Noncausal Page-Wootters circuits

Abstract

One of the most fundamental open problems in physics is the unification of general relativity and quantum theory to a theory of quantum gravity. An aspect that might become relevant in such a theory is that the dynamical nature of causal structure present in general relativity displays quantum uncertainty. This may lead to a phenomenon known as indefinite or quantum causal structure, as captured by the process matrix formalism. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. In this paper we combine the process matrix framework with a generalization of the Page-Wootters formalism in which one considers several agents, each with their own discrete quantum clock. We describe how to extract process matrices from scenarios involving such agents with quantum clocks, and analyze their properties. The description via a history state with multiple clocks imposes constraints on the implementation of process matrices and on the perspectives of the agents as described via causal reference frames. While it allows for scenarios where different definite causal orders are coherently controlled, we explain why certain noncausal processes might not be implementable within this setting.

New title. Close to published version. Veronika Baumann and Marius Krumm share first authorship of this paper

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Cited by in corpus (16)

• Internal quantum reference frames for finite Abelian groups
• Non-inertial quantum clock frames lead to non-Hermitian dynamics
• Flow of time during energy measurements and the resulting time-energy uncertainty relations
• Reassessing thermodynamic advantage from indefinite causal order
• A model of quantum spacetime
• Existence of processes violating causal inequalities on time-delocalised subsystems
• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• Robustness of the Page-Wootters construction across different pictures, states of the universe and system-clock interactions
• Measurement events relative to temporal quantum reference frames
• Nonrelativistic spatiotemporal quantum reference frames
• Quantum Supermaps are Characterized by Locality
• Emergent Time and Time Travel in Quantum Physics
• Parallel-in-time quantum simulation via Page and Wootters quantum time
• A magnetic clock for a harmonic oscillator
• Empirical adequacy of the time operator canonically conjugate to a Hamiltonian generating translations
• Relational Dynamics with Periodic Clocks