History states of systems and operators

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 syste...

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Detalles Bibliográficos
Autores principales: Boette, Alan Pablo, Rossignoli, Raúl
Formato: Articulo
Lenguaje:Español
Publicado: 2018
Materias:
Ciencias Exactas
quantum entanglement
History States
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/75397
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-75397
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Español
topic Ciencias Exactas
quantum entanglement
History States
spellingShingle Ciencias Exactas
quantum entanglement
History States
Boette, Alan Pablo
Rossignoli, Raúl
History states of systems and operators
topic_facet Ciencias Exactas
quantum entanglement
History States
description 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.
format Articulo
Articulo
author Boette, Alan Pablo
Rossignoli, Raúl
author_facet Boette, Alan Pablo
Rossignoli, Raúl
author_sort Boette, Alan Pablo
title History states of systems and operators
title_short History states of systems and operators
title_full History states of systems and operators
title_fullStr History states of systems and operators
title_full_unstemmed History states of systems and operators
title_sort history states of systems and operators
publishDate 2018
url http://sedici.unlp.edu.ar/handle/10915/75397
work_keys_str_mv AT boettealanpablo historystatesofsystemsandoperators
AT rossignoliraul historystatesofsystemsandoperators
bdutipo_str Repositorios
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