Saturation of the production of quantum entanglement between weakly coupled mapping systems in a strongly chaotic region

Tanaka, Atushi; Fujisaki, Hiroya; Miyadera, Takayuki

doi:10.1103/physreve.66.045201

Cited by 62 publications

(77 citation statements)

References 24 publications

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“…3). To complement our previous papers, 4,5) we also discuss the wavefunction properties of the subsystems in the entanglement production region employing the Husimi representation (Sec. 4).…”

Section: )mentioning

confidence: 95%

Dynamical Aspects of Quantum Entanglement for Coupled Mapping Systems

2003

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We investigate how the dynamical production of quantum entanglement for weakly coupled mapping systems is influenced by the chaotic dynamics of the corresponding classical system. We derive a general perturbative formula for the entanglement production rate which is defined by using the linear entropy of the subsystem. This formula predicts that the increment in the strength of chaos does not enhance the production rate of entanglement when the coupling is weak enough and the subsystems are strongly chaotic. The prediction is confirmed by numerical experiments for coupled kicked tops and rotors. We also discuss the entanglement production using the Husimi representation of the reduced density matrix.

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Section: )mentioning

confidence: 95%

Dynamical Aspects of Quantum Entanglement for Coupled Mapping Systems

2003

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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: 96%

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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“…When n < N , the action of the quantum baker's map is similar to (20), but with a crucial difference. After the qubit string is cycled, instead of applying a unitary to the rightmost, least significant qubit, a joint unitary is applied to all of the the N − n+ 1 rightmost qubits.…”

Section: The Quantum Baker's Mapmentioning

confidence: 99%

“…This paper focuses, for the most part, on the first of these questions, investigating the entangling power of the Schack-Caves class of quantum baker's maps. Previous investigations of entanglement in quantized chaotic systems, for the most part, have dealt with the correlations induced by coupling two or more independent systems together [13,14,15,16,17,18,19,20,21,22]. Our approach here is quite different: each of our quantum baker's maps lives in a Hilbert space with a qubit tensor-product structure; strings of qubits form a natural basis, anchoring Hilbert space to the corresponding classical phase space, and the quantum dynamics of our baker's maps is defined explicitly in terms of this connection.…”

Section: Introductionmentioning

confidence: 99%

Entangling power of the quantum baker s map

Scott

Caves

2003

J. Phys. A: Math. Gen.

131

193

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We investigate entanglement production in a class of quantum baker's maps. The dynamics of these maps is constructed using strings of qubits, providing a natural tensor-product structure for application of various entanglement measures. We find that, in general, the quantum baker's maps are good at generating entanglement, producing multipartite entanglement amongst the qubits close to that expected in random states. We investigate the evolution of several entanglement measures: the subsystem linear entropy, the concurrence to characterize entanglement between pairs of qubits, and two proposals for a measure of multipartite entanglement. Also derived are some new analytical formulae describing the levels of entanglement expected in random pure states.

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Saturation of the production of quantum entanglement between weakly coupled mapping systems in a strongly chaotic region

Cited by 62 publications

References 24 publications

Dynamical Aspects of Quantum Entanglement for Coupled Mapping Systems

Dynamical Aspects of Quantum Entanglement for Coupled Mapping Systems

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

Entangling power of the quantum baker s map

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