Quantum operations with indefinite time direction

TL;DR

This paper introduces a mathematical framework for quantum operations that can probe processes in indefinite time directions, including superpositions of forward and backward evolution, revealing new information-theoretic advantages.

Contribution

It develops a formalism for quantum operations with indefinite time direction, including the quantum time flip, and demonstrates their potential advantages and realizability.

Findings

Quantum time flip probes unknown dynamics in superposition of directions.

Operations with indefinite time direction outperform definite-direction operations in information tasks.

Experimental realization possible with photonic systems.

Abstract

The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way round. A fundamental question is whether it is possible to conceive a broader set of operations that probe quantum processes in the backward direction, from the future to the past, or more generally, in a combination of the forward and backward directions. Here we introduce a mathematical framework for these operations, showing that some of them cannot be interpreted as random mixtures of operations that probe processes in a definite direction. As a concrete example, we construct an operation, called the quantum time flip, that probes an unknown dynamics in a quantum superposition of the forward and backward directions. This operation exhibits an information-theoretic advantage over all operations with definite direction. It can be realised probabilistically using quantum teleportation, and can be reproduced experimentally with photonic systems. More generally, we introduce a set of multipartite operations that include indefinite time direction as well as indefinite causal order, providing a framework for potential extensions of quantum theory.