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Mori T, Shirai T. Symmetrized Liouvillian Gap in Markovian Open Quantum Systems. PHYSICAL REVIEW LETTERS 2023; 130:230404. [PMID: 37354419 DOI: 10.1103/physrevlett.130.230404] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Revised: 04/24/2023] [Accepted: 05/23/2023] [Indexed: 06/26/2023]
Abstract
Markovian open quantum systems display complicated relaxation dynamics. The spectral gap of the Liouvillian characterizes the asymptotic decay rate toward the steady state, but it does not necessarily give a correct estimate of the relaxation time because the crossover time to the asymptotic regime may be too long. We here give a rigorous upper bound on the transient decay of autocorrelation functions in the steady state by introducing the symmetrized Liouvillian gap. The standard Liouvillian gap and the symmetrized one are identical in an equilibrium situation but differ from each other in the absence of the detailed balance condition. It is numerically shown that the symmetrized Liouvillian gap always gives a correct upper bound on the decay of the autocorrelation function, but the standard Liouvillian gap does not.
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Affiliation(s)
- Takashi Mori
- RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan
| | - Tatsuhiko Shirai
- Department of Computer Science and Communications Engineering, Waseda University, Tokyo 169-8555, Japan
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2
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Quantum Speed-Up Induced by the Quantum Phase Transition in a Nonlinear Dicke Model with Two Impurity Qubits. Symmetry (Basel) 2022. [DOI: 10.3390/sym14122653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
In this paper, we investigate the effect of the Dicke quantum phase transition on the speed of evolution of the system dynamics. At the phase transition point, the symmetry associated with the system parity operator begins to break down. By comparing the magnitudes of the two types of quantum speed limit times, we find that the quantum speed limit time of the system is described by one of the quantum speed limit times, whether in the normal or superradiant phase. We find that, in the normal phase, the strength of the coupling between the optical field and the atoms has little effect on the dynamical evolution speed of the system. However, in the superradiant phase, a stronger atom–photon coupling strength can accelerate the system dynamics’ evolution. Finally, we investigate the effect of the entanglement of the initial state of the system on the speed of evolution of the system dynamics. We find that in the normal phase, the entanglement of the initial state of the system has almost no effect on the system dynamics’ evolution speed. However, in the superradiant phase, larger entanglement of the system can accelerate the evolution of the system dynamics. Furthermore, we verify the above conclusions by the actual evolution of the system.
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3
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Hu X, Sun S, Zheng Y. Witnessing localization of a quantum state via quantum speed limits in a driven avoided-level crossing system. J Chem Phys 2022; 156:134113. [PMID: 35395892 DOI: 10.1063/5.0078207] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we investigate the witnessing of the localization of quantum states through quantum speed limits (QSLs) in a two-level driven avoided-level crossing system. As the characteristic natures of the localized quantum states, the QSL presents the periodic oscillations and coherence. The coherence partition of QSL is much bigger than the population partition of QSL. Our study gives us the possibilities to manipulate dynamics of quantum states locally by employing the coherent destruction of tunneling, which is significant in quantum information process. In addition, we analyze the effects of the rotating-wave approximation and the generalized Van Vleck approach on QSL and show that they wipe out the quantum coherence.
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Affiliation(s)
- Xianghong Hu
- School of Physics, Shandong University, Jinan 250100, China
| | - Shuning Sun
- School of Physics, Shandong University, Jinan 250100, China
| | - Yujun Zheng
- School of Physics, Shandong University, Jinan 250100, China
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4
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Sun S, Peng Y, Hu X, Zheng Y. Quantum Speed Limit Quantified by the Changing Rate of Phase. PHYSICAL REVIEW LETTERS 2021; 127:100404. [PMID: 34533364 DOI: 10.1103/physrevlett.127.100404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2020] [Revised: 02/17/2021] [Accepted: 07/20/2021] [Indexed: 06/13/2023]
Abstract
The quantum speed limit is important in determining the minimum evolution time of a quantum system, and thus is essential for quantum community. In this Letter, we derive a novel unified quantum speed limit bound for Hermitian and non-Hermitian quantum systems. The bound is quantified by the changing rate of phase of the quantum system, which represents the transmission mode of the quantum states over their evolution. The bound leads to further insights beyond the previous bounds on concrete evolution modes of the quantum system, such as horizontal or parallel transition or horizontal joining of the two quantum states in Hilbert space. The bound is linked to the feasibility of the evolutions of the state vectors, and provides a tighter upper bound. In addition, the generalized Margolus-Levitin bound is discussed.
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Affiliation(s)
- Shuning Sun
- School of Physics, Shandong University, Jinan 250100, China
| | - Yonggang Peng
- School of Physics, Shandong University, Jinan 250100, China
| | - Xianghong Hu
- School of Physics, Shandong University, Jinan 250100, China
| | - Yujun Zheng
- School of Physics, Shandong University, Jinan 250100, China
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5
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Fogarty T, Deffner S, Busch T, Campbell S. Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit. PHYSICAL REVIEW LETTERS 2020; 124:110601. [PMID: 32242725 DOI: 10.1103/physrevlett.124.110601] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 02/18/2020] [Indexed: 06/11/2023]
Abstract
A remarkable feature of quantum many-body systems is the orthogonality catastrophe that describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system, whose variance in ground state energy scales with the system size, exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems-the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model.
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Affiliation(s)
- Thomás Fogarty
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA
| | - Thomas Busch
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
| | - Steve Campbell
- School of Physics, University College Dublin, Belfield Dublin 4, Ireland
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6
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Sun S, Zheng Y. Distinct Bound of the Quantum Speed Limit via the Gauge Invariant Distance. PHYSICAL REVIEW LETTERS 2019; 123:180403. [PMID: 31763894 DOI: 10.1103/physrevlett.123.180403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2019] [Revised: 08/31/2019] [Indexed: 06/10/2023]
Abstract
We derive a distinct bound of the quantum speed limit for a non-Hermitian quantum system by employing the gauge invariant and geometric natures of quantum mechanics. The bound is of geometric properties since it relates to the geometric phase of the quantum system, and it is tighter than the Mandelstam-Tamm and Margolus-Levitin bounds in some cases. Also, by making the geodesic assumption, the analog of the Margolus-Levitin bound is derived for the time-dependent (non-)Hermitian quantum system. These two bounds reflect the impacts of the transmission modes of the state vectors on the evolution path in the manifold.
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Affiliation(s)
- Shuning Sun
- School of Physics, Shandong University, Jinan 250100, China
| | - Yujun Zheng
- School of Physics, Shandong University, Jinan 250100, China
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7
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Song YJ, Tan QS, Kuang LM. Control quantum evolution speed of a single dephasing qubit for arbitrary initial states via periodic dynamical decoupling pulses. Sci Rep 2017; 7:43654. [PMID: 28272546 PMCID: PMC5341562 DOI: 10.1038/srep43654] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2016] [Accepted: 01/26/2017] [Indexed: 01/03/2023] Open
Abstract
We investigate the possibility to control quantum evolution speed of a single dephasing qubit for arbitrary initial states by the use of periodic dynamical decoupling (PDD) pulses. It is indicated that the quantum speed limit time (QSLT) is determined by initial and final quantum coherence of the qubit, as well as the non-Markovianity of the system under consideration during the evolution when the qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir. It is shown that final quantum coherence of the qubit and the non-Markovianity of the system can be modulated by PDD pulses. Our results show that for arbitrary initial states of the dephasing qubit with non-vanishing quantum coherence, PDD pulses can be used to induce potential acceleration of the quantum evolution in the short-time regime, while PDD pulses can lead to potential speedup and slow down in the long-time regime. We demonstrate that the effect of PDD on the QSLT for the Ohmic or sub-Ohmic spectrum (Markovian reservoir) is much different from that for the super-Ohmic spectrum (non-Markovian reservoir).
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Affiliation(s)
- Ya-Ju Song
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| | - Qing-Shou Tan
- College of Physics and Electronic Engineering, Hainan Normal University, Haikou 571158, China
| | - Le-Man Kuang
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
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Marvian M, Lidar DA. Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes. PHYSICAL REVIEW LETTERS 2017; 118:030504. [PMID: 28157358 DOI: 10.1103/physrevlett.118.030504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2016] [Indexed: 06/06/2023]
Abstract
We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. The scheme is general and includes the stabilizer formalism of both subspace and subsystem codes as special cases. We derive performance bounds and show that complete error suppression results in the large penalty limit. To illustrate the power of subsystem-based error suppression, we introduce fully two-local constructions for protection against local errors of the swap gate of adiabatic gate teleportation and the Ising chain in a transverse field.
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Affiliation(s)
- Milad Marvian
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
- Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
| | - Daniel A Lidar
- Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA
- Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
- Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
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9
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Wang J, Wu YN, Mo ML, Zhang HZ. Relationship between quantum speed limit time and memory time in a photonic-band-gap environment. Sci Rep 2016; 6:39110. [PMID: 28008937 PMCID: PMC5180220 DOI: 10.1038/srep39110] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2016] [Accepted: 11/17/2016] [Indexed: 12/27/2022] Open
Abstract
Non-Markovian effect is found to be able to decrease the quantum speed limit (QSL) time, and hence to enhance the intrinsic speed of quantum evolution. Although a reservoir with larger degree of non-Markovianity may seem like it should cause smaller QSL times, this seemingly intuitive thinking may not always be true. We illustrate this by investigating the QSL time of a qubit that is coupled to a two-band photonic-band-gap (PBG) environment. We show how the QSL time is influenced by the coherent property of the reservoir and the band-gap width. In particular, we find that the decrease of the QSL time is not attributed to the increasing non-Markovianity, while the memory time of the environment can be seen as an essential reflection to the QSL time. So, the QSL time provides a further insight and sharper identification of memory time in a PBG environment. We also discuss a feasible experimental realization of our prediction.
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Affiliation(s)
- J. Wang
- School of physics and technology, University of Jinan, Jinan, 250022, China
| | - Y. N. Wu
- College of physics, Jilin University, Changchun, 130023, China
| | - M. L. Mo
- School of physics and technology, University of Jinan, Jinan, 250022, China
| | - H. Z. Zhang
- College of physics, Jilin University, Changchun, 130023, China
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10
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Jing J, Wu LA, Del Campo A. Fundamental Speed Limits to the Generation of Quantumness. Sci Rep 2016; 6:38149. [PMID: 27901118 PMCID: PMC5128863 DOI: 10.1038/srep38149] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2016] [Accepted: 11/04/2016] [Indexed: 01/30/2023] Open
Abstract
Quantum physics dictates fundamental speed limits during time evolution. We present a quantum speed limit governing the generation of nonclassicality and the mutual incompatibility of two states connected by time evolution. This result is used to characterize the timescale required to generate a given amount of quantumness under an arbitrary physical process. The bound is found to be tight under pure dephasing dynamics. More generally, our analysis reveals the dependence on the initial and final states and non-Markovian effects.
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Affiliation(s)
- Jun Jing
- Institute of Atomic and Molecular Physics and Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun 130012, Jilin, China.,Department of Theoretical Physics and History of Science, The University of the Basque Country (EHU/UPV), PO Box 644, 48080 Bilbao, Spain
| | - Lian-Ao Wu
- Department of Theoretical Physics and History of Science, The University of the Basque Country (EHU/UPV), PO Box 644, 48080 Bilbao, Spain.,Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain
| | - Adolfo Del Campo
- Department of Physics, University of Massachusetts, Boston, MA 02125, USA
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11
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Speedup of quantum evolution of multiqubit entanglement states. Sci Rep 2016; 6:27349. [PMID: 27283757 PMCID: PMC4901278 DOI: 10.1038/srep27349] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2016] [Accepted: 05/17/2016] [Indexed: 11/19/2022] Open
Abstract
As is well known, quantum speed limit time (QSLT) can be used to characterize the maximal speed of evolution of quantum systems. We mainly investigate the QSLT of generalized N-qubit GHZ-type states and W-type states in the amplitude-damping channels. It is shown that, in the case N qubits coupled with independent noise channels, the QSLT of the entangled GHZ-type state is closely related to the number of qubits in the small-scale system. And the larger entanglement of GHZ-type states can lead to the shorter QSLT of the evolution process. However, the QSLT of the W-type states are independent of the number of qubits and the initial entanglement. Furthermore, by considering only M qubits among the N-qubit system respectively interacting with their own noise channels, QSLTs for these two types states are shorter than in the case N qubits coupled with independent noise channels. We therefore reach the interesting result that the potential speedup of quantum evolution of a given N-qubit GHZ-type state or W-type state can be realized in the case the number of the applied noise channels satisfying M < N.
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12
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Wei YB, Zou J, Wang ZM, Shao B. Quantum speed limit and a signal of quantum criticality. Sci Rep 2016; 6:19308. [PMID: 26782296 PMCID: PMC4725993 DOI: 10.1038/srep19308] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2015] [Accepted: 12/09/2015] [Indexed: 11/12/2022] Open
Abstract
We study the quantum speed limit time (QSLT) of a coupled system consisting of a central spin and its surrounding environment, and the environment is described by a general XY spin-chain model. For initial pure state, we find that the local anomalous enhancement of the QSLT occurs near the critical point. In addition, we investigate the QSLT for arbitrary time-evolution state in the whole dynamics process and find that the QSLT will decay monotonously and rapidly at a large size of environment near the quantum critical point. These anomalous behaviors in the critical vicinity of XY spin-chain environment can be used to indicate the quantum phase transition point. Especially for the XX spin-chain environment, we find that the QSLT displays a sudden transition from discontinuous segmented values to a steady value at the critical point. In this case, the non-Makovianity and the Loschmidt echo are incapable of signaling the critical value of the transverse field, while the QSLT can still witness the quantum phase transition. So, the QSLT provides a further insight and sharper identification of quantum criticality.
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Affiliation(s)
- Yong-Bo Wei
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Jian Zou
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Zhao-Ming Wang
- Department of Physics, Ocean University of China, Qingdao 266100, China
| | - Bin Shao
- School of Physics, Beijing Institute of Technology, Beijing 100081, China
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