Entanglement via entangled-boundary-condition trajectories: Long-time accuracy

Lara, Arlans J. S. de; Ribeiro, A. D.

doi:10.1103/physreva.100.042123

Cited by 3 publications

(9 citation statements)

References 48 publications

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“…IV. The sum in S sc (T ) indicates that all sets of classical trajectories respecting the boundary conditions (23) and (24) are, in principle, important to approach the quantum linear entropy (1). Notice that this consideration recovers the arbitrary exclusion of the summation in Eq.…”

Section: Saddle Point Methodsmentioning

confidence: 99%

“…Because of this property, we also call these four trajectories, used to evaluate the semiclassical linear entropy, as entangled-boundary-condition trajectories, in accordance with the nomenclature adopted in Ref. [24]. The eight equalities of Eq.…”

Section: Saddle Point Methodsmentioning

confidence: 99%

“…There is a vast literature concerning the application of semiclassical approximations to the forward quantum propagator K + , for both canonical and spin degrees of freedom [40][41][42][43][44][45][46][47][48][49][50][51][52][53]. On the other hand, concerning the backward propagator K − , we point out that we have worked with its semiclassical version in the last decade [17,19,24,54]. Very shortly, to deduce a semiclassical expression for K ± , one starts from its path integral formulation, identifying, under proper assumptions (j → ∞ and/or → 0), certain classical trajectories as the critical paths of integration.…”

Section: B Semiclassical Propagatormentioning

confidence: 96%

“…The comprehension of this process will clarify aspects of the quantum-classical connection related to the entanglement phenomenon. As an effort to unravel this issue, in the present section, we will explore the vicinity of the real contributing trajectory, searching for complex trajectories satisfying the boundary conditions (23) and (24).…”

Section: Sets Of Quasi-real Trajectoriesmentioning

confidence: 99%

“…In the present paper, we semiclassically investigate the entanglement dynamics between two spins, adding new elements in this research field. Our work can be seen as an extension of another contribution [24], where only canonical degrees of freedom were considered. Here, we contemplate spin variables.…”

Section: Introductionmentioning

confidence: 99%

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Entanglement dynamics of spins using a few complex trajectories

Scherer,

Ribeiro

2021

Preprint

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In this work, we consider two spins initially prepared in a product of coherent states and study their entanglement dynamics due to a general interacting Hamiltonian. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator, assumed as an entanglement quantifier. The resulting expression depends on sets of four trajectories, originated from the underlying classical description, and having mutually connected final phase-space points. Such classical elements, which are capable to reproduce the quantum entanglement even for long values of propagation time, arise when we assume a proper analytical continuation of the classical phase space onto a complex domain. We apply this theory to a particular physical system, showing that taking into account only a few sets of complex trajectories is enough to get an excellent agreement between the semiclassical linear entropy of the reduced density operator and its quantum counterpart.

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Section: Saddle Point Methodsmentioning

confidence: 99%

Section: Saddle Point Methodsmentioning

confidence: 99%