A purification postulate for quantum mechanics with indefinite causal order

TL;DR

This paper introduces a purification postulate for quantum processes with indefinite causal order, providing criteria to distinguish physically realizable processes from mathematical constructs, and highlighting that some known processes are not physically purifiable.

Contribution

It proposes a purification postulate for quantum processes with indefinite causal order and derives necessary conditions for their physical realizability.

Findings

Several known processes do not satisfy the purifiability conditions.

The purification postulate helps identify which indefinite causal order processes are physically plausible.

Necessary conditions for process purifiability are established.

Abstract

To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov et al. introduced the notion of a process: a resource shared between some parties that allows for quantum communication between them without a predetermined causal order. These processes can be used to perform several tasks that are impossible in standard quantum mechanics: they allow for the violation of causal inequalities, and provide an advantage for computational and communication complexity. Nonetheless, no process that can be used to violate a causal inequality is known to be physically implementable. There is therefore considerable interest in determining which processes are physical and which are just mathematical artefacts of the framework. Here we make the first step in this direction, by proposing a purification postulate: processes are physical only if they are purifiable. We derive necessary conditions for a process to be purifiable, and show that several known processes do not satisfy them.