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arXiv:cond-mat/0702519 · Physical Review B

Characterizing electron entanglement in multiterminal mesoscopic conductors

Vittorio Giovannetti, Diego Frustaglia, Fabio Taddei, Rosario Fazio

Published Jun 25, 2007• 17 citations
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Abstract

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 us to discriminate between occupation-number and degree-of-freedom entanglement.

DOI
10.1103/physrevb.75.241305

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We show that multimode entanglement of electrons in a mesoscopic conductor can be detected by a measurement of the zero-frequency current correlations in an electronic Hong-Ou-Mandel interferometer. By this means, one can further establish a lower bound to the entanglement of formation of two-electron input states. Our results extend the work of Burkard and Loss [Phys. Rev. Lett. 91, 087903 (2003)] to many channels and provide a way to test the existence of entangled states involving both orbital and spin degrees of freedom.
We determine a lower bound for the entanglement of formation of pairs of electron spins injected into a mesoscopic conductor. The bound can be expressed in terms of experimentally accessible quantities, the zero-frequency current correlators (shot noise power or cross correlators) after transmission through an electronic beam splitter and can be used to gain information about the entanglement from experiment. Spin relaxation (T1 processes) and decoherence (T2) during the ballistic coherent transmission of carriers are taken into account within Bloch theory. A variable inhomogeneous magnetic field gives rise to a useful lower bound for the entanglement of arbitrary states. The decrease in entanglement due to thermally mixed states is studied. Both the entanglement of the output of a source (entangler) and T(1,2) can be determined from current correlators.
A Cooper-pair or electron-hole splitter is a device capable of spatially separating entangled fermionic quasiparticles into mesoscopic solid-state systems such as quantum dots or quantum wires. We theoretically study such a splitter based on a pair of helical Luttinger liquids, which arise naturally at the edges of a quantum spin Hall insulator. Equipping each helical liquid with a beam splitter, current-current cross correlations can be used to construct a Bell inequality whose violation would indicate nonlocal orbital entanglement of the injected electrons and/or holes. Due to the Luttinger-liquid correlations, however, the entanglement is suppressed depending on ambient temperature and voltage bias.
We discuss various approaches to create and detect electron spin entanglement, with a special emphasis on the study of the efficiency of a beam splitter as a detector for entangled electron pairs. In particular, we focus on the consequence of considering wavepacket states for the electrons as they enter the beam splitter in order to illustrate their particle characteristics. We then introduce double quantum dot as a possible source of spin entangled electrons. In particular, we show that a double quantum dot turnstile is, in principle, an efficient electron spin entangler or entanglement filter because of the exchange coupling between the dots and the tunable input/output potential barriers.
Entanglement acts as a fundamental resource for many applications in quantum communication. We propose and theoretically analyze methods for preparing and detecting entanglement between the spins of electrons in a mesoscopic environment. The entanglement production mechanism which we present is based on two quantum dots coupled to a superconductor from which paired electrons are injected via Andreev tunneling. The spin-correlated electrons can then hop from the quantum dots into normal leads. For detection we propose to measure the shot noise which is produced by the entangled electrons after they have passed a beam splitter. The enhancement of the noise by a factor of two turns out to be a unique signature for the spin singlet, a maximally entangled state. In a different setting, the entangled ground state in two tunnel-coupled quantum dots is detected via the Aharonov–Bohm oscillations in the co-tunneling current.