Mechanism for quantum speedup in open quantum systems

Abstract

The quantum speed limit (QSL) time for open system characterizes the most efficient response of the system to the environmental influences. Previous results showed that the non-Markovianity governs the quantum speedup. Via studying the dynamics of a dissipative two-level system, we reveal that the non-Markovian effect is only the dynamical way of the quantum speedup, while the formation of the system-environment bound states is the essential reason for the quantum speedup. Our attribution of the quantum speedup to the energy-spectrum character can supply another vital path for experiments when the quantum speedup shows up without any dynamical calculations. The potential experimental observation of our quantum speedup mechanism in the circuit QED system is discussed. Our results may be of both theoretical and experimental interests in exploring the ultimate QSL in realistic environments, and may open new perspectives for devising active quantum speedup devices.PACS numbers: 03.65.Yz, 03.67.-a Introduction.-As one of the fundamental laws of nature, quantum mechanics imposes a bound on the evolution speed to quantum systems, the so-called quantum speed limit (QSL) [1][2][3][4][5]. It has recently attracted considerable attention and played remarkable roles in various areas of quantum physics including nonequilibrium thermodynamics [6], quantum metrology [7][8][9][10], quantum optimal control [11][12][13][14][15][16], quantum computation [17][18][19], and quantum communication [1,20]. The QSL time sets a bound on the minimal time a system needs to evolve between two distinguishable states, and it can be understood as a generalization of the time-energy uncertainty principle. For isolated systems, the QSL time under unitary evolution is determined by the maximum [21] of the Mandelstam-Tamm bound τ MT = π /(2∆E) [2,3] and Margolus-Levitin bound τ ML = π /(2Ē) [22], where ∆E andĒ are the fluctuation and mean value of the initialstate energy, respectively.Because of the inevitable interactions with the environments, quantum systems should be generally regarded as open systems. The decoherence effect resulting from the system-environment interactions would introduce remarkable influences on the QSL. Much effort has been made to explore the QSL of open system under the environment governed nonunitary evolution. A MandelstamTamm-type bound on the QSL time for pure initial states has been derived by using positive nonunitary maps [23,24]. Using a geometric approach, a unified bound on the QSL time including both Mandelstam-Tamm and Margolus-Levitin types has also been formulated [25]. The generic bound on the QSL time for both mixed and pure initial states has been obtained by introducing the relative purity [26] and the Hilbert-Schmidt product of operators [27,28] as distance measure. Deffner and Lutz [25] showed that non-Markovian effect character-

Detecting quantum speedup in closed and open systems

“…The shortest possible time for this dynamical process, characterized by Mandelstam-Tamm [1] or Margolus-Levitin lower bound [2], is typically called the quantum speed limit (QSL) time, and this quantity plays an important and fundamental role in the study of quantum computation [3], quantum metrology [4,5], quantum thermodynamics [6,7], and quantum control [8,9]. Recent decades have witnessed considerable research on the QSL time, both in closed systems [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and in more general open systems [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] . One important discovery is the fact that entanglement is able to speed up the evolution of closed quantum systems [14,17,…”

There is no general connection between the quantum speed limit and non-Markovianity

“…Their result suggests that in the Markovian case the dynamics saturates the bound, giving the most efficient evolution, whereas in the non-Markovian case the actual limit can still be lower than the evolution time. The explicitly derived dependency between QSL and non-Markovianity has proven useful in several applications [10,[15][16][17][18][19][20][21][22][23][24][25][26][27][28].Our main goal is to tackle the question of the connection between non-Markovianity and the QSL not starting from a specific model but in full generality, looking in detail at the role played by the dynamical map, the evolution time τ, and the initial state, in the achievement of the QSL bound. We show that, for the most general cases, there is no simple connection between the Markovian to non-Markovian crossover and the QSL.…”

Quantum speed-up process of atom in dissipative cavity

“…If σ(t, ρ 1,2 (0)) > 0, D(ρ 1 (t), ρ 2 (t)) increases with time increasing because the information flows back from the environment to the system, there is N > 0, the dynamics process of the system is non-Markovian. When σ(t, ρ 1,2 (0)) < 0, there is N = 0, the dynamics process of the system is Markovian because the information flows irreversibly from the system to the environment [7,12,37]. Thus the non-Markovianity describes the total backflow of quantum information between the system and the environment.…”