Quantum operations with indefinite time direction

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.

7 + 21 pages, 4 figures

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• Experimental superposition of time directions
• Uniqueness of quantum state over time function
• Quantum communication through devices with indefinite input-output direction
• Quantum switch instabilities with an open control
• Memory in quantum processes with indefinite time direction and causal order
• Dimension-independent weak value estimation via controlled SWAP operations
• Role of Dilations in Reversing Physical Processes: Tabletop Reversibility and Generalized Thermal Operations
• The quantum switch is uniquely defined by its action on unitary operations
• Tsirelson bounds for quantum correlations with indefinite causal order
• Variations on the Choi-Jamiolkowski isomorphism
• Indefinite Time Directed Quantum Metrology
• Toward an Experimental Device-Independent Verification of Indefinite Causal Order
• Quantifying information flow in quantum processes
• Expressibility, entangling power and quantum average causal effect for causally indefinite circuits
• Characterising transformations between quantum objects, 'completeness' of quantum properties, and transformations without a fixed causal order
• Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises
• Entropic uncertainty under indefinite causal order and input-output direction
• Informationally Complete Distributed Metrology Without a Shared Reference Frame