System-time entanglement in a discrete time model

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

Paraty, Río de Janeiro.

Workshop; VI Quantum Information School and Workshop; 2017

We present a model of discrete quantum evolution based on quantum correlations between the evolving systemand a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constantHamiltonian is able to represent the evolution over 2^n time steps in terms of justn 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 statesand is maximum for systems jumping onto a new orthogonal state at each time step. In the case of a constant Hamiltonian 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. Analytical expressions for the basic case of a qubit clock, as well as for the continuous limit in the evolution between twostates, are provided.