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Zhang HX, Fan CH, Wu JH. In-phase and anti-phase entanglement dynamics of Rydberg atomic pairs. OPTICS EXPRESS 2020; 28:35350-35362. [PMID: 33182983 DOI: 10.1364/oe.408799] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2020] [Accepted: 10/19/2020] [Indexed: 06/11/2023]
Abstract
We study the correlated evolutions of two far-spaced Rydberg atomic pairs with different resonant frequencies, interacting via van der Waals (vdW) potentials and driven by a common laser field. They are found to exhibit in-phase (anti-phase) beating dynamics characterized by identical (complementary) intra-pair entanglements under a specific condition in regard of inter-pair vdW potentials and driving field detunings. This occurs when each atomic pair just oscillates between its ground state and symmetric entangled state because its doubly excited state and asymmetric entangled state are forbidden due to rigid dipole blockade and perfect destructive interference, respectively. More importantly, optimal inter-pair overall entanglement can be attained at each beating node corresponding to semi-optimal intra-pair entanglements, and inevitable dissipation processes just result in a slow decay of intra-pair and inter-pair entanglements yet without destroying in-phase and anti-phase beating dynamics.
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2
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Entanglement concentration for arbitrary four-particle linear cluster states. Sci Rep 2017; 7:1982. [PMID: 28512331 PMCID: PMC5434068 DOI: 10.1038/s41598-017-02146-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2016] [Accepted: 04/06/2017] [Indexed: 11/21/2022] Open
Abstract
Cluster states, whose model are a remarkably rich structure in measurement-based quantum computation, hold high degree of entanglement, while entanglement is very fragile during the process of transmission because of the inevitable interaction with the environment. We propose two entanglement concentration protocols for four-particle linear cluster states which and are susceptible to the decoherence and the imperfect communication setups. In the first protocol, POVM operators are introduced to maximize the success probability, and the second protocol is based on cross-Kerr nonlinearity which is utilized to check the parity between the original particle and the ancillary particle. Both of the protocols have their own advantages. The first one can be easily realized in experiment by linear optics, while the one with cross-Kerr nonlinearity reach more than 90% success probability by iteration. Since the wide application of cluster states, the two protocols are efficient and valuable to different fields of quantum communication.
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3
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Han JX, Hu Y, Jin Y, Zhang GF. Influence of intrinsic decoherence on tripartite entanglement and bipartite fidelity of polar molecules in pendular states. J Chem Phys 2016; 144:134308. [PMID: 27059571 DOI: 10.1063/1.4945384] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An array of ultracold polar molecules trapped in an external electric field is regarded as a promising carrier of quantum information. Under the action of this field, molecules are compelled to undergo pendular oscillations by the Stark effect. Particular attention has been paid to the influence of intrinsic decoherence on the model of linear polar molecular pendular states, thereby we evaluate the tripartite entanglement with negativity, as well as fidelity of bipartite quantum systems for input and output signals using electric dipole moments of polar molecules as qubits. According to this study, we consider three typical initial states for both systems, respectively, and investigate the temporal evolution with variable values of the external field intensity, the intrinsic decoherence factor, and the dipole-dipole interaction. Thus, we demonstrate the sound selection of these three main parameters to obtain the best entanglement degree and fidelity.
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Affiliation(s)
- Jia-Xing Han
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics and Nuclear Energy Engineering, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
| | - Yuan Hu
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics and Nuclear Energy Engineering, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
| | - Yu Jin
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics and Nuclear Energy Engineering, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
| | - Guo-Feng Zhang
- Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics and Nuclear Energy Engineering, Beihang University, Xueyuan Road No. 37, Beijing 100191, China
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4
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Hauke P, Tagliacozzo L. Spread of correlations in long-range interacting quantum systems. PHYSICAL REVIEW LETTERS 2013; 111:207202. [PMID: 24289707 DOI: 10.1103/physrevlett.111.207202] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2013] [Indexed: 06/02/2023]
Abstract
The nonequilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address this issue by analyzing a local quantum quench in the long-range Ising model in a transverse field, where interactions decay as a variable power law with distance ∝r(-α), α>0. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for α>2, weakly long range for 1<α<2 without a clear light cone but with a finite propagation speed of almost all excitations, and fully nonlocal for α<1 with instantaneous transmission of correlations. This last regime breaks generalized Lieb-Robinson bounds and thus locality. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasiparticles remains valid, allowing an intuitive interpretation of our findings via divergences of quasiparticle velocities. Our results may be tested in state-of-the-art trapped-ion experiments.
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Affiliation(s)
- P Hauke
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, A-6020 Innsbruck, Austria and Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
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Wei Q, Kais S, Friedrich B, Herschbach D. Entanglement of polar molecules in pendular states. J Chem Phys 2011; 134:124107. [PMID: 21456645 DOI: 10.1063/1.3567486] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Qi Wei
- Department of Physics, Texas A & M University, College Station, Texas 77843, USA
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Li B, Li SH, Zhou HQ. Quantum phase transitions in a two-dimensional quantum XYX model: ground-state fidelity and entanglement. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:060101. [PMID: 19658453 DOI: 10.1103/physreve.79.060101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2008] [Indexed: 05/28/2023]
Abstract
A systematic analysis is performed for quantum phase transitions in a two-dimensional anisotropic spin-1/2 antiferromagnetic XYX model in an external magnetic field. With the help of an innovative tensor network algorithm, we compute the fidelity per lattice site to demonstrate that the field-induced quantum phase transition is unambiguously characterized by a pinch point on the fidelity surface, marking a continuous phase transition. We also compute an entanglement estimator, defined as a ratio between the one-tangle and the sum of squared concurrences, to identify both the factorizing field and the critical point, resulting in a quantitative agreement with quantum Monte Carlo simulation. In addition, the local order parameter is "derived" from the tensor network representation of the system's ground-state wave functions.
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Affiliation(s)
- Bo Li
- Department of Physics and Centre for Modern Physics, Chongqing University, Chongqing 400044, People's Republic of China
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7
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Giovannetti V, Montangero S, Fazio R. Quantum multiscale entanglement renormalization ansatz channels. PHYSICAL REVIEW LETTERS 2008; 101:180503. [PMID: 18999805 DOI: 10.1103/physrevlett.101.180503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/03/2008] [Indexed: 05/27/2023]
Abstract
Tensor network representations of many-body quantum systems can be described in terms of quantum channels. We focus on channels associated with the multiscale entanglement renormalization ansatz tensor network that has been recently introduced to efficiently describe critical systems. Our approach allows us to compute the multiscale entanglement renormalization ansatz correspondent to the thermodynamical limit of a critical system introducing a transfer matrix formalism, and to relate the system critical exponents to the convergence rates of the associated channels.
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Affiliation(s)
- V Giovannetti
- NEST CNR-INFM and Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
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Zhou HQ, Orús R, Vidal G. Ground state fidelity from tensor network representations. PHYSICAL REVIEW LETTERS 2008; 100:080601. [PMID: 18352611 DOI: 10.1103/physrevlett.100.080601] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2007] [Revised: 01/15/2008] [Indexed: 05/26/2023]
Abstract
For any D-dimensional quantum lattice system, the fidelity between two ground state many-body wave functions is mapped onto the partition function of a D-dimensional classical statistical vertex lattice model with the same lattice geometry. The fidelity per lattice site, analogous to the free energy per site, is well defined in the thermodynamic limit and can be used to characterize the phase diagram of the model. We explain how to compute the fidelity per site in the context of tensor network algorithms, and demonstrate the approach by analyzing the two-dimensional quantum Ising model with transverse and parallel magnetic fields.
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Affiliation(s)
- Huan-Qiang Zhou
- Department of Physics, Chongqing University, Chongqing 400044, The People's Republic of China
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9
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Gross D, Eisert J. Novel schemes for measurement-based quantum computation. PHYSICAL REVIEW LETTERS 2007; 98:220503. [PMID: 17677826 DOI: 10.1103/physrevlett.98.220503] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2006] [Revised: 01/29/2007] [Indexed: 05/16/2023]
Abstract
We establish a framework which allows one to construct novel schemes for measurement-based quantum computation. The technique develops tools from many-body physics-based on finitely correlated or projected entangled pair states-to go beyond the cluster-state based one-way computer. We identify resource states radically different from the cluster state, in that they exhibit nonvanishing correlations, can be prepared using nonmaximally entangling gates, or have very different local entanglement properties. In the computational models, randomness is compensated in a different manner. It is shown that there exist resource states which are locally arbitrarily close to a pure state. We comment on the possibility of tailoring computational models to specific physical systems.
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Affiliation(s)
- D Gross
- Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom
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10
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Cramer M, Eisert J, Plenio MB. Statistics dependence of the entanglement entropy. PHYSICAL REVIEW LETTERS 2007; 98:220603. [PMID: 17677829 DOI: 10.1103/physrevlett.98.220603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2006] [Revised: 03/09/2007] [Indexed: 05/16/2023]
Abstract
The entanglement entropy of a distinguished region of a quantum many-body system reflects the entanglement in its pure ground state. Here we establish scaling laws for this entanglement in critical quasifree fermionic and bosonic lattice systems, without resorting to numerical means. We consider the setting of D-dimensional half-spaces which allows us to exploit a connection to the one-dimensional case. Intriguingly, we find a difference in the scaling properties depending on whether the system is bosonic-where an area law is proven to hold-or fermionic where we determine a logarithmic correction to the area law, which depends on the topology of the Fermi surface. We find Lifshitz quantum phase transitions accompanied with a nonanalyticity in the prefactor of the leading order term.
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Affiliation(s)
- M Cramer
- Institut für Physik, Universität Potsdam, Am Neuen Palais 10, D-14469 Potsdam, Germany
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11
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Eisert J, Osborne TJ. General entanglement scaling laws from time evolution. PHYSICAL REVIEW LETTERS 2006; 97:150404. [PMID: 17155303 DOI: 10.1103/physrevlett.97.150404] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2006] [Revised: 07/30/2006] [Indexed: 05/12/2023]
Abstract
We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an entanglement-boundary law. These results apply to any ground state of a gapped model resulting from dynamics generated by a local Hamiltonian, as well as, dually, to states that are generated via a sudden quench of an interaction as recently studied in the case of dynamics of quantum phase transitions. We achieve these results by exploiting ideas from quantum information theory and tools provided by Lieb-Robinson bounds. We also show that there exist noncritical fermionic systems and equivalent spin chains with rapidly decaying interactions violating this entanglement-boundary law. Implications for the classical simulatability are outlined.
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Affiliation(s)
- Jens Eisert
- Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom and Institute for Mathematical Sciences, Imperial College London, Prince's Gardens, London SW7 2PE, United Kingdom
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12
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Anders S, Plenio MB, Dür W, Verstraete F, Briegel HJ. Ground-state approximation for strongly interacting spin systems in arbitrary spatial dimension. PHYSICAL REVIEW LETTERS 2006; 97:107206. [PMID: 17025851 DOI: 10.1103/physrevlett.97.107206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2006] [Indexed: 05/12/2023]
Abstract
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These states allow for the efficient computation of all local observables (e.g., energy) and include states with diverging correlation length and unbounded multiparticle entanglement. As a demonstration, we apply our approach to the Ising model on 1D, 2D, and 3D square lattices. We also present generalizations to higher spins and continuous-variable systems, which allows for the investigation of lattice field theories.
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Affiliation(s)
- S Anders
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria
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Unanyan RG, Fleischhauer M. Entanglement and criticality in translationally invariant harmonic lattice systems with finite-range interactions. PHYSICAL REVIEW LETTERS 2005; 95:260604. [PMID: 16486330 DOI: 10.1103/physrevlett.95.260604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2005] [Indexed: 05/06/2023]
Abstract
We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with nonrandom, finite-range interactions. We show that the criticality of the system as well as validity or breakdown of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular, for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bipartite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strong evidence for the multidimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest-neighbor coupling is analyzed.
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Affiliation(s)
- R G Unanyan
- Fachbereich Physik, Technische Universität Kaiserslautern, Germany
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14
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Calsamiglia J, Hartmann L, Dür W, Briegel HJ. Spin gases: quantum entanglement driven by classical kinematics. PHYSICAL REVIEW LETTERS 2005; 95:180502. [PMID: 16383883 DOI: 10.1103/physrevlett.95.180502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2005] [Indexed: 05/05/2023]
Abstract
A spin gas is a natural extension of a classical gas. It consists of a large number of particles whose (random) motion is described classically, but, in addition, have internal (quantum mechanical) degrees of freedom that interact during collisions. For specific types of quantum interactions we determine the entanglement that occurs naturally in such systems. We analyze how the evolution of the quantum state is determined by the underlying classical kinematics of the gas. For the Boltzmann gas, we calculate the rate at which entanglement is produced and characterize the entanglement properties of the equilibrium state.
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Affiliation(s)
- J Calsamiglia
- Institut für Theoretische Physik, Universität Innsbruck, Innsbruck, Austria
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