Physical Review B

Geometric constraints for orbital entanglement production in normal conductors

Sergio Rodríguez-Pérez, Marcel Novaes

Published May 9, 2012• 9 citations

Abstract

We investigate entanglement production in a generic normal conductor, connected to two single-channel left leads and two single-channel right leads. We consider the joint statistics of the number of entangled pairs produced during a given time and amount of entanglement carried by them. We find a constraint that implies that more entangled states are less likely to be detected. Namely, if $\mathcal{C}$ is the concurrence and $\mathcal{N}$ is the squared norm of the entangled state, then production occurs only if $\mathcal{N}(1+\mathcal{C})<1$. For the particular case of a chaotic cavity working as quantum entangler, we obtain explicit expressions for the joint distribution of $\mathcal{C}$ and $\mathcal{N}$, both for systems with and without time-reversal symmetry.

DOI: 10.1103/physrevb.85.205414

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Physical Review B

Geometric constraints for orbital entanglement production in normal conductors

Sergio Rodríguez-Pérez, Marcel Novaes

Published May 9, 2012• 9 citations

Publisher

Abstract

\mathcal{C}

is the concurrence and

\mathcal{N}

is the squared norm of the entangled state, then production occurs only if

\mathcal{N}(1+\mathcal{C})<1

. For the particular case of a chaotic cavity working as quantum entangler, we obtain explicit expressions for the joint distribution of

\mathcal{C}

and

\mathcal{N}

, both for systems with and without time-reversal symmetry.

DOI: 10.1103/physrevb.85.205414

Related papers

Orbital entanglement production in Andreev billiards with time-reversal symmetry

Sergio Rodríguez-Pérez, Marcel Novaes

We study orbital entanglement production in a chaotic cavity connected to four single-channel normal-metal leads and one superconducting lead, assuming the presence of time-reversal symmetry (TRS). The scattered state of two incident electrons is written as the superposition of several two-outgoing quasi-particle states, four of which are orbitally entangled in a left-right bipartition. We calculate numerically the mean value of the squared norm of each scattered state's component, as functions of the number of channels in the superconducting lead. Its behavior is explained as resulting from the proximity effect. We also study statistically the amount of entanglement carried by each pair of outgoing quasi-particles. When the influence of the superconductor is more intense, the average entanglement is found to be considerably larger than that obtained using normal cavities.We study orbital entanglement production in a chaotic cavity connected to four single-channel normal-metal leads and one superconducting lead, assuming the presence of time-reversal symmetry (TRS). The scattered state of two incident electrons is written as the superposition of several two-outgoing quasi-particle states, four of which are orbitally entangled in a left-right bipartition. We calculate numerically the mean value of the squared norm of each scattered state's component, as functions of the number of channels in the superconducting lead. Its behavior is explained as resulting from the proximity effect. We also study statistically the amount of entanglement carried by each pair of outgoing quasi-particles. When the influence of the superconductor is more intense, the average entanglement is found to be considerably larger than that obtained using normal cavities.

arXiv:1304.5920Apr 22, 20130 citations

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Physical Review BSep 13, 201013 citations

\mathcal{C}

is the concurrence and

\mathcal{N}

is the squared norm of the entangled state, then production occurs only if

\mathcal{N}(1+\mathcal{C})<1

. For the particular case of a chaotic cavity working as quantum entangler, we obtain explicit expressions for the joint distribution of

\mathcal{C}

and

\mathcal{N}

, both for systems with and without time-reversal symmetry.

We compute analytically the distributions of concurrence

\text{C}

and squared norm

\text{N}

for the production of electronic entanglement in a chaotic quantum dot. The dot is connected to the external world via one ideal and one partially transparent lead, characterized by the opacity $\ensuremath{\gamma}$. The average concurrence increases with $\ensuremath{\gamma}$ while the average squared norm of the entangled state decreases, making it less likely to be detected. When a minimal detectable norm

{\text{N}}_{0}

is required, the average concurrence is maximal for an optimal value of the opacity ${\ensuremath{\gamma}}^{\ensuremath{\star}}({\text{N}}_{0})$ which is explicitly computed as a function of

{\text{N}}_{0}

. If

{\text{N}}_{0}

is larger than the critical value ${\text{N}}_{0}^{\ensuremath{\star}}\ensuremath{\simeq}0.3693\ensuremath{\cdots}$, the average entanglement production is maximal for the completely ideal case, a direct consequence of an interesting bifurcation effect.

We compute analytically the distributions of concurrence

\bm{\mathcal{C}}

and squared norm

\bm{\mathcal{N}}

for the production of electronic entanglement in a chaotic quantum dot. The dot is connected to the external world via one ideal and one partially transparent lead, characterized by the opacity

\gamma

. The average concurrence increases with

\gamma

while the average squared norm of the entangled state decreases, making it less likely to be detected. When a minimal detectable norm

\bm{\mathcal{N}}_0

is required, the average concurrence is maximal for an optimal value of the opacity

\gamma^\star(\bm{\mathcal{N}}_0)

which is explicitly computed as a function of

\bm{\mathcal{N}}_0

. If

\bm{\mathcal{N}}_0

is larger than the critical value

\bm{\mathcal{N}}_0^\star\simeq 0.3693\dots

, the average entanglement production is maximal for the completely ideal case, a direct consequence of an interesting bifurcation effect.