Statistics of entanglement production in a chaotic dot with non-ideal contacts

Dario Villamaina, Pierpaolo Vivo

Published Jul 19, 2012• 0 citations

Abstract

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.

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Statistics of entanglement production in a chaotic dot with non-ideal contacts

Dario Villamaina, Pierpaolo Vivo

Published Jul 19, 2012• 0 citations

OpenAlex

Abstract

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.

Related papers

Entanglement production in nonideal cavities and optimal opacity

Dario Villamaina, Pierpaolo Vivo

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 $\text{C}$ 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.

arXiv:1207.4623Physical Review BJul 3, 201311 citations

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C. W. J. Beenakker, M. Kindermann, Charles M. Marcus +1 more

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.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.

arXiv:cond-mat/0310199Kluwer Academic Publishers eBooksMar 9, 20063 citations

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.

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.

\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.