Relational time in anyonic systems

Abstract

In a seminal paper (Page and Wootters 1983) Page and Wootters suggest time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing with the "problem of time" stemming from vanishing Hamiltonian dynamics in many theories of quantum gravity. Their approach to relational time centres around the existence of a Hamiltonian and the subsequent constraint on physical states. In this paper we present a "state-centric" reformulation of the Page and Wootters model better suited to theories which intrinsically lack Hamiltonian dynamics, such as Chern--Simons theories. We describe relational time by encoding logical "clock" qubits into anyons---the topologically protected degrees of freedom in Chern--Simons theories. The timing resolution of such anyonic clocks is determined by the universality of the anyonic braid group, with non-universal models naturally exhibiting discrete time. We exemplify this approach using SU(2)${}_2$ anyons and discuss generalizations to other states and models.

arXiv comment5 pages, 2 figures

References in corpus (15)

• Anyons in an exactly solved model and beyond
• Quantum Teleportation is a Universal Computational Primitive
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Problem of Time in Quantum Gravity
• Conditional probabilities with Dirac observables and the problem of time in quantum gravity
• Time from quantum entanglement: an experimental illustration
• Universal Quantum Computation with Metaplectic Anyons
• Implementation of Clifford gates in the Ising-anyon topological quantum computer
• Computing Spin Networks
• Consistent discretization and loop quantum geometry
• System-time entanglement in a discrete time model
• A practical phase gate for producing Bell violations in Majorana wires
• Nonlocality as a Benchmark for Universal Quantum Computation in Ising Anyon Topological Quantum Computers
• Non-locality of non-Abelian anyons
• Generalised state spaces and non-locality in fault tolerant quantum computing schemes

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• Spacetime Quantum Actions
• Time as a Consequence of Internal Coherence
• Parallel-in-time optical simulation of history states
• Path Integrals from Spacetime Quantum Actions
• Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
• History states of one-dimensional quantum walks
• Relational Dynamics with Periodic Clocks