Indefinite causal order and the arrow of time

Abstract

At the fundamental level, the dynamics of quantum particles and fields is time-symmetric: their dynamical equations are invariant under inversion of the time coordinate, possibly in conjunction with the change of other physical properties, such as charge and parity. At the operational level, the time-symmetry of the fundamental equations implies that certain quantum devices are bidirectional, meaning that the role of their inputs and outputs can be exchanged. Here we characterize the largest set of operations that can in principle be implemented on bidirectional devices, and show that this set includes operations in which the role of the input and output ports of the given devices becomes indefinite. An example of such an operation, called the “quantum time flip,” achieves input-output indefiniteness by adding quantum control to the direction in which a single device is used. We show that quantum operations with indefinite input-output directions can in principle achieve information-theoretic advantages over all possible operations with definite time direction, and can lead to an exetremely strong form of indefinite causal order.