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arXiv:cond-mat/0303209 · Physical Review Letters

Lower Bound for Electron Spin Entanglement from Beam Splitter Current Correlations

Guido Burkard, Daniel Loss

Published Aug 22, 2003• 51 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.91.087903

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We report experimental research into the possibility of using shot noise mea-surements to detect the entangled states of electron spins. The study is part of the effort towards the demonstration of the use of electron spins as quantum bits (qubits) for quantum computing and quantum information processing. Electrons are electrically injected into two neighboring quantum dots and interact with each other through the exchange coupling, after which they tunnel out of the dots and are incident on a beam splitter, which introduces quantum interference between electron states. Depending on the state of the electrons exiting the dots, the outgoing states of electrons scattering off the beam splitter are different, corresponding to different shot noise in the electrical currents flowing into the channels after the beam splitter. Our experimental data is consistent with most theoretical predictions and provides initial evidence of electron spin entanglement. A comprehensive study of the shot noise in mesoscopic semiconductor tunnel barriers is also reported. Besides the theoretically predicted full shot noise, sup-pressed and enhanced shot noise are also observed. Normal conductance measure-ments and numerical simulations are done to understand the shot noise deviation. Our study shows that shot noise in mesoscopic systems is extremely sensitive to the microscopic details, such as potential disorder and impurity configuration.
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.
In this article, we have discussed about the scattering of charge and spin in spin-resolved mesoscopic systems. We have proposed a method to generate and detect the entanglement of electronic spin and electronic orbital degrees of freedom. It is observed that in a spin-resolved mesoscopic system, all form of entanglement existing between different electronic degrees of freedom can be generated. A method to detect Bell's inequality violation in terms of zero frequency current cross-correlators has been mentioned. Further, we have also studied the effect of quantum interference between spin flip and non-spin flip scattering matrices in determining the current and noise. We have obtained the expression for shot noise of spin and charge current when an arbitrarily polarised charge current is scattered at the spin resolved potential.
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