History states of systems and operators

A. Boette and R. Rossignoli
Phys. Rev. A 98, 032108 – Published 12 September 2018

Abstract

We discuss some fundamental properties of discrete system-time history states. Such states arise for a quantum reference clock of finite dimension and lead to a unitary evolution of system states when satisfying a static discrete Wheeler-DeWitt-type equation. We consider the general case where system-clock pairs can interact, analyzing first their different representations and showing there is always a special clock basis for which the evolution for a given initial state can be described by a constant Hamiltonian H. It is also shown, however, that when the evolution operators form a complete orthogonal set, the history state is maximally entangled for any initial state, as opposed to the case of a constant H, and can be generated through a simple double-clock setting. We then examine the quadratic system-time entanglement entropy, providing an analytic evaluation and showing it satisfies strict upper and lower bounds determined by the energy spread and the geodesic evolution connecting the initial and final states. We finally show that the unitary operator that generates the history state can itself be considered as an operator history state, whose quadratic entanglement entropy determines its entangling power. Simple measurements on the clock enable one to efficiently determine overlaps between system states and also evolution operators at any two times.

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  • Received 29 May 2018

DOI:https://doi.org/10.1103/PhysRevA.98.032108

©2018 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

A. Boette1 and R. Rossignoli1,2

  • 1Departamento de Física-IFLP/CONICET, Universidad Nacional de La Plata, C.C. 67, La Plata (1900), Argentina
  • 2Comisión de Investigaciones Científicas (CIC), La Plata (1900), Argentina

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Issue

Vol. 98, Iss. 3 — September 2018

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