System-time entanglement in a discrete time model

• Autores: Boette, Alan Pablo; Rossignoli, Raúl Dante; Gigena, Nicolás; Cerezo de la Rocca, Marco Vinicio
• Año de publicación: 2016
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Ciencias Naturales y Exactas; Quantum time models; Quantum entanglemen
• Institución: Comisión de Investigaciones Científicas de la Provincia de Buenos Aires

We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is able to represent the evolution over2ntime steps in terms of justntime qubits andncontrol 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 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 two states, are provided.