Distributing Entanglement with Separable States

We experimentally demonstrate a protocol for entanglement distribution by a separable quantum system. In our experiment, two spatially separated modes of an electromagnetic field get entangled by local operations, classical communication, and transmission of a correlated but separable mode between them. This highlights the utility of quantum correlations beyond entanglement for the establishment of a fundamental quantum information resource and verifies that its distribution by a dual classical and separable quantum communication is possible.

Figure 1

Sketch of the Gaussian entanglement distribution protocol. David prepares a momentum squeezed vacuum mode $A$, a position squeezed vacuum mode $C$, and a vacuum mode $B$. He then applies random displacements (green boxes) of the $\widehat{x}$ quadrature (horizontal arrow) and the $\widehat{p}$ quadrature (vertical arrow) as in Eq. (1), which are correlated via a classical communication channel (green line). David passes modes $A$ and $C$ to Alice and mode $B$ to Bob. Alice superimposes modes $A$ and $C$ on a balanced beam splitter ${\mathrm{BS}}_{AC}$ and communicates the separable output mode $C^{\prime }$ to Bob (red line connecting Alice and Bob). Bob superimposes the received mode $C^{\prime }$ with his mode $B$ on another balanced beam splitter ${\mathrm{BS}}_{BC}$, which establishes entanglement between the output modes $A^{\prime }$ and $B^{\prime }$ (black lemniscata). Note the position of the displacement on mode $B$. In the original protocol, the displacement is performed before ${\mathrm{BS}}_{BC}$, which is depicted by the corresponding box with a dashed green line. Equivalently, this displacement on mode $B$ can be performed after ${\mathrm{BS}}_{BC}$ (the dashed arrow indicates the respective relocation of the displacement) on mode $B^{\prime }$, and even a posteriori after the measurement of mode $B^{\prime }$.

Figure 2

Sketch of the experimental setup. Used abbreviations: HWP, half-wave plate; QWP, quarter-wave plate; EOM, electro-optical modulator; BS, beam splitter; WS, Wollaston prism; and AD, analog-to-digital. State preparation: The polarization of two polarization squeezed states ($A$ and $C$) is modulated using EOMs and sinusoidal voltages from a function generator (dotted lines). The HWPs before the EOMs are used to adjust the direction of modulation to the squeezed Stokes variable, whereas the QWPs compensate for the stationary birefringence of the EOMs. Such prepared modes interfere with a relative phase of $\pi /2$ on a balanced beam splitter ${\mathrm{BS}}_{AC}$. In the last step of the protocol, the mode $C^{\prime }$ interferes with the vacuum mode $B$ on a second balanced beam splitter ${\mathrm{BS}}_{BC}$. Measurement process: A rotatable HWP, followed by a WS and a pair of detectors, from which the difference signal is taken, allows us to measure all possible Stokes observables in the ${\widehat{S}}_1\mathrm{\text{−}}{\widehat{S}}_2$ plane. To determine the two-mode covariance matrix ${\gamma }_{A^{\prime }{B}^{\prime }}$, all necessary combinations of Stokes observables are measured. Removing the second beam splitter of the state preparation allows us to measure the covariance matrix of the two-mode state ${\widehat{\rho }}_{A^{\prime }{C}^{\prime }}$. Data acquisition: To achieve displacements of the modes in the ${\widehat{S}}_1\mathrm{\text{−}}{\widehat{S}}_2$ plane, we electronically mix the Stokes signals with a phase matched electrical local oscillator and sample them by an analog-to-digital converter.

Figure 3

Entanglement distributed between modes $A^{\prime }$ and $B^{\prime }$. The experimental values for the criterion (2) are depicted in dependence of the gain factor $g$. Because of the attenuation of mode $B$ by 50%, a gain factor of about 0.5 yields a value smaller than 1, i.e., below the limit for entanglement (solid red line). The inset zooms into the interesting section around the minimum. The depicted estimated errors are so small because of the large amount of data taken.