Experimental Generation of Robust Entanglement from Classical Correlations via Local Dissipation

We experimentally show how classical correlations can be turned into quantum entanglement, via the presence of dissipation and the action of a cnot gate. We first implement a simple two-qubit protocol in which entanglement production is not possible in the absence of such kind of noise, while it arises with its introduction, and is proportional to its amount. We then perform a more elaborate four-qubit experiment, by employing two hyperentangled photons initially carrying only classical correlations. We demonstrate a scheme where the entanglement is generated via local dissipation, with the advantage of being robust against local unitaries performed by an adversary.

Figure 1

(a) Two-qubit scheme: the entangled output state ${\rho }_{\text{out}}$ is generated by starting from the initial state $\frac{\mathbb{I}}{2}\otimes |0⟩⟨0|$, and using local unitaries $U_A$ and $U_C$ and a cnot gate. A local nonunital noisy element can be switched on by turning the knob. (b) The same protocol in the presence of an adversary player using a local unitary $V_A$ to try and prevent the generation of entanglement. (c) Four-qubit scheme: here ${\rho }_{AB}^d$ represents a bipartite state, diagonal in the computational basis, with the same block of gates defined in the two-qubit scenario. The aim is to switch on entanglement of ${\rho }_{\text{out}}$ with respect to the cut $AB|CD$ by exploiting local noise.

Figure 2

(a) Experimental setup for the four-qubit protocol (the two-qubit experiment employs the same apparatus with the cnot on the idler photon removed: this photon serves only as trigger). BSs: balanced beam splitters, ${\mathrm{BS}}_0$ and ${\mathrm{BS}}_3$ implement the Hadamard gates $H$; ${\mathrm{BS}}_1$ and ${\mathrm{BS}}_2$, together with the tunable attenuation filters ${\alpha }_0$, ${\alpha }_1$ and ${\alpha }_2$, constitute the amplitude damping channel ${\mathrm{\Lambda }}_{\eta }$. Path analysis of photons is performed through the phase plate $\phi$ and ${\mathrm{BS}}_4$, ${\mathrm{BS}}_5$. Polarization analysis is performed through a standard polarization tomography setup. PBS: polarizing beam splitter, HWP (QWP): half-(quarter-)wave plate. SPAD: single photon avalanche photodiode. Eve’s attack is simulated by removing ${\mathrm{BS}}_3$. (b) SPDC source. A cw 355 nm pump is injected into a type I BBO crystal, generating 710 nm correlated photon pairs through SPDC. A 4-hole mask selects path qubits; qubit $A$ ($B$) is encoded in the path of the signal (idler) photon, qubit $C$ ($D$) is encoded in the polarization of the signal (idler) photon.

Figure 3

Experimental results. (a) Two-qubit protocol: negativity $N({\rho }_{\text{out}})$ vs the noise parameter $\eta$. (b) Four-qubit protocol: expectation value $⟨W^{\prime }⟩=-⟨W⟩$ of the entanglement witness applied to ${\rho }_{\text{out}}$ as a function of $\eta$. The dashed lines correspond to a theoretical calculation that takes into account the actual experimental apparatus. The red dots represent the adversary’s best strategy. In the four-qubit case they report a simulation of the minimal amount of entanglement (quantified by $N$) that can be generated after the application of local rotations on qubits $A$ and $B$ by an adversary. Error bars are calculated from photon counting statistics (see Supplemental Material [14]).