Spin entanglement loss by local correlation transfer to the momentum

We show the decrease of spin-spin entanglement between two $s=\frac{1}{2}$ fermions or two photons due to local transfer of correlations from the spin to the momentum degree of freedom of one of the two particles. We explicitly show how this phenomenon operates in the case where one of the two fermions (photons) passes through a local homogeneous magnetic field (optically active medium), losing its spin correlations with the other particle.

Figure 1

(Color online) Negativity $N$ in Eq. (6) as a function of ${\theta }_{{\mathbf{p}}_1}$ and ${\theta }_{{\mathbf{p}}_2}$.

Figure 2

Sketch of the two-fermion case explained in the text. Fermion $A$ traverses a constant magnetic field ${\mathbf{B}}_0$ located in region $\mathcal{D}$ with a width $L$ along the direction of ${\mathbf{p}}_0^{\left(a\right)}$.

Figure 3

(Color online) Negativity $N$ in Eq. (19) as a function of $\gamma B_0$ for $m=100$, $p_0^{\left(a\right)}=10$, $L=3$, and ${\sigma }^{\left(a\right)}=1$, 2, and 3. The higher curves correspond to the thinner $\sigma$’s. All quantities are given in $0.1p_0^{\left(a\right)}$ units.

Figure 4

(Color online) Negativity $N$ in Eq. (19) as a function of $L$ for $m=100$, $p_0^{\left(a\right)}=10$, $\gamma B_0=0.2$, and ${\sigma }^{\left(a\right)}=2$. All quantities are given in $0.1p_0^{\left(a\right)}$ units.

Figure 5

(Color online) Negativity $N$ in Eq. (24) as a function of $\tilde{B}L$ for $p_0=10$, $\sigma =2$, and $w_0=10$. All quantities are given in $0.1p_0$ units.

Figure 6

(Color online) Negativity $N$ in Eq. (24) as a function of $\sigma$ for $p_0=10$, $\tilde{B}L=4$, and $w_0=10$. All quantities are given in $0.1p_0$ units.

Figure 7

(Color online) Negativity $N$ in Eq. (24) as a function of $w_0$ for $p_0=10$, $\tilde{B}L=2$, and $\sigma =0.5,1,2$. The higher curves correspond to wider $\sigma$’s. All quantities are given in $0.1p_0$ units.