IFLP   13074
INSTITUTO DE FISICA LA PLATA
Unidad Ejecutora - UE
artículos
Título:
History states of systems and operators
Autor/es:
ROSSIGNOLI, R.; BOETTE, A.
Revista:
Physical Review A
Editorial:
American Physical Society
Referencias:
Lugar: N.Y.; Año: 2018 vol. 98 p. 321081 - 3210810
ISSN:
2469-9926
Resumen:
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.