Entanglement and the quantum brachistochrone problem

Abstract

Entanglement is closely related to some fundamental features of the dynamics of composite quantum systems: quantum entanglement enhances the "speed" of evolution of certain quantum states, as measured by the time required to reach an orthogonal state. The concept of "speed" of quantum evolution constitutes an important ingredient in any attempt to determine the fundamental limits that basic physical laws impose on how fast a physical system can process or transmit information.Here we explore the relationship between entanglement and the speed of quantum evolution in the context of the quantum brachistochrone problem. Given an initial and a final state of a composite system we consider the amount of entanglement associated with the brachistochrone evolution between those states, showing that entanglement is an essential resource to achieve the alluded time-optimal quantum evolution.

Quantum dating market

“…The advantage increases for C in this game for increasing N because the opportunities for C are N/2 while Q has only one. As quantum entanglement enhances the "speed" of evolution of certain quantum states [23] in future analysis we will introduce entanglement between players in order to see if it provides any advantage to entangled players and changes the stable solutions.…”

Genuine tripartite entanglement in quantum brachistochrone evolution of a three-qubit system

“…Borras et al [15,16] showed that quantum brachistochrone evolution between orthogonal states cannot be implemented without the typical entanglement of two subsystems (such as linear entropy or concurrence). For a three-qubit entangled quantum system, its concurrence satisfies the following relation,…”

“…Rev. A 80, 052106 (2009) † Email: fgdeng@bnu.edu.cn orthogonal and nonorthogonal, pure and mixed, as well as bipartite and multipartite cases [11,12,13,14,15,16].…”

“…Recently, Borras et al [15] investigated the role of entanglement in quantum brachistochrone evolution of quantum system in a pure state and found that " brachistochrone quantum evolution between orthogonal states cannot be implemented without entanglement". Moreover, they [16] discussed quantum brachistochrone evolution of systems of two identical particles and found that entanglement plays a fundamental role in the brachistochrone evolution of composite quantum systems.…”

Efficient generation of random multipartite entangled states using time-optimal unitary operations

“…The minimization of this time is as important, from the experimental point of view, as the gate complexity. A considerable amount of work has recently been devoted to the time-optimal quantum computation problem, with emphasis in the quantum Brachistochrone formalism [21,22,23,24]. Making use of the analogy with the brachistochrone problem from classic mechanics, Carlini et.…”