Entangling power of quantized chaotic systems

Lakshminarayan, Arul

doi:10.1103/physreve.64.036207

Cited by 148 publications

(166 citation statements)

References 32 publications

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“…This interesting connection provides insight into a variety of interesting aspects of quantum intrinsic decoherence dynamics [18,19,20,21,22]. For example, for chaotic dynamics in which classical trajectories are highly unstable and therefore in which |M ij | increases rapidly, S c (t) should increase much faster than for the case of integrable dynamics.…”

Section: Localized Initial States a Simple Classical Approachmentioning

confidence: 99%

Intrinsic decoherence dynamics in smooth Hamiltonian systems: Quantum-classical correspondence

Gong

Brumer

2003

Phys. Rev. A

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A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stability nature of classical trajectories is revealed in a simple approximate classical theory of intrinsic decoherence dynamics. The results offer new insights into decoherence, dynamics of quantum entanglement, and quantum chaos.

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Section: Localized Initial States a Simple Classical Approachmentioning

confidence: 99%

Intrinsic decoherence dynamics in smooth Hamiltonian systems: Quantum-classical correspondence

Gong

Brumer

2003

Phys. Rev. A

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“…While these latter works have explored complexity from the viewpoint of many particle, thermodynamic, systems, few particle systems that are classically chaotic are also complex in their own way with well-studied spectral transitions occurring in the quantum systems [9,10]. For bipartite systems of this kind pure-state entanglement has been shown to be sensitive to the presence of classical chaos and the typical value of entanglement has been calculated from random matrix theory (RMT), including the distribution of the eigenvalues of the reduced density matrices [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Entanglement sharing in one-particle states

Lakshminarayan

Subrahmanyam

2003

Phys. Rev. A

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Entanglement sharing among sites of one-particle states is considered using the measure of concurrence. These are the simplest in an hierarchy of number-specific states of many qubits and corresponds to "one-magnon" states of spins. We study the effects of onsite potentials that are both integrable and nonintegrable. In the integrable case we point to a metal-insulator transition that reflects on the way entanglement is shared. In the nonintegrable case the average entanglement content increases and saturates along with a transition to classical chaos. Such quantum chaotic states are shown to have universal concurrence distributions that are modified Bessel functions derivable within random matrix theory. Time-reversal breaking and time evolving states are shown to possess significantly higher entanglement sharing capacity that eigenstates of time-reversal symmetric systems. We use the ordinary Harper and kicked Harper Hamiltonians as model systems.

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“…It has been extensively studied both theoretically and experimentally for over two decades [1][2][3][4][5][6][7][8][9] and continues to be investigated today [10,11].…”

Section: Introductionmentioning

confidence: 99%

Entanglement and its relationship to classical dynamics

2017

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We present an analysis of the entangling quantum kicked top focusing on the few qubit case and the initial condition dependence of the time-averaged entanglement SQ for spin-coherent states. We show a very strong connection between the classical phase space and the initial condition dependence of SQ even for the extreme case of two spin-1/2 qubits. This correlation is not related directly to chaos in the classical dynamics. We introduce a measure of the behavior of a classical trajectory which correlates far better with the entanglement and show that the maps of classical and quantum initial-condition dependence are both organized around the symmetry points of the Hamiltonian. We also show clear (quasi-)periodicity in entanglement as a function of number of kicks and of kick strength.

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Entangling power of quantized chaotic systems

Cited by 148 publications

References 32 publications

Intrinsic decoherence dynamics in smooth Hamiltonian systems: Quantum-classical correspondence

Intrinsic decoherence dynamics in smooth Hamiltonian systems: Quantum-classical correspondence

Entanglement sharing in one-particle states

Entanglement and its relationship to classical dynamics

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