System-time entanglement in a discrete-time model

A. BOETTE; M. CEREZO; R. ROSSIGNOLI; N. GIGENA

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2016 vol. 93 p. 621271 - 6212717

1050-2947

We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system.Aquantum circuit for the model is provided, which in the case of a constantHamiltonian is able to represent the evolution over 2n time steps in terms of just n time qubits and n control gates. We then introduce the concept of system-time entanglement as a measure of distinguishable quantum evolution,based on the entanglement between the system and the reference clock. This quantity vanishes for stationary states and is maximum for systems jumping onto a new orthogonal state at each time step. In the case of a constantHamiltonian leading to a cyclic evolution it is a measure of the spread over distinct energy eigenstates and satisfies an entropic energy-time uncertainty relation. The evolution of mixed states is also examined. Analyticalexpressions for the basic case of a qubit clock, as well as for the continuous limit in the evolution between two states, are provided.