Abstract
A new theoretical framework describes the dynamics of causal structures in quantum mechanics and finds that a scenario where the order of events is definite cannot transform into one where the order of events is not well defined, and vice versa, if the dynamics is continuous and reversible.
Highlights
We are accustomed to the fact that events occur in a fixed temporal order
The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal structures, where the order between operations of local laboratories is not definite
Because the causal structure in general relativity is determined by a dynamical field— the space-time metric—and dynamical quantities can be indefinite in quantum mechanics, one might expect indefiniteness with respect to the question of whether an interval between two events is timelike, null, or spacelike, or even whether event A is before or after event B
Summary
We are accustomed to the fact that events occur in a fixed temporal order. Given two events A and B, either A is in the causal past of B, A is in the causal future of B, or they are causally disconnected (spacelike separated). Operations generalizes the notion of a quantum circuit [7] and reduces to it in the case where the causal order between the laboratories is fixed. The quantum-switch technique offers the possibility to implement certain information-theoretical tasks that quantum circuits with a fixed order of operations cannot perform [10,11,12] For this reason, it is important to understand how these processes, as useful quantum information resources, can be obtained dynamically, e.g., from separable process matrices. If one takes the view that physical transformations are continuous and reversible, our results mean that no process that violates causal inequalities can be obtained from physically realizable causal structures with a definite causal order—states and channels. Assuming that transformations are reversible but might not even be continuous, we prove a result in favor of the conjecture that the original process from Ref. [3] is not physically realizable by showing that it cannot be “reached” from any causally separable process via a reversible map
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