Lyapunov Generation of Entanglement and the Correspondence Principle

Petitjean, Cyril; Jacquod, Philippe

doi:10.1103/physrevlett.97.194103

Cited by 37 publications

(30 citation statements)

References 24 publications

(42 reference statements)

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“…This restriction leads to a 4-dimensional torus phase space for the corresponding classical system [25,41,42]. The kicking strengths (K A , K B ) = (10,14), (18,22), . .…”

Section: Coupled Kicked Rotorsmentioning

confidence: 99%

Entanglement production by interaction quenches of quantum chaotic subsystems

et al. 2020

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The entanglement production in bipartite quantum systems is studied for initially unentangled product eigenstates of the subsystems, which are assumed to be quantum chaotic. Based on a perturbative computation of the Schmidt eigenvalues of the reduced density matrix, explicit expressions for the time-dependence of entanglement entropies, including the von Neumann entropy, are given. An appropriate re-scaling of time and the entropies by their saturation values leads a universal curve, independent of the interaction. The extension to the non-perturbative regime is performed using a recursively embedded perturbation theory to produce the full transition and the saturation values. The analytical results are found to be in good agreement with numerical results for random matrix computations and a dynamical system given by a pair of coupled kicked rotors. arXiv:1909.04733v1 [quant-ph]

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“…This restriction leads to a 4-dimensional torus phase space for the corresponding classical system [25,41,42]. The kicking strengths (K A , K B ) = (10,14), (18,22), . .…”

Section: Coupled Kicked Rotorsmentioning

confidence: 99%

Entanglement production by interaction quenches of quantum chaotic subsystems

et al. 2020

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“…The time dependence of the entanglement entropy for a state that is not an eigenstate of the Hamiltonian has been studied using a variety of methods [43][44][45][46][47][48]. For a chaotic system the rate of the entanglement entropy growth is expected to be related to the Lyapunov exponents of the system [49][50][51][52][53]. In Sec.…”

Section: Scalar Field On a Lattice And Squeezed Vacuamentioning

confidence: 99%

Entanglement entropy of squeezed vacua on a lattice

2015

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We derive a formula for the entanglement entropy of squeezed states on a lattice in terms of the complex structure J. The analysis involves the identification of squeezed states with group-theoretical coherent states of the symplectic group and the relation between the coset Sp(2N, R)/Isot(J 0 ) and the space of complex structures. We present two applications of the new formula: (i) we derive the area law for the ground state of a scalar field on a generic lattice in the limit of small speed of sound, (ii) we compute the rate of growth of the entanglement entropy in the presence of an instability and show that it is asymptotically bounded from above by the Kolmogorov-Sinai rate. *

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“…Only recently [1,2,3,4,5,6,7] have there been first theoretical and experimental attempts to characterize entanglement dynamics under decoherence, but a sufficiently general picture still has to emerge. In particular, most studies did so far focus on specific classes of highly entangled W, GHZ, or cluster states, and on their specific robustness against certain sources of decoherence [8,9].…”

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confidence: 99%

Entanglement Screening by Nonlinear Resonances

et al. 2007

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We show that nonlinear resonances in a classically mixed phase space allow to define generic, strongly entangled multi-partite quantum states. The robustness of their multipartite entanglement increases with the particle number, i.e. in the semiclassical limit, for those classes of diffusive noise which assist the quantum-classical transition.PACS numbers: 03.65. Yz, 03.67.Lx,03.67.Mn,03.67.Pp, 05.45.Mt The ultimate success of the quantum information and computation program will depend on our theoretical understanding and experimental control of quantum entanglement. In order to compete with the available classical supercomputing resources, a future quantum computer will have to be composed of a large, i.e., at least mesoscopic number of qubits, and their coherence will need to be preserved over a significant period of time. Contemplating the fact that entanglement is a manifestation of multi-particle coherence, and that the density of states explodes exponentially with the particle number, it is easy to appreciate the dimension of the challenge ahead.So far, little is known about entanglement in open quantum systems -where "open" refers to the unavoidable coupling to uncontrolled degrees of freedom in the "environment", which eventually induces decoherence in the system dynamics. Only recently [1,2,3,4,5,6,7] have there been first theoretical and experimental attempts to characterize entanglement dynamics under decoherence, but a sufficiently general picture still has to emerge. In particular, most studies did so far focus on specific classes of highly entangled W, GHZ, or cluster states, and on their specific robustness against certain sources of decoherence [8,9]. As the number of particles increases, the faithful experimental generation and probing of these states tends to become more and more difficult, with rapidly increasing experimental overhead. Furthermore, whether and in which sense their entanglement properties can be considered as "generic" is a largely open issue, given the complicated topology of state space.In our present contribution, we will adopt a different perspective, which imports some generic features of quantum dynamics with underlying mixed, regular-chaotic phase space structure, i.e., from quantum chaos [10]. In contrast to earlier studies of the impact of mixed phase space dynamics [11,12,13] and nonlinear light-matter interaction [14,15] on bipartite entanglement, we are here interested in the multipartite limit of large particle numbers. This is of crucial importance in the context of entanglement scaling alluded to above, and will be identified with the semiclassical limit of progressively finer (quantum) resolution of classical phase space structures, by a suitable definition of many-particle basis states in terms of classical phase space coordinates. We will see that nonlinear resonances, which are ubiquitous in classical Hamiltonian systems [16], naturally define strongly -though not maximally -entangled multipartite quantum states. This non-optimality is compensated by the n...

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Lyapunov Generation of Entanglement and the Correspondence Principle

Cited by 37 publications

References 24 publications

Entanglement production by interaction quenches of quantum chaotic subsystems

Entanglement production by interaction quenches of quantum chaotic subsystems

Entanglement entropy of squeezed vacua on a lattice

Entanglement Screening by Nonlinear Resonances

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