambiguous discrimination is unknown. In this paper, we formulate an approximate unambiguous discrimination scenario, and derive the ultimate limits of the performance for both states and channels. In particular, in the channel case, our lower bound of the inconclusive probability holds for arbitrary adaptive sensing protocols. For the special class of `teleportation-covariant' channels, the lower bound is achievable with maximum entangled inputs and no adaptive strategy is necessary.