Entanglement localization after coupling to an incoherent noisy system

We report the experimental realization of entanglement localization which restores the polarization entanglement completely redirected after a linear coupling with incoherent and noisy surrounding photon. The method based only on measurements of the surrounding photon after the coupling and on postselection can localize the entanglement back to original systems for any linear coupling.

Figure 1

(Color online) Schematic representation of the entanglement localization procedure. The first dashed box (from left) indicates the inaccessible surrounding system.

Figure 2

(Color online) Experimental setup [10]. The main source of the experiment is a Ti:sapphire mode-locked laser with wavelength (wl) $\lambda =795\text{nm}$. A small portion of the laser beam generates the single noise photon over the mode $k_E$ using an attenuator (Att), which gives rise to a mean photon number equal to $\overline{n}=0.1$. Hence, single-photon contribution is achieved a posteriori. The main part of the laser beam passes through the second-harmonic generation (SHG) where a bismuth borate (BiBO) crystal generates a UV laser beam having wave vector $k_p$ and wl ${\lambda }_p=397.5\text{nm}$ with power equal to 800 mW. The transformation used to map the state ${|H⟩}_E$ into ${\rho }_E=\frac{I_E}{2}$ is achieved through a stochastically rotated $\lambda /2$ waveplate [11]. The trombone is used to randomly shift the surrounding single photon $E$ out of the coherence time of the photon B. The UV laser beam pumps a 1.5-mm-thick nonlinear crystal of $\beta$-barium borate (BBO) cut for type II phase matching which generates polarization-entangled pairs with equal wavelength $\lambda =795\text{nm}$ [12]. The dashed boxes indicate the polarization analysis setup adopted by Alice and Bob. The photons are coupled to a single mode fiber and detected by single-photon counting modules $D_i$. On output modes $k_B$ and $k_E$, the photons are filtered adopting filters (IF) with $\Delta \lambda =3\text{nm}$ centered at 795 nm, while on mode $k_A$ $\Delta \lambda =4.5\text{nm}$ for the distinguishable photons.

Figure 3

(Color online) Concurrence between $A$ and $B$ versus $T$ after the coupling with an incoherent unpolarized (distinguishable) photon $E$: before measurement on $E$ (dotted line), after measurement on $E$ (dashed-dotted line), after measurement on $E$ and filtration with $\epsilon =0.15$ on $A,B$ (dashed line), and after measurement on $E$ and filtration with $\epsilon \to 0$ on $A,B$ (continuous line).

Figure 4

(Color online) Experimental density matrix for distinguishable photons: (a) ${\tilde{\rho }}_{AB}^{in}$, $\left(I\right)$ ${\tilde{\rho }}_{AB}^I$, $\left(II\right)$ ${\tilde{\rho }}_{AB}^{II}$, and $\left(III\right)$ ${\tilde{\rho }}_{AB}^{III}$. We reconstruct the two-qubit density matrix ${\rho }_{AB}$ through the quantum state tomography procedure [17]. For each tomographic setting, the measurement lasts from (a) 5 s to $\left(III\right)$ 30 min; the latter case corresponding to about 500 triple coincidences.