Single-shot antidistinguishability of unitary operations
Phys. Rev. A 113, 022218 – Published 23 February, 2026
DOI: https://doi.org/10.1103/d183-k1x3
Abstract
The notion of antidistinguishability captures the possibility of ruling out certain alternatives in a quantum experiment without identifying the actual outcome. Although extensively studied for quantum states, the antidistinguishability of quantum channels remains largely unexplored. In this work, we investigate the single-shot antidistinguishability of unitary operations. We analyze two scenarios: antidistinguishability with single-system probes and with entangled probes. For sets of three unitaries, we first prove that all maximally entangled states are equivalent in their performance as probes. In the qubit case, we further establish that maximally entangled probes are always sufficient for perfect antidistinguishability: if a set of three unitaries acting on two-dimensional Hilbert space is antidistinguishable with either a single-system or nonmaximally entangled probe, then it is also antidistinguishable with a maximally entangled one. However, in higher dimension, this sufficiency fails. From dimension 3, there exists a set of unitaries that are antidistinguishable with a nonmaximally entangled probe or a single-system probe but not with a maximally entangled probe. We also establish that the union of two antidistinguishable sets of three unitaries acting on a two-dimensional Hilbert space also forms a set of antidistinguishable unitaries. Lastly, we provide methods to construct antidistinguishable unitaries from non-antidistinguishable ones.
