---
title: Point-to-Multipoint COW QKD Protocol
url: https://www.emergentmind.com/topics/point-to-multipoint-cow-qkd-protocol
type: topic
---

# Point-to-Multipoint COW QKD Protocol

The point-to-multipoint extension of the Coherent-One-Way (COW) Quantum Key Distribution (QKD) protocol is an experimentally validated architecture enabling a single quantum transmitter to distribute secret keys simultaneously to multiple receivers over separate channels. By leveraging component and post-processing optimizations, this protocol addresses experimental bottlenecks arising from detector limitations, while extending standard two-party QKD to a network regime suitable for secure group communication. Security analysis, implementation details, and empirical benchmarks demonstrate the protocol’s viability under realistic device constraints and collective attack models [2601.04543].

## 1. Fundamentals of the COW QKD Protocol

The Coherent-One-Way (COW) protocol encodes logical bits using time-bin qubits, where Alice—serving as the transmitter—sends either
\[
\ket{0}_t\ket{\sqrt\mu}_{t-\tau} \quad(\text{bit } 1)
\]
or
\[
\ket{\sqrt\mu}_t\ket{0}_{t-\tau} \quad(\text{bit } 0)
\]
in consecutive time bins $t$ and $t-\tau$. With probability $f$, Alice introduces "decoy" states $\ket{\sqrt\mu}_t\ket{\sqrt\mu}_{t-\tau}$ to enable quantum channel monitoring. Here, $\mu$ is the mean photon number per pulse, and $\tau = 1/F$, with $F$ the system repetition rate.

After transmission, Bob(s) announce detected pulses (time bins), Alice identifies decoys, and sifting yields a sifted-basis rate $S_Z$ (bits/s). The quantum bit error rate (QBER) is defined as
\[
e_Z = \frac{\text{erroneous detections}}{\text{all detections}}
\]
With error correction inefficiency $f \geq 1$ (e.g., $1.1\!-\!1.2$), the asymptotic Devetak–Winter bound gives the secure key rate:
\[
R \;=\; S_Z \;-\; f\,S_Z\,H_2(e_Z)\;-\;\Delta_{\mathrm{PA}}
\]
where $H_2$ is the binary entropy and $\Delta_{\mathrm{PA}}$ is the privacy amplification penalty.

## 2. Experimental Apparatus and Detector Enhancement

The experimental setup features a 1550.12 nm CW laser carved by an intensity modulator controlled at $F=1$ GHz, stabilized via a 1% bias-controller loop, and followed by two variable optical attenuators (VOA\(_1\), VOA\(_2\)) to set $\mu$. The attenuation $\alpha$ is determined by
\[
\alpha = 10 \log_{10}\left(\frac{P_f}{P_i}\right), \quad P_f = \mu F \frac{hc}{\lambda}
\]
where $P_i$ is modulator output, $\lambda=1550$ nm.

Bob, the receiver, employs a 90:10 fiber beamsplitter (BS) to route 90% of incoming photons to the data line and 10% to a monitoring interferometer (not used for this improvement). On the data line, an additional $1 \times 2$ (50:50) splitter feeds two InGaAs/InP single-photon detectors (SPDs), labeled SPD\(_a\) and SPD\(_b\), each characterized by quantum efficiency $\eta$ and dead time $\tau_d$.

Theoretical per-detector count rates (accounting for fiber loss $\alpha_d\approx0.22$ dB/km and distance $L$) are given by
\[
C_{\rm th}^{(0)} = 0.9\,\eta\,\mu\,(F/2)\,10^{-\alpha_d L/10}
\]
Factoring in detector dead time,
\[
C_{\rm th} = \frac{C_{\rm th}^{(0)}}{1 + \tau_d\,C_{\rm th}^{(0)}}
\]
Experimental rates $C_{\rm exp}$ approach $C_{\rm th}$ for a single SPD and $2\,C_{\rm th}$ for dual SPDs before saturation, thus the data line split between two SPDs mitigates the throughput limit imposed by detector dead time.

## 3. Point-to-Multipoint Network Architecture

Point-to-multipoint extension involves distributing Alice’s modulated quantum pulse train to two independent receivers (Bobs), establishing two parallel COW QKD channels. Post-attenuation, a 50:50 BS splits the modulated sequence, and each branch passes through individual attenuator chains and fiber spools of length $L$. Synchronized by a shared FPGA clock (or calibrated with fixed delay), both Bobs maintain time alignment for coherent state detection.

Each Bob's measurement setup mirrors the single-receiver configuration: a 90:10 BS, a 50:50 splitter, and two SPDs. This two-channel extension is directly compatible with generic COW protocol deployments.

## 4. Secret-Key Generation and Post-Processing Workflow

The secret-key generation process for the dual-receiver architecture comprises the following steps:

- **Sifting:** Each Bob $i$ records counts $n_0^{(i)}, n_1^{(i)}$ in non-decoy time bins; decoy bins are excluded. Sifted key rate is $S_Z^{(i)} \approx n_0^{(i)} + n_1^{(i)}$ (minus decoys).
- **Error Correction:** A disclosure ratio $\mathrm{DR}=10\%$ of sifted bits estimates $e_Z^{(i)}$. Error correction—via low-density parity-check codes—leaks $f\,S_Z^{(i)}\,H_2(e_Z^{(i)})$ bits.
- **Privacy Amplification:** With compression ratio $\mathrm{CR}$ (up to 90%), the final SKR per Bob is
  \[
  R_i = S_Z^{(i)} (1-\mathrm{DR})(1-\mathrm{CR}) - \Delta_{\mathrm{PA}}^{(i)}
  \]
- **Key Combination:** Alice aligns key lengths $|k_{A1}| = |k_{A2}|$ and broadcasts the XOR $k_{12} = k_{A1} \oplus k_{A2}$ using one-time pad. Bob 1 can reconstruct $k_{A2}$; Bob 2 reconstructs $k_{A1}$, and all three share $k_{12}$ of length $\min\{R_1, R_2\}$.
- **Aggregate Key Rate:** Since one raw key is sacrificed by XOR, the end-user shared SKR is
  \[
  R_{\rm total} = \max\{R_1, R_2\}
  \]

## 5. Empirical Performance Benchmarks

Experimental benchmarking demonstrates efficiency gains from both dual-SPD and dual-Bob approaches:

| Channel Length ($L$) | $\eta$ | $\tau_d$ ($\mu$s) | 1 SPD SKR (kb/s) | 2 SPDs SKR (kb/s) | QBER (%) |
|----------------------|--------|--------------------|------------------|-------------------|----------|
| 80 km                | 0.15   | 15                 | 2.1              | 3.7               | 3–5      |
| 100 km               | 0.20   | 20                 | 1.8              | 2.9               | 4–6      |
| 120 km               | –      | –                  | –                | 50–80% gain       | <6       |

In the dual-Bob scenario at $L=100$ km:
- For $\mu=0.5, \eta=0.2$, each Bob achieves SKR $\approx1.8$ kb/s, QBER $<5$\%.
- For $\mu=0.2$, SKR $\approx1.2$ kb/s per Bob with improved QBER.
- The shared-key rate $k_{12}$ reflects $\min \{ R_1, R_2 \}$; aggregate SKR $\approx1.8$ kb/s.

## 6. Security Analysis and Parameter Optimization

The security proof utilizes the asymptotic, collective-attack model (Devetak–Winter bound). The principal threat modeled is the collective beam-splitting attack (BSA), where Eve replaces the transmission line by a lossless channel and a beamsplitter of transmission $t_B = 10^{-\alpha_d L/10}$, retaining a mode with amplitude $\sqrt{\mu t_E}$ and inter-bit overlap $\gamma_E = e^{-\mu t_E}$. The Holevo information per pulse is
\[
\chi_E = H_2\left(\frac{1-\gamma_E}{2}\right)
\]
and Bob’s per-pulse detection probability is $p_{\rm click} = \tfrac12(1-e^{-\mu t_B \eta})$. The per-pulse secure rate is
\[
r_{\rm COW} = p_{\rm click}[1-\chi_E]
\]
In the dual-Bob configuration, a worst-case scenario is assumed: Eve attacks both branches coherently, doubling her Holevo gain $\chi_E \to 2\chi_E$.

Optimizing $\mu$ is crucial: higher $\mu$ raises Bob’s click rate but increases $\chi_E$, reducing long-distance security. For $L>80$ km in the dual-Bob scenario, $\mu=0.2$ offers superior security rates relative to $\mu=0.5$. Detector settings ($\tau_d \approx 20\!-\!50~\mu$s, $\eta \approx 0.2$) are adjusted to optimize throughput against QBER and loss constraints.

## 7. Conclusion and Practical Implications

By (i) splitting each data line into two SPDs to bypass detector saturation limits, and (ii) constructing a three-party shared key via the XOR of two independently generated keys, the point-to-multipoint COW QKD protocol demonstrates substantial increases in achievable secret-key rates and user scalability. Experimentally, QBER remains within the established threshold ($\leq$6%), and the approach is generalizable to further COW implementations. Both empirical observation and theoretical BSA-derived limits confirm that lower $\mu$ values (around 0.2) are optimal under broadcast-channel and collective attack security conditions [2601.04543].

Source: https://www.emergentmind.com/topics/point-to-multipoint-cow-qkd-protocol