Experimental Direct Observation of Mixed State Entanglement

We report on the direct estimation of concurrence for mixed quantum states. The used method relies on joint measurements on two copies of an entangled state. In the experimental demonstration two polarization-entangled photon pairs emitted from spontaneous parametric down-conversion are analyzed together using a linear optics controlled phase gate. We demonstrate that the measured data, without need for further numerical processing, directly yield reliable estimates, despite experimental imperfections.

Figure 1

Experimental setup for the direct measurement of concurrence. The two copies of the state are provided by two Bell-pairs originating from type II spontaneous parametric down-conversion (SPDC) processes in the spatial modes $a$, $b$ and $c$, $d$. After passing the crystal, the beam is reflected back by a UV mirror. If a photon pair is created in each of the two passages, two copies of an entangled state are obtained. Half- and quarter wave plates in conjunction with polarizing beam splitters are used for the polarization analysis (PA). The projection of the subsystem parts onto the symmetric and antisymmetric state space is achieved by a measurement in the Bell basis using a controlled phase gate (CPHASE).

Figure 2

Circuit diagram for the direct measurement of concurrence. In this configuration, the circuit yields an estimation for $\mathcal{C}({\rho }_{ab})\mathcal{C}({\rho }_{cd}^{\prime })$ with ${\rho }^{\prime }=({\mathcal{H}}_2\otimes {\mathcal{H}}_5){\rho }_{cd}({\mathcal{H}}_2\otimes {\mathcal{H}}_5{)}^{†}$.

Figure 3

Bounds on concurrence ${\mathcal{C}}_{\mathrm{sim}}$ obtained with the imperfect experimental phase gate versus the smallest bound on concurrence ${\mathcal{C}}_{\min }$ that would have been observed with a perfect gate, where the minimization is taken over all initial states that give rise to following measurement outcomes: ★, ${\wp }_{--}$, ${\wp }_{+-}$; ◆, ${\wp }_{--}$, ${\wp }_{-+}$; large solid circle, ${\wp }_{--}=0.208$, ${\wp }_{-+}=0.05$; medium solid circle, ${\wp }_{--}=0.208$, ${\wp }_{+-}=0.061$; solid circle, ${\wp }_{--}=0.0208$, ${\wp }_{+-}=0.061$, ${\wp }_{-+}=0.05$.