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Physica E Low-dimensional Systems and Nanostructures

Statistics of orbital entanglement for the full scattering state in a chaotic quantum dot

Eduardo H. Santos, Francisco A. G. Almeida

Published Nov 9, 2018• 2 citations
Publisher
DOI
10.1016/j.physe.2018.10.037

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We investigate the statistics of orbital entanglement production between electrons in a chaotic quantum dot with two-channel leads. Through a random-matrix simulation, we obtain the probability density of two entanglement measures, concurrence and entanglement formation, by varying the transparency of the contacts in the presence and absence of time-reversal invariance of the electron dynamics inside the cavity. The results suggest that orbital entanglement production is optimized by increasing the asymmetry between the transparency of the contacts, especially when time-reversal invariance is broken.
The production of orbitally entangled electrons in quantum-chaotic dots is investigated from a statistical point of view. The degree of entanglement is quantified through the concurrence and the entanglement of formation. We calculate the complete statistical distributions of the entanglement measures by using random matrix theory. Simple analytical expressions are provided for the concurrence distributions. We identify clear signatures of time-reversal invariance in the production of entanglement at the level of the entanglement-measure distributions, such as the ability of producing maximally entangled (Bell) states, which passed unnoticed in previous works, where only the first two moments of the distributions were studied.
It has recently been shown theoretically that elastic scattering in the Fermi sea produces quantum mechanically entangled states. The mechanism is similar to entanglement by a beam splitter in optics, but a key distinction is that the electronic mechanism works even if the source is in local thermal equilibrium. An experimental realization was proposed using tunneling between two edge channels in a strong magnetic field. Here we investigate a low-magnetic field alternative, using multiple scattering in a quantum dot. Two pairs of single-channel point contacts define a pair of qubits. If the scattering is chaotic, a universal statistical description of the entanglement production (quantified by the concurrence) is possible. The mean concurrence turns out to be almost independent on whether time-reversal symmetry is broken or not. We show how the concurrence can be extracted from a Bell inequality using low-frequency noise measurements, without requiring the tunneling assumption of earlier work.