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arXiv:1608.06455 · physica status solidi (b)

On‐demand entanglement generation using dynamic single‐electron sources

Patrick P. Potts, David Dasenbrook, Christian Flindt

Published Dec 7, 2016• 26 citations
arXivHTMLPDF

Abstract

Abstract We review our recent proposals for the on‐demand generation of entangled few‐electron states using dynamic single‐electron sources. The generation of entanglement can be traced back to the single‐electron entanglement produced by quantum point contacts (QPCs) acting as electronic beam splitters. The coherent partitioning of a single electron leads to entanglement between the two outgoing arms of the QPC. We describe our various approaches for generating and certifying entanglement in dynamic electronic conductors and we quantify the influence of detrimental effects such as finite electronic temperatures and other dephasing mechanisms. The prospects for future experiments are discussed and possible avenues for further developments are identified. (a) The coherent partitioning of a single electron on a QPC leads to entanglement between the outgoing arms. The entanglement can be detected using two copies of the state. (b) A time‐bin entangled state is generated by partitioning two electrons on a QPC followed by projection onto the subspace with one electron in each arm. The two‐electron entanglement is due to the entanglement of the individual single‐electron states. In both panels, circles represent single‐electron sources and squares represent detectors.

DOI
10.1002/pssb.201600582

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Abstract We review our recent proposals for the on‐demand generation of entangled few‐electron states using dynamic single‐electron sources. The generation of entanglement can be traced back to the single‐electron entanglement produced by quantum point contacts (QPCs) acting as electronic beam splitters. The coherent partitioning of a single electron leads to entanglement between the two outgoing arms of the QPC. We describe our various approaches for generating and certifying entanglement in dynamic electronic conductors and we quantify the influence of detrimental effects such as finite electronic temperatures and other dephasing mechanisms. The prospects for future experiments are discussed and possible avenues for further developments are identified. (a) The coherent partitioning of a single electron on a QPC leads to entanglement between the outgoing arms. The entanglement can be detected using two copies of the state. (b) A time‐bin entangled state is generated by partitioning two electrons on a QPC followed by projection onto the subspace with one electron in each arm. The two‐electron entanglement is due to the entanglement of the individual single‐electron states. In both panels, circles represent single‐electron sources and squares represent detectors.
We review recent theoretical investigations on the two-particle Aharonov–Bohm effect and its relation to entanglement production and detection. The difficulties of the entanglement detection due to dephasing and finite temperature are discussed regarding a recent experimental realization of a two-particle Aharonov–Bohm interferometer [15]. We also discuss a theoretical proposal for a two-particle Aharonov–Bohm interferometer, which as against the finite bias setup is driven with dynamical single-electron sources allowing for the tunable production of time-bin entanglement.
Mesoscopic shot noise is not only probabilistic: it has features which reflect quantum mechanical entanglement. We discuss recent proposals of orbital entanglement generation and detection in mesoscopic coherent conductors. Orbital entanglement avoids the difficulty of manipulating spin and leads to simpler structures. Orbital entanglement schemes invoke two two‐particle sources. The index of the source plays the role of a pseudo‐spin. The rotation of qubits can be implemented with beam‐splitters or even just quantum point contacts. Entanglement is detected via violation of a Bell inequality. The necessary correlations can be extracted from shot noise measurements.
The entanglement of coherently split electron-hole pairs in an electronic conductor is typically not considered accessible due to particle number conservation and fermionic superselection rules. We demonstrate here that current cross-correlation measurements at the outputs of an electronic Mach-Zehnder interferometer can nevertheless provide a robust witness of electron-hole entanglement. Specifically, we consider neutral excitations generated by modulating the transmission of an unbiased quantum point contact periodically in time. For an optimized modulation profile, an entangled state with one positively-charged leviton (a hole) and one negatively-charged leviton (an electron) gets delocalized over the two paths of the interferometer and is detected at the output arms. We evaluate the influence of finite electronic temperatures and dephasing corresponding to recent experiments.
We propose a method for the optimal time-controlled generation of entangled itinerant particles, using on-demand sources in a conductor in the quantum Hall regime. This entanglement pump is realized by applying periodic, tailored voltage pulses to pairs of quantum dots or quantum point contacts. We show that the pump can produce orbital Bell pairs of both electrons and holes at the optimal rate of half a pair per pumping cycle. The entanglement can be detected by a violation of a Bell inequality formulated in terms of low-frequency current cross correlations.
We investigate the generation of an entangled electron pair emerging from a system composed of two quantum dots attached to a superconductor Cooper-pair beam splitter. We take into account three processes: crossed Andreev reflection, cotunneling, and Coulomb interaction. Together, these processes play crucial roles in the formation of entangled electronic states, with electrons being in spatially separated quantum dots. By using perturbation theory, we derive an analytical effective model that allows a simple picture of the intricate process behind the formation of the entangled state. Several entanglement quantifiers, including quantum mutual information, negativity, and concurrence, are employed to validate our findings. Finally, we define and calculate the covariance associated with the detection of two electrons, each originating from one of the quantum dots with a specific spin value. The time evolution of this observable follows the dynamics of all entanglement quantifiers, thus suggesting that it can be a useful tool for mapping the creation of entangled electrons in future applications within quantum information protocols.
In this article we discuss our two recent proposals on producing and detecting of entangled states in quantum conductors. First we analyze a setup where two electrons are scattered on a quantum dot with Coulomb repulsion and became orbitally entangled. Second, for identical noninteracting particles we suggest an operating scheme for the deliberate generation of spin‐entangled electron pairs in a normal‐metal mesoscopic structure with a fork geometry. The spin‐entangled pair is created through a post‐selection in the two branches of the fork. We also make comments on different ways of producing and quantifying the degree of entanglement.