Quantum-speed-limit time for multiqubit open systems

Abstract

Quantum-speed-limit (QSL) time captures the intrinsic minimal time interval for a quantum system evolving from an initial state to a target state. In single qubit open systems, it was found that the memory (non-Markovian) effect of environment plays an essential role in shortening QSL time or, say, increasing the capacity for potential speedup. In this paper, we investigate the QSL time for multiqubit open systems. We find that for a certain class of states the memory effect still acts as the indispensable requirement for cutting the QSL time down, while for another class of states this takes place even when the environment is of no memory. In particular, when the initial state is in product state |111...1>, there exists a sudden transition from no capacity for potential speedup to potential speedup in a memoryless environment. In addition, we also display evidence for the subtle connection between QSL time and entanglement that weak entanglement may shorten QSL time even more.Comment: 5pages, 3 figure

Control quantum evolution speed of a single dephasing qubit for arbitrary initial states via periodic dynamical decoupling pulses

“…As was mentioned in the introduction section, by first fixing the actual driving time τ, τ QSL  =  τ means that the quantum evolution possesses no potential capacity for further acceleration. While for the case of τ QSL  <  τ , the shorter τ QSL indicates the greater speedup potential capacity1314. In addition, the QSLT is defined as the minimal time a system needs to evolute from an initial state ρ 0 to a final state ρ τ , which is governed by the time-dependent master equation .…”

Speedup of quantum evolution of multiqubit entanglement states

“…Although a similar study of QSLT for open multiqubit system has been analyzed in the case each qubit respectively interacting with its own noise channel ( M  =  N ), the investigations mainly focus on the QSLT of a few special states (such as two-qubit Bell states, the multiqubit product state ), and do not concern the role of the number of the qubits N on the QSLT31. Here, by considering the controllable noise channels number M , we have clearly illustrated the roles of the number of qubits N , the number of noise channels M and the entanglement of the initial state on the QSLT of the multiqubit open system.…”

“…So far, a few studies have been done on the QSLT in the multiqubit systems172331373839, it has been shown that entanglement could accelerate the evolution of the closed quantum system. For the multiqubit open system, in refs 23 and 24, the authors mainly consider Markovian dephasing of N-qubits system where each qubit interacts only with its own noise channel.…”

Quantum speed limit based on the bound of Bures angle

“…Utilizing the Bures angle, Deffner and Lutz arrived a unified QSL bound for initial pure state, and showed that non-Markovian effects could speed up the quantum evolution [22]. Other forms of QSL in open system were also reported, such as the QSL in different environments [23][24][25][26][27][28][29], the initialstate dependence [30], the geometric form for Wigner phase space [31], the experimentally realizable metric [32]. In addition, many other aspects of QSL were also widely studied such as using the fidelity [33,34] and function of relative purity [35,36], the mechanism for quantum speedup [37], the connection with generation of quantumness [38], generalization of geometric QSL form [39], via gauge invariant distance [40], even the QSL for almost all states [41], and so on.…”