Consequences of preserving reversibility in quantum superchannels.

Similarly to quantum states, quantum operations can also be transformed by means of quantum superchannels, also known as process matrices. Quantum superchannels with multiple slots are deterministic transformations which take quantum operations as inputs and are enforced to respect the laws of quantum mechanics but the use of input operations may lack a definite causal order. While causally ordered superchannels admit a characterization in terms of quantum circuits, a similar characterization of general superchannels in terms of standard quantum objects with a clearer physical interpretation has been missing. In this paper we provide a mathematical characterization for pure superchannels with two slots (also known as bipartite pure processes), which are superchannels preserving the reversibility of quantum operations. We show that the reversibility preserving condition restricts all pure superchannels with two slots to be either a causally ordered quantum circuit only consisting of unitary operations or a coherent superposition of two pure causally ordered circuits. The latter may be seen as a generalization of the {quantum switch}, allowing a physical interpretation for pure two-slot superchannels. An immediate corollary is that purifiable bipartite processes cannot violate device-independent causal inequalities.