Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies

Abstract

For minimum-error channel discrimination tasks that involve only unitary channels, we show that sequential strategies may outperform parallel ones. Additionally, we show that general strategies that involve indefinite causal order are also advantageous for this task. However, for the task of discriminating a uniformly distributed set of unitary channels that forms a group, we show that parallel strategies are indeed optimal, even when compared to general strategies. We also show that strategies based on the quantum switch cannot outperform sequential strategies in the discrimination of unitary channels. Finally, we derive an ultimate upper bound for the maximal probability of successfully discriminating any set of unitary channels with any number of copies, for the most general strategies that are suitable for channel discrimination. Our bound is tight since it is saturated by sets of unitary channels forming a group k-design.

Causality in Higher Order Process Theories

“…More recently, however, there has been a growing interest in an extended class of theories, where processes can themselves evolve under a higher level type of operations called supermaps [15,16,22,20,26,67,12]. In quantum information, the development of supermaps stimulated the study of new protocols involving the manipulation of quantum processes and quantum causal structures [21,10,11,44,19,60,74,18,35,5,52,1,90,27,75,69,70,93,79,62,63,87,8,9,42,43,92,71,50,51]. In addition, quantum supermaps serve as a lens through which one can examine the kinds of causal structures which are compatible with quantum theory [54,25,66,20,14].…”

Experimental semi-device-independent certification of indefinite causal order

“…The study of such causal structures has shown that indefinite causal order brings advantages to the performance of several quantum information tasks [10][11][12][13][14][15][16][17][18][19]. From a fundamental perspective, the investigation of quantum causal structures not only renews our understanding of causality in nature but also helps to address the long-standing problem of reconciling quantum theory and general relativity in a theory of quantum gravity [20][21][22].…”