Counting statistics for entangled electrons

Taddei, F.; Fazio, Rosario

doi:10.1103/physrevb.65.075317

Cited by 72 publications

(86 citation statements)

References 22 publications

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“…For α = 0 and α = 1 at T B = 1 the third cumulant is zero for every angle both for entangled and for mixed states (the probability distribution of the current is symmetric for those parameters as was previously noted in the α = 0 case in Ref. [21] Fig. 4 as a function of the transmission between left and right arms T B (where simple backscattering has been considered).…”

Section: Higher Order Cumulantsmentioning

confidence: 88%

“…It relied on the use of the mentioned Pauli blocking mechanism in a perfect four-arm beam splitter supplemented by the bunching (antibunching) behavior expected for symmetric (antisymmetric) spatial two-electron wavefunctions. This was done through the analysis of current noise [19], cross-correlators [20], and full counting statistics (FCS) [21]. It was also shown that it is possible to distinguish between different incoming entangled states [20,22].…”

Section: Introductionmentioning

confidence: 99%

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Effect of inelastic scattering on spin entanglement detection through current noise

San-José

Prada

2006

Phys. Rev. B

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We study the effect of inelastic scattering on the spin entanglement detection and discrimination scheme proposed by Egues, Burkard, and Loss [Phys. Rev. Lett. 89, 176401 (2002)]. The finitebackscattering beam splitter geometry is supplemented by a phenomenological model for inelastic scattering, the charge-conserving voltage probe model, conveniently generalized to deal with entangled states. We find that the behavior of shot-noise measurements in one of the outgoing leads remains an efficient way to characterize the nature of the non-local spin correlations in the incoming currents for an inelastic scattering probability up to 50%. Higher order cumulants are analyzed, and are found to contain no additional useful information on the spin correlations. The technique we have developed is applicable to a wide range of systems with voltage probes and spin correlations.

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Section: Higher Order Cumulantsmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Effect of inelastic scattering on spin entanglement detection through current noise

San-José

Prada

2006

Phys. Rev. B

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“…Bunching (enhanced) and antibunching (suppressed) behavior in the shot noise were predicted for spin singlet and triplet entangled states, respectively [3]. The role of entanglement was later analyzed in the whole probability distribution of the current fluctuations (being the noise power only its second moment) [4]. Further analysis were subsequently performed in the presence of spin-orbit coupling [5], and for states generated in an Andreev double-dot entangler [6].…”

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confidence: 99%

Characterizing electron entanglement in multiterminal mesoscopic conductors

et al. 2007

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We show that current correlations at the exit ports of a beam splitter can be used to detect electronic entanglement for a fairly general input state. This includes the situation where electron pairs can enter the beam splitter from the same port or be separated due to backscattering. The proposed scheme allows to discriminate between occupation-number and degree-of-freedom entanglement.PACS numbers: 03.65. Ud,03.67.Mn, Generation, manipulation and detection of entangled electrons is central for realizing integrated solid-state quantum computers. Among the several possibilities, a lot of attention has been devoted to the study of entanglement in multiterminal mesoscopic conductors (see Refs. [1, 2] for a review). In this context, it was shown that entanglement between spatially separated electrons can be detected by means of a beam splitter (BS) [3]. Indeed the BS, allowing the incoming (and possibly entangled) electrons to be interchanged, gives rise to twoparticle interference effects. As a result, the symmetry of the incoming state influences the current-noise correlations at the exit ports. Bunching (enhanced) and antibunching (suppressed) behavior in the shot noise were predicted for spin singlet and triplet entangled states, respectively [3]. The role of entanglement was later analyzed in the whole probability distribution of the current fluctuations (being the noise power only its second moment) [4]. Further analysis were subsequently performed in the presence of spin-orbit coupling [5], and for states generated in an Andreev double-dot entangler [6]. More recently, Burkard and Loss [7] found a bound for the entanglement of arbitrary mixed spin states through shot-noise measurements by applying a reduction mapping into Werner states [8]. We generalized this result to multi-mode input states by introducing an electronic Hong-Ou-Mandel interferometer [9].All the previous analysis rely on the assumption that only one electron per port enters the analyzer. Most of the electronic entangler devices proposed so far [1, 2], however, generate states having a finite probability amplitude that two electrons enter the analyzer at the same input port [10]. This gives rise to two distinct forms of entanglement: occupation-number and electronic degreeof-freedom entanglement [11,12]. Under this generalized initial condition the analysis of the entanglement is complicated by super-selection rules (SSR) induced by particle number conservation [1,11,12,13].In this paper we present a detection strategy which addresses this more general situation. As in Ref. [9], it is based on the study of current correlations at the exit ports of a BS as a function of controllable phase shifts. (1) and injects them into ports 1 and 2. The electrons are allowed to enter the analyzer from the same port (cases |Φ11 and |Φ22 ), from different ports (case |Φ12 ), or in any superposition of the previous cases. Electrons propagating along lead 2 undergo an additional (orbital/spin-dependent) controllable phase shift (white circle in the figure) be...

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“…Previous works have proposed to detect the entanglement present in the spin degrees of freedom of a Cooper pair via correlation measurements. 29,[34][35][36][37][38][39][40][41][42][43] The Franson interferometer we consider here, on the other hand, is suited for probing the coherence properties of the spatial degrees of freedom of the emitted Cooper pair. By looking at the interference fringes in the coincidence counts at the output ports, varying the relevant parameters of the Franson interferometer, we can measure the pair correlation length of the emitted Cooper pair, which is proportional to Pippard's length characterizing the extension of the Cooper pair in the superconducting source, as well as the momentum of the center-of-mass motion of the emitted Cooper pair, i.e., the de Broglie wavelength of the emitted Cooper pair as a single object.…”

Section: 33mentioning

confidence: 99%

Probing Cooper pairs with Franson interferometry

Giovannetti

Yuasa

2012

Phys. Rev. B

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A setup based on the Franson optical interferometer is analyzed, which allows us to detect the coherence properties of Cooper pairs emerging via tunneling from a superconductor in contact with two one-dimensional channels. By tuning the system parameters we show that both the internal coherence of the emitted Cooper pairs, which is proportional to Pippard's length, and the de Broglie wavelength of their center-of-mass motion can be measured via current-current correlation measurements.

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Counting statistics for entangled electrons

Cited by 72 publications

References 22 publications

Effect of inelastic scattering on spin entanglement detection through current noise

Effect of inelastic scattering on spin entanglement detection through current noise

Characterizing electron entanglement in multiterminal mesoscopic conductors

Probing Cooper pairs with Franson interferometry

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