On the discrimination of qubit channels

Milajiguli Rexiti, Stefano Mancini

Zoe G. del Toro, Marco Túlio Quintino, Jessica Bavaresco

Purifications are often used as a convenient mathematical representation of quantum states and channels when constructing protocols for quantum information processing tasks. Although powerful, this perspective can suggest that the purifying degrees of freedom and its correlations with an environment are just a useful change of representation. Here we show how they can instead be exploited as an operational resource in sequential quantum channel discrimination, even when the environmental reference frame is unknown or averaged. In contrast to state discrimination and parallel channel discrimination, for which bare and averaged-purification access are equivalent, sequential access to purified resources exhibits a strict advantage in probability of success. We prove this strict separation via two main results. In the first, we construct a pair of families of qubit-qubit channels with a strict separation in the two-query case, and in the second, we show an example of a pair of qubit-qubit channels whose purifications are perfectly distinguishable with three queries while no finite number of bare (non-purified) queries suffices for perfect discrimination. These separations imply an advantage of sequential over parallel strategies for channel discrimination and establish the impossibility of converting bare channel queries into averaged-purification queries via transformations that allow arbitrary interventions between queries, strengthening previous results.

Tanner Crowder, Keye Martin

Francisco Neves, Raul Rato

Joonwoo Bae, Tanmay Singal

Dynamics of many-qubit systems, that may correspond to computational processing with quantum systems, can be efficiently and generally approximated by a sequence of two- and single-qubit gates. In practical applications, however, a quantum gate prepared as a unitary transformation may appear as a noisy channel and consequently may inhibit quantum advantages. In this work, we apply the scheme of channel discrimination to detect if a quantum gate that is actually realized is unitary or noisy. We show that a two-qubit unitary transformation and its noisy counterpart can be optimally discriminated by local resources, without the necessity of creating entanglement repeatedly. It is also shown that the scheme can be applied to estimation of the fraction of noise existing in quantum gates.

Keye Martin