Strategies for entanglement distribution in optical fiber networks

TL;DR

The paper addresses how to distribute entanglement over optical-fiber networks by comparing direct entanglement distribution (DED) with two entanglement distribution via separable states (EDSS) protocols that use a non-entangled carrier. It develops realistic models for photon loss and depolarizing fiber noise, analyzes node architectures, and computes distillable entanglement and entanglement-generation rates after distillation, using DEJMPS as the distillation protocol. The key findings show that DED is generally more robust to noise, while EDSS1 can outperform DED in rate when the optical-CNOT gate success probability is high (P > ~0.388); EDSS2 yields high raw pair counts but much lower distillable entanglement and rates. These results delineate regimes where EDSS is advantageous and inform the design of quantum-network nodes, gates, and distillation strategies for scalable quantum communications, especially under realistic loss and noise conditions.

Abstract

Distributing entanglement over long distances remains a challenge due to its fragility when exposed to environmental effects. In this work, we compare various entanglement distribution protocols in a realistic noisy fiber network. We focus specifically on two schemes that only require the sending of a non-entangled carrier photon to remote nodes of the network. These protocols rely on optical CNOT gates and we vary the probability with which they can be successfully performed. Encoding our entangled states in photon polarization, we analyse the effect of depolarizing noise on the photonic states as the carrier passes through the fibers. Building a robust model of photon loss and calculating the distillable entanglement of the noisy states, we find the entanglement distribution rate. We discover that methods involving a separable carrier can reach a higher rate than the standard entanglement distribution protocol, provided that the success probability of the optical CNOT gates is sufficiently high.

Figures (11)

• Figure 1: (i) Direct entanglement distribution (DED) versus (ii) entanglement distribution via separable states (EDSS).
• Figure 2: An example six-node mesh network used to analyze DED and the EDSS-based protocols. We show the fiber link distances within the considered network.
• Figure 3: Node architecture for direct entanglement distribution (DED) in a network. Here, $\text{SPDC}_{1,2}$ stands for the spontaneous parametric down-conversion settings responsible for the generation of EPR pairs. WSS stands for wavelength-selective switch. The scheme uses a dual-SPDC-based heralded entanglement source.
• Figure 4: Node architecture for EDSS across a network. Here, $\text{DEMUX}_j$ is the $j^\text{th}$ demultiplexer. Other symbols and acronyms as in Fig. \ref{['fig:dedsource']}. The cnot gates in the encoder and decoder should be replaced by cphase gates for EDSS2 protocol.
• Figure 5: (a) Rate of entangled photon pairs distributed when considering losses in the nodes and transmission fibers. Note that for EDSS2, the state of the distributed photon pair is not maximally entangled. (b) Average photon pair distribution rate over all the node pairs as the success probability $P$ of the encoding operation increases. The vertical black dashed lines highlight the typical experimental value for the success probability of an all-optical cnot gate OBrien2003Politi2008Bao2007Li2021Pittman2003Gasparoni2004Stolz2022.