No Arabic abstract
We report the first experimental realization of entanglement swapping over large distances in optical fibers. Two photons separated by more than two km of optical fibers are entangled, although they never directly interacted. We use two pairs of time-bin entangled qubits created in spatially separated sources and carried by photons at telecommunication wavelengths. A partial Bell state measurement is performed with one photon from each pair which projects the two remaining photons, formerly independent onto an entangled state. A visibility high enough to violate a Bell inequality is reported, after both photons have each travelled through 1.1 km of optical fiber.
Transferring entangled states between photon pairs is essential for quantum communication technologies. Semiconductor quantum dots are the most promising candidate for generating polarization-entangled photons deterministically. Recent improvements in photonic quality and brightness now make them suited for complex quantum optical purposes in practical devices. Here we demonstrate for the first time swapping of entangled states between two pairs of photons emitted by a single quantum dot. A joint Bell measurement heralds the successful generation of the Bell state $Psi^+$ with a fidelity of up to $0.81 pm 0.04$. The states nonlocal nature is confirmed by violating the CHSH-Bell inequality. Our photon source is compatible with atom-based quantum memories, enabling implementation of hybrid quantum repeaters. This experiment thus is a major step forward for semiconductor based quantum communication technologies.
We construct a theory for long-distance quantum communication based on sharing entanglement through a linear chain of $N$ elementary swapping segments of length~$L=Nl$ where $l$ is the length of each elementary swap setup. Entanglement swapping is achieved by linear optics, photon counting and post-selection, and we include effects due to multi-photon sources, transmission loss and detector inefficiencies and dark counts. Specifically we calculate the resultant four-mode state shared by the two parties at the two ends of the chain, and we derive the two-photon coincidence rate expected for this state and thereby the visibility of this long-range entangled state. The expression is a nested sum with each sum extending from zero to infinite photons, and we solve the case $N=2$ exactly for the ideal case (zero dark counts, unit-efficiency detectors and no transmission loss) and numerically for $N=2$ in the non-ideal case with truncation at $n_text{max}=3$ photons in each mode. For the general case, we show that the computational complexity for the numerical solution is $n_text{max}^{12N}$.
We report entanglement swapping with time-bin entangled photon pairs, each constituted of a 795 nm photon and a 1533 nm photon, that are created via spontaneous parametric down conversion in a non-linear crystal. After projecting the two 1533 nm photons onto a Bell state, entanglement between the two 795 nm photons is verified by means of quantum state tomography. As an important feature, the wavelength and bandwidth of the 795 nm photons is compatible with Tm:LiNbO3-based quantum memories, making our experiment an important step towards the realization of a quantum repeater.
We develop a theory and accompanying mathematical model for quantum communication via any number of intermediate entanglement swapping operations and solve numerically for up to three intermediate entanglement swapping operations. Our model yields two-photon interference visibilities post-selected on photon counts at the intermediate entanglement-swapping stations. Realistic experimental conditions are accommodated through parametric down-conversion rate, photon-counter efficiencies and dark-count rates, and instrument and transmission losses. We calculate achievable quantum communication distances such that two-photon interference visibility exceeds the Bell-inequality threshold.
A 2015 experiment by Hanson and Delft colleagues provided further confirmation that the quantum world violates the Bell inequalities, being the first Bell test to close two known experimental loopholes simultaneously. The experiment was also taken to provide new evidence of spooky action at a distance. Here we argue for caution about the latter claim. The Delft experiment relies on entanglement swapping, and our main claim is that this geometry introduces an additional loophole in the argument from violation of the Bell inequalities to action at a distance: the apparent action at a distance may be an artifact of collider bias. In the absence of retrocausality, the sensitivity of such experiments to this Collider Loophole (CL) depends on the temporal relation between the entanglement swapping measurement C and the two measurements A and B between which we seek to infer a causal connection. CL looms large if the C is in the future of A and B, but not if C is in the past. The Delft experiment itself is the intermediate case, in which the separation is spacelike. We argue that this leaves it vulnerable to CL, unable to establish conclusively that it avoids it. An Appendix discusses the implications of permitting retrocausality for the issue of causal influence across entanglement swapping measurements.