Geometric constraints for orbital entanglement production in normal conductors

Rodríguez-Pérez, S.; Novaes, Marcel

doi:10.1103/physrevb.85.205414

Cited by 10 publications

(11 citation statements)

References 21 publications

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“…The distribution can be computed generalizing the procedure used in [13] for the ideal case. The general solution can then be written in this form…”

Section: Joint Distribution Of Concurrence and Squared Normmentioning

confidence: 99%

“…3). The simultaneous increase in the average entanglement of the two-qubit state and decrease in the average likelihood to detect it is the statistical analogue of the geometrical inequality N(1 + C) < 1, first discovered for ideal leads [13]. However, having now a tunable parameter (the opacity γ) at our disposal it is natural to ask whether the two competing effects above may be used to optimize the entanglement production process.…”

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confidence: 98%

“…The full distribution of the concurrence (again in the case of ideal leads) was computed by Gopar and Frustaglia [12], and indeed they found remarkable differences in the distributions between the cases with preserved (β = 1) and broken (β = 2) TRI (here β denotes the Dyson index of the cavity), although the first moments are only very mildly affected. Still in the domain of ideal cavities, geometrical constraints on the entanglement production were discovered in [13]. The explicit calculation of the joint distribution of concurrence and the squared norm N of the entangled state yields the relation N(1 + C) < 1, which implies that more entangled states are less likely to be detected as they are bound to have a smaller norm.…”

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confidence: 99%

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Entanglement production in nonideal cavities and optimal opacity

Villamaina

Vivo

2013

Phys. Rev. B

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We compute analytically the distributions of concurrence C and squared norm N for the production of electronic entanglement in a chaotic quantum dot. The dot is connected to the external world via one ideal and one partially transparent lead, characterized by the opacity γ. The average concurrence increases with γ while the average squared norm of the entangled state decreases, making it less likely to be detected. When a minimal detectable norm N0 is required, the average concurrence is maximal for an optimal value of the opacity γ ⋆ (N0) which is explicitly computed as a function of N0. If N0 is larger than the critical value N ⋆ 0 ≃ 0.3693 . . . , the average entanglement production is maximal for the completely ideal case, a direct consequence of an interesting bifurcation effect. The phenomenon of entanglement between spatially separated particles is probably one of the most baffling predictions of quantum mechanics. Initially, the idea that entangled quantum states could be subject to non-classical correlations was seen as a possible evidence of the incompleteness of quantum theory [1]. Nowadays, thanks to fascinating experimental developments, the reality of quantum entanglement is no longer disputed. Besides its fundamental and intellectually challenging interest, modern research on entanglement mainly focuses on its possible applications to quantum information processing, cryptography and teleportation [2, 3]. As a consequence, it is of paramount interest to discover feasible pathways for the production, manipulation, and detection of quantum entanglement in a variety of physical devices.Among the most promising routes, the entanglement in solid-state electronic systems [4, 5] plays a prominent role. As far as the production of entangled electrons is concerned, several proposals based on interacting [6] and noninteracting [7][8][9] electron mechanisms are already available. A very interesting interactionless mechanism was recently proposed by Beenakker et al. [9] where a ballistic quantum dot (see sketch in Fig. 1) is used as an orbital entangler for pairs of noninteracting electrons [10]. A quantum dot is basically a mesoscopic electronic billiard connected to the external world by two double-channel leads and brought out of equilibrium by an applied external voltage. Assuming that the classical electron dynamics inside the cavity is chaotic, experimental observables such as conductance and shot noise fluctuate from sample to sample and their statistics (about which nearly everything is known [11]) is governed by the transmission eigenvalues of the cavity.In order to quantify the degree of entanglement produced inside the cavity, one uses a standard measure C called concurrence, which is related to the violation of a Bell inequality for current correlators. The average and variance of the concurrence for a chaotic dot with ideal leads (i.e. when the tunnelling probability across the leads is unity) was computed in [9]. It was found that these two moments are practically unaffected by the breaking of t...

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“…The distribution can be computed generalizing the procedure used in [13] for the ideal case. The general solution can then be written in this form…”

Section: Joint Distribution Of Concurrence and Squared Normmentioning

confidence: 99%

mentioning

confidence: 98%

mentioning

confidence: 99%

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Entanglement production in nonideal cavities and optimal opacity

Villamaina

Vivo

2013

Phys. Rev. B

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“…Effects of quantum chaotic scattering on orbital entanglement production in quantum dots have been studied in the past [16,[18][19][20][21][22][23]. In these ballistic microstructures, electrons are elastically scattered, while the chaotic character of the scattering produces stochastic fluctuations of the orbital entanglement.…”

Section: Introductionmentioning

confidence: 99%

Orbital entanglement and electron localization in quantum wires

et al. 2014

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We study the signatures of disorder in the production of orbital electron entanglement in quantum wires. Disordered entanglers suffer the effects of localization of the electron wave function and random fluctuations in entanglement production. This manifests in the statistics of the concurrence, a measure of the produced two-qubit entanglement. We calculate the concurrence distribution as a function of the disorder strength within a randommatrix approach. We also identify significant constraints on the entanglement production as a consequence of the breaking/preservation of time-reversal symmetry. Additionally, our theoretical results are independently supported by simulations of disordered quantum wires based on a tight-binding model.

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“…[10] has argued that the two first moments of entanglement measures do not capture the full information about quantum dynamics, and the complete information about fundamental symmetries of nature emerges only on the distribution probabilities. More recently, the effects of tunneling barriers 11,12 on statistic of concurrence and joint probability distribution of concurrence and squared norm 12,13 for SB were also studied.…”

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confidence: 99%

Anomalous entanglement in chaotic Dirac billiards

Ramos¹,

Silva²,

Barbosa³

2014

Phys. Rev. B

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We present analytical and numerical results that demonstrate the presence of anomalous entanglement behavior on the Dirac Billiards. We investigate the statistical distribution of the characteristic entangled measures, focusing on the mean, on the variance and on the quantum interference terms. We show a quite distinct behavior of the Dirac Billiard compared with the non-relativist (Schrödinger) ones. Particularly, we show a very plausible Bell state and a sharp amplitude of quantum interference term on entangled electrons left from the Dirac Billiards. The results have remarkable relevance to the novel quantum dots build of materials like graphene or topological insulators.PACS numbers: 73.21.La,05.45.Mt The entanglement is one the most fundamental effect on quantum mechanics, with no classical analog 1 . Two or more particles are entangled if they support a nonlocal correlation which cannot be acquired by the dynamics of classical mechanics 2 . Because its non-classical characteristics, the control of entangled states has attracted the interest of numerous science communities 3 . The technological applications of the effect has a broad range as quantum computation, teleportation, telecommunication and cryptography [2][3][4] .A large number of mechanism to entangle electronic particles, with or without interaction, can be found in the literature 4-6 , and the quantum chaotic devices are a promising option 7,8 . In a recent work, Beenakker et al.9 proposed the possibility to entangle two noninteracting electrons using, as an orbital entangler, a quantum (Schrödinger) chaotic billiard or, as we will call henceforth, the Schrödinger Billiard (SB). They obtained the averages and variances of concurrence and entanglement. However the results were found to be nearly invariant under the presence or absence of time-reversal symmetry (TRS). This means that the quantum interference corrections (weak-localization) of two arbitrary entanglement measures are approximately null, in contrast with another physical observables of electronic transport as conductance and shot-noise power. Nevertheless, the Ref.[10] has argued that the two first moments of entanglement measures do not capture the full information about quantum dynamics, and the complete information about fundamental symmetries of nature emerges only on the distribution probabilities. More recently, the effects of tunneling barriers 11,12 on statistic of concurrence and joint probability distribution of concurrence and squared norm 12,13 for SB were also studied. 22 . Through this device, the wave functions of the electrons are described by massless Dirac equation of the corresponding relativistic quantum mechanics, instead of Schrödinger equation. The two categories of billiards show blunt differences on the corresponding electronic transport statistics, which leads us to suspect that a subtle difference occurs also on the quantum entanglement statistical moments.In this work, we analyze the concurrence and entanglement statistics of two non-interacting electro...

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Geometric constraints for orbital entanglement production in normal conductors

Cited by 10 publications

References 21 publications

Entanglement production in nonideal cavities and optimal opacity

Entanglement production in nonideal cavities and optimal opacity

Orbital entanglement and electron localization in quantum wires

Anomalous entanglement in chaotic Dirac billiards

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