Relational time in anyonic systems

authored by: A. Nikolova, G. K. Brennen, Tobias J. Osborne, G. J. Milburn, T. M. Stace
Abstract: In a seminal paper [Phys. Rev. D 27, 2885 (1983)10.1103/PhysRevD.27.2885], Page and Wootters suggest that 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 seeks to identify relational dynamics given a Hamiltonian constraint on the physical states. Here we present a "state-centric" reformulation of the Page and Wootters model better suited to cases where the Hamiltonian constraint is satisfied, such as anyons emerging in Chern-Simons theories. We describe relational time by encoding logical "clock" qubits into topologically protected anyonic degrees of freedom. The minimum temporal increment of such anyonic clocks is determined by the universality of the anyonic braid group, with nonuniversal models naturally exhibiting discrete time. We exemplify this approach by using SU(2)2 anyons and discuss generalizations to other states and models.
Organisation(s): Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQ-mat)
External Organisation(s): University of Queensland
Macquarie University
Australian Research Council (ARC)
Type: Article
Journal: Physical Review A
Volume: 97
ISSN: 2469-9926
Publication date: 03.2018
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Atomic and Molecular Physics, and Optics
Electronic version(s): https://doi.org/10.1103/PhysRevA.97.030101 (Access: Closed)
https://doi.org/10.15488/9158 (Access: Open)

BibTeX

@article{9a25c6e7e8774511b27c3bc6b93e8cf4,
title = "Relational time in anyonic systems",
abstract = "In a seminal paper [Phys. Rev. D 27, 2885 (1983)10.1103/PhysRevD.27.2885], Page and Wootters suggest that 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 seeks to identify relational dynamics given a Hamiltonian constraint on the physical states. Here we present a {"}state-centric{"} reformulation of the Page and Wootters model better suited to cases where the Hamiltonian constraint is satisfied, such as anyons emerging in Chern-Simons theories. We describe relational time by encoding logical {"}clock{"} qubits into topologically protected anyonic degrees of freedom. The minimum temporal increment of such anyonic clocks is determined by the universality of the anyonic braid group, with nonuniversal models naturally exhibiting discrete time. We exemplify this approach by using SU(2)2 anyons and discuss generalizations to other states and models.",
author = "A. Nikolova and Brennen, {G. K.} and Osborne, {Tobias J.} and Milburn, {G. J.} and Stace, {T. M.}",
note = "Funding information: This work was supported by the Australian Research Council Centre of Excellence for Engineered Quantum Systems (Grant No. CE 110001013). T.J.O. was supported by the DFG through SFB 1227 (DQ-mat) and the RTG 1991, the ERC grants QFTCMPS and SIQS, and the cluster of excellence EXC201 Quantum Engineering and Space-Time Research.",
year = "2018",
month = mar,
doi = "10.1103/PhysRevA.97.030101",
language = "English",
volume = "97",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "3",
}