Superposition of causal orders for quantum discrimination of quantum processes

Abstract

We address the superposition of causal orders in the quantum switch as a convenient framework for quantum process discrimination in the presence of noise in qubit systems, using Bayes strategy. We show that, for different kinds of qubit noises, the indefinite causal order between the unitary to be discriminated and noise gives enhancement compared to the definite causal order case without reaching the ultimate bound of discrimination in general. Whereas, for entanglement breaking channels, the enhancement is significant, where the quantum switch allows for the attainability of the ultimate bound for discrimination posed by quantum mechanics. Memory effects escorting the superposition of causal orders are discussed, where we point out that processes describing an indefinite causal order, violate the notion of Markov locality. Accordingly, a suggestion for the simulation of indefinite causal orders in more generic scenarios beyond the quantum switch is given.