'Interaction-Free' Channel Discrimination

TL;DR

This paper establishes a criterion for perfect discrimination of quantum channels using 'interaction-free' measurements, providing protocols with optimal decay rates for interaction probability and minimal resource requirements.

Contribution

It generalizes 'interaction-free' measurement to quantum channels, offers an explicit protocol with optimal decay rate, and characterizes when perfect discrimination is impossible.

Findings

Interaction-free discrimination is possible under a specific criterion.

The protocol's interaction probability decays as 1/N, which is optimal.

When the criterion is not met, a trade-off inequality is proven.

Abstract

In this work, we investigate the question, which objects one can discriminate perfectly by 'interaction-free' measurements. To this end, we interpret the Elitzur-Vaidman bomb-tester experiment as a quantum channel discrimination problem and generalize the notion of 'interaction-free' measurement to arbitrary quantum channels. Our main result is a necessary and sufficient criterion for when it is possible or impossible to discriminate quantum channels in an 'interaction-free' manner (i.e., such that the discrimination error probability and the 'interaction' probability can be made arbitrarily small). For the case where our condition holds, we devise an explicit protocol with the property that both probabilities approach zero with an increasing number of channel uses, $N$. More specifically, the 'interaction' probability in our protocol decays as $\frac{1}{N}$ and we show that this rate is the optimal achievable one. Furthermore, our protocol only needs at most one ancillary qubit and might thus be implementable in near-term experiments. For the case where our condition does not hold, we prove an inequality that quantifies the trade-off between the error probability and the 'interaction' probability.