Experimental Distribution of Entanglement with Separable Carriers

The key requirement for quantum networking is the distribution of entanglement between nodes. Surprisingly, entanglement can be generated across a network without direct transfer—or communication—of entanglement. In contrast to information gain, which cannot exceed the communicated information, the entanglement gain is bounded by the communicated quantum discord, a more general measure of quantum correlation that includes but is not limited to entanglement. Here, we experimentally entangle two communicating parties sharing three initially separable photonic qubits by exchange of a carrier photon that is unentangled with either party at all times. We show that distributing entanglement with separable carriers is resilient to noise and in some cases becomes the only way of distributing entanglement through noisy environments.

Figure 1

(Quantum) communication scenario. Alice locally interacts her system $A$ with the carrier system $C$, which is then sent to Bob’s site. It is possible to establish entanglement between their respective laboratories even though there was no initial entanglement between them and no entanglement is communicated. This is accomplished as follows: In step (1), the fully separable initial state of the three systems is prepared. In step (2), Alice applies a suitable operation on $A$ and $C$, which keeps the latter separable from the rest of the systems but creates entanglement between $A$ and joint systems made out of $B$ and $C$ together. In step (3), the unentangled carrier $C$ is transmitted to Bob. As shown in panel (4), this establishes entanglement between the laboratories of Alice and Bob.

Figure 2

Entanglement distribution scheme. (a) Equivalent quantum circuit diagram for our protocol. (b) Two pairs of single photons at 820 nm are created via spontaneous parametric down-conversion in a $\beta$–barium borate crystal (BBO) pumped by a frequency-doubled femtosecond Ti:sapphire laser. One photon serves as a trigger, while the other three are initialized with polarizing beam splitters (PBS) and half-wave (HWP) and quarter-wave plates (QWP). The photons representing systems $A$ and $C$ are subjected to a probabilistic controlled-phase gate based on two-photon interference at a partially polarizing beam splitter (PPBS) [23]. Projective measurements are carried out with a combination of HWPs, QWPs, and PBSs, before the photons are detected by singe-photon avalanche photodiodes (APD) connected to a coincidence logic.

Figure 3

Real (left) and imaginary (right) parts of the output state ${\beta }_{ABC}$. (a) Experimental density matrix, obtained via three-qubit state tomography. (b) Ideal density matrix. The fidelity between (a) and (b) is 98%, see text.

Figure 4

(a) Minimum eigenvalue after partial transposition ${\lambda }^{\min }$ for each bipartition of ${\beta }_{ABC}$, against a white-noise admixture $p$. The dash-dotted (dashed) black lines show the theoretical values for infinite counts for the $A|BC$ ($C|AB$ and $B|AC$) bipartitions, respectively. Error bars represent 1 standard deviation of the distributions described in (b). (b) ${\lambda }^{\min }$ for $p=0.1667$, with experimental data (solid lines) and Monte Carlo distribution (histogram) based on a population of 10 000 tomographic reconstructions with Poissonian variation of the measured counts. (c) Proportion of the Monte Carlo population for which only bipartition ${\beta }_{A|BC}$ has ${\lambda }^{\min }<0$. The solid line is a guide to the eye constructed by ideally adding white noise to the $p=0$ experimental state. (d) Box-and-whisker plot representing the fidelity distribution of the theoretical state with the Monte Carlo population for $p=0.1667$; the whiskers indicate maximum and minimum values. The data point represents the fidelity of the experimentally obtained state with the ideal one. See Sec. III of [27] for a discussion of statistical effects of limited photon counts in our experiment.