Control Protocol for Entangled Pair Verification in Quantum Optical Networks

TL;DR

The relationship between the latency of the non-ideal IP network and the decoherence time of the quantum memories is characterized, providing a comparison of promising quantum memory technologies.

Abstract

We consider quantum networks, where entangled photon pairs are distributed using fibre optic links from a centralized source to entangling nodes. The entanglement is then stored (via an entanglement swap) in entangling nodes' quantum memories until used in, e.g., distributed quantum computing, quantum key distribution, quantum sensing, and other applications. Due to the fibre loss, some photons are lost in transmission. Noise in the transmission link and the quantum memory also reduces fidelity. Thus, entangling nodes must keep updated records of photon-pair arrivals to each destination, and their use by the applications. This coordination requires classical information exchange between each entangled node pair. However, the same fibre link may not admit both classical and quantum transmissions, as the classical channels can generate enough noise (i.e., via spontaneous Raman scattering) to make the quantum link unusable. Here, we consider coordinating entanglement distribution using a standard Internet protocol (IP) network instead, and propose a control protocol to enable such. We analyse the increase in latency from transmission over an IP network, together with the effect of photon loss, quantum memory noise and buffer size, to determine the fidelity and rate of entangled pairs. We characterize the relationship between the latency of the non-ideal IP network and the decoherence time of the quantum memories, providing a comparison of promising quantum memory technologies.

Figures (5)

• Figure 1: Quantum network integrated with IP network. After receiving entangled qubits, the entangling nodes exchange control information via IP network.
• Figure 2: This depicts a scenario where an entangled photon pair is distributed to node A and node B. Due to the difference in channel lengths from source to node A and B, when a photon arrives at node A after time $T_Q$, its paired photon is still in flight and it reaches node B after time $T_Q+\Delta T_{Q}$. $T_C$ is the latency of classical channel (IP network) over which information exchange happens to verify photon pair reception.
• Figure 3: Degradation of state fidelity in realistic quantum memories. Evolution of the quantum state fidelity $\mathcal{F}$ (left ordinate) with the Bell singlet state as a function of total classical latency time $T_C$. Different quantum memory technologies are characterized by $T_1$ and $T_2$ relaxation times sourced from \ref{['tab:tab1']}. Technologies are ordered by decreasing $T_2$ times, highlighting the impact of $T_2$-error dominance ($T_1 \gg T_2$). Dotted black line indicates the threshold value $\mathcal{F} = 0.81$ required for QKD. Shaded pink region shows the distribution of IP network latencies for the Dublin Metro Area. Probability density (right ordinate) is fitted to the empirical data extracted from ookla2024speedtest.
• Figure 4: Buffer size required for idling qubits for different node pairs. Increased network latency leads to higher consumption of quantum memory slots due to longer queuing delays of entangled qubits in the memory for $T_1 = 1.14~\text{s},~T_2 = 0.5~\text{s}$.
• Figure 5: Impact of timeout duration on entangled pair rates across different fidelity thresholds. The timeout for each fidelity threshold is determined by \ref{['eq:time_elapsed']} and maximum tolerable latency that maintains fidelity above the threshold is interpolated from the fidelity curve in \ref{['Fig:fidelity-fixed_latency']} for $T_1$ = 1.14 s and $T_2$ = 0.5 s. The result is shown for C-E node pair in \ref{['fig:Network_fig']}.