On Bounding Entangling Rates and Mixing Rates in Some Special Cases

Qi, Ning; Guo, Fen-Zhuo; Zhang, Jie; Wen, Qiaoyan

doi:10.1007/s10773-015-2806-9

Cited by 3 publications

(4 citation statements)

References 24 publications

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“…al. [1], improved by Audenaert [4] with constant 2, and proved by Ning et al [11] with constant 1 for a specific class of states.…”

Section: Small Incremental Mixingmentioning

confidence: 88%

“…The bound was improved by Lieb and Vershynina [9] providing an upper bound Γ(H) ≤ 4 H ln d for an arbitrary Hamiltonian in ancilla-assisted system. Finally the question was answered by Van Acoleyen et al [1] arriving at Γ(H) ≤ 18 H ln d. Few months later an independent proof was presented by Audenaert [4] that gives an upper bound Γ(H) ≤ 8 H ln d. In [11] Ning et. al.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Entanglement rates for Rényi, Tsallis, and other entropies

Vershynina

2019

Journal of Mathematical Physics

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We provide an upper bound on the maximal entropy rate at which the entropy of the expected density operator of a given ensemble of two states changes under nonlocal unitary evolution. A large class of entropy measures in considered, which includes Rényi and Tsallis entropies. The result is derived from a general bound on the trace-norm of a commutator, which can be expected to find other implementations. We apply this result to bound the maximal rate at which quantum dynamics can generate entanglement in a bipartite closed system with Rényi and Tsallis entanglement entropy taken as measures of entanglement in the system.

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“…al. [1], improved by Audenaert [4] with constant 2, and proved by Ning et al [11] with constant 1 for a specific class of states.…”

Section: Small Incremental Mixingmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Entanglement rates for Rényi, Tsallis, and other entropies

Vershynina

2019

Journal of Mathematical Physics

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“…Consequently, the entanglement rate cannot in general be maximized by changing the value of ϕ in a local fashion. However, from equation (16) we see that for fixed τ there are two (positive) possible values of p, namely…”

Section: Optimization Of γ Involving a Qubit Flipmentioning

confidence: 99%

“…In [10] a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits is developed. Bounds for the entanglement capabilities have been further explored in [11][12][13][14][15][16]. Other related approaches attempt to answer what is the minimum time for reaching a target entangled state, leading for example to the study of the quantum braquistochrone problem [17].…”

Section: Introductionmentioning

confidence: 99%

Optimal entanglement generation in GHZ-type states

Giovenale,

Hernandez-Martinez,

Majtey

et al. 2023

J. Phys. A: Math. Theor.

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The entanglement production is key for many applications in the realm of quantum information, but so is the identification of processes that allow to create entanglement in a fast and sustained way. Most of the advances in this direction have been circumscribed to bipartite systems only, and the rate of entanglement in multipartite system has been much less explored. Here we contribute to the identification of processes that favor the fastest and sustained generation of tripartite entanglement in a class of 3-qubit GHZ-type states. By considering a three-party interaction Hamiltonian, we analyze the dynamics of the 3-tangle and the entanglement rate to identify the optimal local operations that supplement the Hamiltonian evolution in order to speed-up the generation of three-way entanglement, and to prevent its decay below a predetermined threshold value. The appropriate local operation that maximizes the speed at which a highly-entangled state is reached has the advantage of requiring access to only one of the qubits, yet depends on the actual state of the system. Other universal (state-independent) local operations are found that conform schemes to maintain a sufficiently high amount of 3-tangle. Our results expand our understanding of entanglement rates to multipartite systems, and offer guidance regarding the strategies that improve the efficiency in various quantum information processing tasks.

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Bounds on Rényi entropy growth in many-body quantum systems

Shi

2024

Phys. Rev. A

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On Bounding Entangling Rates and Mixing Rates in Some Special Cases

Cited by 3 publications

References 24 publications

Entanglement rates for Rényi, Tsallis, and other entropies

Entanglement rates for Rényi, Tsallis, and other entropies

Optimal entanglement generation in GHZ-type states

Bounds on Rényi entropy growth in many-body quantum systems

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