2015/12/31 by A. Boette, R. Rossignoli, N. Gigena +1 · 34 citations
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Discrete time and continuous time #Hamiltonian (control theory) #Mathematics #Measure (data warehouse) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum mechanics #Quantum system #Qubit #Statistical physics #Time evolution #quant-ph
paper · pdf · open access · doi:10.1103/physreva.93.062127
published in Physical Review A 93(6) (American Physical Society) · 7 pages, 2 figures, examples added
openalex publication_date 2016/06/27 · arxiv created 2016/06/28 · arxiv updated 2016/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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 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.