Sharing quantum nonlocality and teleportation over long distance using optical hybrid states

TL;DR

The paper presents a protocol for distributing Bell-type nonlocal correlations and performing quantum teleportation over long fiber links using optical hybrid states that couple a discrete polarization qubit with a continuous-variable coherent state. By implementing entanglement swapping at a central station, the hybrid resource yields a DV entangled pair whose CHSH violation and teleportation fidelity can be optimized under realistic transmission losses and detector inefficiencies. The analysis provides closed-form expressions for the CHSH parameter and teleportation fidelity, reveals an optimal coherent amplitude balancing success probability and loss sensitivity, and demonstrates viability up to hundreds of kilometers in fiber with practical detector efficiencies. The work highlights optical hybrid states as a promising middle ground between DV and CV approaches, offering practical paths toward long-distance quantum networks while outlining key challenges such as phase stabilization and wavelength conversion.

Abstract

We analyze sharing Bell-type nonlocal correlation between two distant parties with optical hybrid states comprising a single photon polarization state and a multiphoton coherent state. By deploying entanglement swapping over the coherent state parts at the middle station, we show that the optical hybrid states can efficiently generate a polarization-entangled state that violates Clauser-Horne-Shimony-Holt (CHSH) Bell-inequality well over a metropolitan distance. We further assess the quality of the shared entangled state in the information processing task of quantum teleportation of an unknown polarization qubit. Our results with realistic devices, embedding detection inefficiency and transmission losses, indicate the viability of faithful quantum teleportation over large distances, consistent with the quality of the shared correlation.

Figures (6)

• Figure 1: Schematic for sharing distant DV Bell-pair using optical hybrid states. Two parties, say alice and Bob, send the coherent states $\lbrace \left\vert \alpha \right\rangle, \left\vert -\alpha \right\rangle \rbrace$ to a third party in the middle, say Charlie. Subsequently, Charlie mixes the incoming signals through a balanced beam splitter followed by photon measurement by two on-off detectors. Upon receiving the information about which detectors clicks, Alice and Bob post-select the overall state to the desired form.
• Figure 2: Contour plot for the probability ($\text{Pr}$) of obtaining the shared DV state with $L_\text{ab}$ and $\alpha$. Various curves show different contour values. We consider $\eta_0=1$.
• Figure 3: Contour plot of \ref{['subfig:bell100']} Bell-CHSH violation ($\mathcal{B}>2$) and \ref{['subfig:teleport100']} quantum teleportation ($F_\text{av}>2/3$) vs lab separation ($L_\text{ab}$) and coherent amplitude ($\alpha$) with ideal detectors, i.e., $\eta_0=1$.
• Figure 4: Contour plot of \ref{['bell95']} Bell-CHSH violation ($\mathcal{B}>2$) and \ref{['teleport95']} quantum teleportation ($F_\text{av}>2/3$) vs lab separation ($L_\text{ab}$) and coherent amplitude ($\alpha$) with $5\%$ detection inefficiency, i.e., $\eta_0=0.95$.
• Figure 5: Contour plot of \ref{['bell90']} Bell-CHSH violation ($\mathcal{B}>2$) and \ref{['teleport90']} quantum teleportation ($F_\text{av}>2/3$) vs lab separation ($L_\text{ab}$) and coherent amplitude ($\alpha$) with $10\%$ detection inefficiency, i.e., $\eta_0=0.90$.