---
title: Continuous-Variable Quantum Access Networks
url: https://www.emergentmind.com/topics/continuous-variable-quantum-access-networks
type: topic
---

# Continuous-Variable Quantum Access Networks

Continuous-variable quantum access networks are multiuser quantum communication systems that extend continuous-variable quantum key distribution and entanglement distribution from point-to-point links to access-network topologies such as passive optical networks, hub-and-spoke repeater networks, and relay-mediated star networks. They encode information in optical-field quadratures, rely on coherent detection, and exploit the fact that a coherently prepared optical field can be passively split and measured concurrently by many receivers. As a result, the subject now spans downstream broadcast access, upstream time-division access, passive simultaneous multiuser PONs, round-trip and multiband schemes, entanglement-in-the-middle networks, thermal-state and frequency-comb broadcast systems, and CV quantum switches for multi-flow entanglement service [2501.12801][2402.16044][2209.08350].

## 1. Physical basis and channel description

Continuous-variable quantum networking is built on bosonic modes whose information-bearing observables are the Hermitian quadrature operators. One widely used convention writes
\[
\hat{q}=\frac{\hat{a}+\hat{a}^\dagger}{\sqrt{2}},\qquad
\hat{p}=\frac{\hat{a}-\hat{a}^\dagger}{(\sqrt{2}i)},
\]
with \(\hbar=1\), while much of the CV-QKD literature normalizes vacuum shot noise to \(1\) SNU by choosing \(\hbar=2\) [2209.08350][2501.12801]. Gaussian states dominate access-network proposals because they are compatible with telecom lasers, electro-optic modulation, and homodyne or heterodyne detection. In the phase-space description, a coherent state has covariance \(\gamma_{\mathrm{coh}}=\mathrm{diag}(1,1)\), a squeezed state has \(\gamma_{\mathrm{sq}}=\mathrm{diag}(e^{-2r},e^{2r})\), and a two-mode squeezed vacuum is
\[
\gamma_{\mathrm{TMSV}}=
\begin{pmatrix}
V\mathbb I & \sqrt{V^2-1}\,\mathbb Z\\
\sqrt{V^2-1}\,\mathbb Z & V\mathbb I
\end{pmatrix},
\qquad
\mathbb Z=\mathrm{diag}(1,-1),
\]
with the Fock-basis form
\[
|{\chi}\rangle_{AB} = \sqrt{1-\chi^2}\sum_{n=0}^{\infty}\chi^n|n,n\rangle_{AB}
\]
used as the canonical entangled resource in repeater-oriented architectures [2501.12801][2209.08350].

The access-network relevance of CV encodings is twofold. First, by “virtue of the infinite dimensionality of the associated Hilbert space,” CV states “can enable higher communication rates compared to single photon-based qubit encodings” [2209.08350]. Second, passive optical splitting is deterministic for coherent-state CV signals. In downstream broadcast models, a beamsplitter with user-port ratio \(r\) gives an effective per-user transmittance \(T_i=T_{\mathrm{fiber}}\,r_i\), or \(T_i=T_{\mathrm{fiber}}\prod_k r_k\) for cascaded stages, with \(T_{\mathrm{fiber}}(L)=10^{-\alpha L/10}\) and equal \(m\)-way splitting incurring \(10\log_{10}m\) dB loss per user [2107.01800]. In passive-broadcast PONs, the received quadrature can therefore be modeled as
\[
X_i=\sqrt{T_i}\,X+\text{noise},
\]
which is the elementary relation underpinning downstream CV-QKD and simultaneous multiuser CV-QPON protocols [2402.16044].

For entanglement distribution rather than key distribution, the pure-loss benchmark remains fundamental. Direct transmission with TMSV states over a channel of transmissivity \(\eta\) achieves
\[
C_{\mathrm{direct}}(\eta)=-\log_2(1-\eta)\ \text{ebits/mode},
\]
with \(C(\eta)\propto\eta\) for \(\eta\ll1\). The CV repeater architecture used in the CV quantum switch replaces this scaling by end-to-end rates \(\propto\eta^{3/4}\) through multiplexed TMSV generation, quantum-scissors noiseless linear amplification, and dual-homodyne entanglement swapping [2209.08350].

## 2. Architectural families

A central architectural divide is between downstream broadcast, upstream aggregation, and relay- or entanglement-based access. In downstream CV-QKD, the transmitter is centralized at the optical line terminal and broadcasts Gaussian-modulated coherent states through a passive optical distribution network to multiple optical network units. The ODN requires only passive beamsplitters or couplers, no active switching, and either a transmitted LO or a local LO can be used at the receivers. A security reduction based on a strengthened Eve allows key extraction with one activated ONU at a time using only OLT–ONU data, while passive broadcast remains deterministic for coherent-state CV signals [2107.01800]. A different downstream model, the continuous-variable quantum passive optical network, uses the same modulated optical field for all users and exploits “the inherent wave-like property of coherent states split at a beam splitter and electric-field quadrature measurements” to achieve deterministic and simultaneous secret-key generation for all users [2402.16044].

Upstream CV access reverses the terminal roles. In the first experimental upstream transmission quantum access network, each ONU hosts a GG02 transmitter and sends a polarization-multiplexed signal and transmitted LO toward a single centralized OLT receiver through a shared ODN, with time-division multiplexing used to avoid slot collisions [2305.01966]. A round-trip variant centralizes even more hardware: the quantum line terminal launches a continuous-wave carrier, each quantum network unit is a simple plug-in modulator node, and all returned signals are recombined onto a single fiber and measured by one coherent receiver at the QLT. Multiuser separation is then performed in the RF domain by assigning each user a distinct subcarrier band on the same optical carrier [2305.05919].

Relay and entanglement-based architectures widen the access-network design space. In the untrusted-relay model, two end-users send Gaussian-modulated coherent states to a central access point that performs a CV Bell detection and broadcasts the result; security is maintained even when the relay is fully untrusted and the links are insecure [1312.4104]. In a more connected star architecture, an entangled optical frequency comb generated by a type-II OPO sits at a central node and routes signal-idler comb teeth to user pairs, yielding a fully connected multi-user CVQKD network in which simultaneous pairwise keys are limited by the number \(M\) of usable entangled pairs and full connectivity requires \(M\ge N(N-1)/2\) [2512.24718]. At larger scale, a passive thermal-state QAN replaces active Gaussian modulation by a broadband ASE thermal source, slices it into \(19\) frequency modes, and then broadcasts each slice through \(16\) power branches, creating \(304\) user channels from a single source [2605.20077].

Entanglement-service access networks also admit a hub-and-spoke repeater interpretation. The CV quantum switch is a central repeating switch that attempts heralded CV entanglement generation on each spoke, stores successful elementary links for one time step, and performs dual-homodyne entanglement swapping across selected ports under a Max-Weight scheduler. The same hub-and-spoke logic underlies multi-flow access service for bipartite entanglement requests, rather than secret-key generation alone [2209.08350].

## 3. Security models and rate formulas

The dominant security framework is reverse-reconciled CV-QKD under collective Gaussian attacks. A generic asymptotic key rate is
\[
K=\beta I_{AB}-\chi_{BE},
\]
with \(\beta\) the reconciliation efficiency, \(I_{AB}\) the classical mutual information, and \(\chi_{BE}\) Eve’s Holevo information. For coherent-state CV-QKD, standard expressions include
\[
I_{AB}^{(\mathrm{hom})}=\frac{1}{2}\log_2\!\left(\frac{V_B}{V_{B|A}}\right),
\qquad
I_{AB}^{(\mathrm{het})}=\log_2\!\left(\frac{V_B+1}{V_{B|A}+1}\right),
\]
and the input-referred total noise is often written as
\[
\chi_{\mathrm{tot}}=\chi_{\mathrm{line}}+\frac{\chi_{\mathrm{det}}}{T},
\qquad
\chi_{\mathrm{line}}=\frac{1-T}{T}+\epsilon
\]
[2107.01800]. In broadcast field trials with heterodyne detection and local LO reception, the per-user formulas are written as
\[
I_{AB,i}=\log_2\!\left(\frac{V+\chi_{\mathrm{tot},i}}{1+\chi_{\mathrm{tot},i}}\right),
\qquad
K_i=\beta I_{AB,i}-\chi_{BE,i},
\]
with the shared modulation variance \(V_A\) set before passive splitting and therefore common to all users [2606.18840].

Multiuser access modifies the adversary model. In downstream passive broadcast, other ONUs and all non-activated ODN outputs can be absorbed into a strengthened Eve \(E'\), so that the Holevo term is computed from the two-mode covariance matrix \(\gamma_{A,C_1}\) between Alice and the activated ONU, while secrecy against honest-but-curious or malicious in-network parties follows by monotonicity of the Holevo bound [2107.01800]. In untrusted-relay networks, any joint attack compatible with the observed statistics can be reduced to a scenario in which the relay performs the proper CV Bell detection and Eve attacks only the links, which is the continuous-variable measurement-device-independent reduction for this topology [1312.4104]. In CV-QPON, the untrusted broadcast protocol conservatively places the other \(N-1\) users inside Eve’s system, whereas the trusted broadcast protocol hierarchically moves selected users into a trusted subsystem, reducing \(\chi_{EB_i}\) without changing \(I_{AB_i}\) [2402.16044].

Finite-size and composable analyses are no longer peripheral. In the active \(1{:}4\) multi-user CV-QN, the composable finite-size key length for user \(B_k\) is written as
\[
\ell_k \ge n\big[\beta I_{AB_k}-\chi_{B_kE}\big]
- \mathrm{leak}_{\mathrm{EC}}
- \Delta(n,\varepsilon_{\mathrm{sec}})
- \log_2\!\left(\frac{2}{\varepsilon_{\mathrm{cor}}}\right),
\]
and the paper also introduces a chain-rule decomposition of the joint network key into per-user increments without double counting shared correlations [2604.27943]. The field QTTH trial remains asymptotically secure in its main results, but its composable simulation makes the block-length challenge explicit: for User 1 under a \(1{:}16\) split, positive composable SKR requires \(N\approx 10^{11}\) symbols under the chosen security parameters [2606.18840].

## 4. Multiple access, scheduling, and routing

Once CV links are shared, access-network control becomes a resource-allocation problem. In the entanglement-service setting, requests of type \(i\) arrive at a switch with mean \(\lambda_i\), and a matching vector \(\mathbf r\) is feasible only if no user participates in more than one served request in the same time step. The CV quantum switch chooses
\[
\mathbf{W}(n)=\arg\max_{\mathbf r\in\mathcal M}
\sum_i r_i q_i Q_i(n)\,I_{\{T_j(n)>0,\forall j\in U_i\}},
\]
where \(Q_i(n)\) is the request backlog, \(T_j(n)\in\{0,1\}\) is link availability, and \(q_i\) is the swapping success probability; in the model with dual homodyne swapping, \(q_i=1\). Under one-time-step switch memories, Max-Weight stabilizes all arrival rates in the capacity region, and explicit request-rate regions were computed for contending, partially disjoint, and fully disjoint three-flow networks [2209.08350].

Broadcast QKD access networks face a different control problem because the same modulation variance must serve heterogeneous users. The field QTTH study formulates this through the \(\alpha\)-fair utility
\[
U_{\mathrm{sys}}(V_A,\alpha)=
\begin{cases}
\sum_{j=1}^N \dfrac{\mathrm{SKR}_j(V_A)^{\,1-\alpha}}{1-\alpha}, & \alpha\neq 1,\\[6pt]
\sum_{j=1}^N \ln\!\big(\mathrm{SKR}_j(V_A)\big), & \alpha=1,
\end{cases}
\]
with the shared-variance choice \(V_A^\star(\alpha)=\arg\max_{V_A\in\mathcal V}U_{\mathrm{sys}}(V_A,\alpha)\). The limits \(\alpha\to0\) and \(\alpha\to\infty\) recover sum-rate maximization and max-min fairness, respectively; in the reported field trial, the max-min solution selected \(V_A=4.3\) SNU [2606.18840].

At the physical and MAC layers, several multiple-access schemes have been proposed. AMQD-MQA divides each user’s Gaussian-modulated input into Gaussian subcarrier CVs via an inverse CVQFT and dynamically assigns subcarriers and quadratures through a binary rate-selection matrix \(\mathbf M_{\mathcal A^{[j]}}\). In the low-SNR regime characteristic of long-distance CV-QKD, it is capacity-achieving with constant per-subcarrier modulation variance and only partial channel side information [1312.3614]. A different approach, q-CDMA-based CV-QKD, uses chaotic phase shifters and synchronization so that the intended user survives decoding with gain \(\sqrt{\eta}/2\), whereas the cross-user term is suppressed by \(\sqrt{M_1M_2\eta}/2\), with \(M_i\) determined by the chaotic phase spectrum [2502.09019].

Routing and network design also appear in entanglement-distribution models. For CV graph-state networks, the squeezing cost
\[
G(\sigma)=\sum_{i=1}^N 10\log_{10}\!\big(2\lambda_i^+(\sigma)\big)
\]
is determined by the adjacency spectrum, and homodyne routing along parallel paths can boost end-to-end entanglement; for diamond networks with \(N\) parallel paths,
\[
\nu_-^2=\frac{1}{1+2NRg^2},
\qquad
\mathcal N=\log_2(1+2NRg^2)
\]
after measuring the central nodes in \(p\) [2108.08176]. In heterogeneous fiber/free-space CVQKD networks, dynamic routing has been formulated through the link-capacity metric
\[
C=\mathrm{SKR}_{\mathrm{fin}}(t)\times t,
\]
which treats secret-key distribution as a graph problem over time-varying access and backbone links [2502.11746]. A complementary monitoring layer is provided by capacity-detection methods that certify non-zero quantum capacity of CV channels and memories without full process tomography, using either finitely squeezed states and homodyne measurements or coherent states and heterodyne detection [2108.13348].

## 5. Experimental realizations and reported regimes

Representative demonstrations already span passive broadcast, centralized upstream reception, active finite-size networks, and high-capacity passive thermal broadcasting.

| System | Topology | Reported result |
|---|---|---|
| Downstream CV-QKD access | OLT to passive ODN to ONUs | Up to 64 ONUs feasible at 30 km [2107.01800] |
| Upstream CV-QKD access | Two ONUs to one OLT via TDM | 390 kbps aggregate at 5 MHz; scaling analysis to 8 ONUs with 25 ns slots [2305.01966] |
| CV-QPON | \(1{:}8\) passive broadcast, 11 km per user | 1.5 Mbit/s untrusted and 2.1 Mbit/s trusted total network key generation [2402.16044] |
| Round-trip multi-band QAN | Single QLT laser/receiver, three simultaneous QNUs | 600–800 bits/s per user under 30 km standard fiber [2305.05919] |
| Active \(1{:}4\) finite-size CV-QN | 10 km backbone + 1 km last-mile | Total about \(1.9\times10^{-1}\) bits/channel use [2604.27943] |
| Field QTTH broadcast CV-QAN | \(1{:}16\) commercial-fiber deployment | Per-user asymptotic SKRs \(0.97\)–\(2.20\) Mbit/s; \(\approx 8.74\) Mbit/s over six analyzed users [2606.18840] |
| Thermal-state passive QAN | 19 frequency slices \(\times\) 16 branches | 13.76 Gbps @ 304 users over 5 km asymptotic; 3.60 Gbps finite-size [2605.20077] |

These demonstrations illustrate several distinct operating regimes. First, passive broadcast can already support deterministic simultaneous service over standard access fibers, with the untrusted and trusted CV-QPON protocols showing how the assumed trust hierarchy directly changes aggregate network rate [2402.16044]. Second, centralized-receiver designs remain viable in both upstream and round-trip form, but their rates are constrained by slotting, detector bandwidth, and crosstalk control [2305.01966][2305.05919]. Third, field-deployed broadcast CV-QANs have reached Mbit/s-level per-user asymptotic secure key rates over commercial fiber while explicitly confronting link asymmetry and shared-parameter optimization [2606.18840]. Fourth, passive broadcast can scale well beyond tens of users when Gaussian randomness is supplied by a single broadband thermal source instead of per-channel modulators and QRNGs [2605.20077].

A separate experimental direction emphasizes connectivity rather than fan-out. The entangled optical frequency-comb network is designed for simultaneous fully connected pairwise CVQKD, is analyzed asymptotically, and is reported to be feasible for short-distance deployment when loss and noise are tightly controlled; in that setting, loss is identified as the main performance limiter [2512.24718].

## 6. Limitations, trust assumptions, and open directions

The main constraints are now well characterized. In passive broadcast systems, splitting loss lowers per-user SNR, and in downstream security models the strengthened-Eve treatment of other ONUs increases the Holevo penalty as user count grows [2107.01800]. Field deployments add asymmetry in drop-fiber length, splitter-port imbalance, and insertion loss, so a single shared \(V_A\) cannot simultaneously optimize all users; larger splits such as \(1{:}32\) and \(1{:}64\) therefore demand lower-noise coherent receivers, higher detector efficiency, stronger coding, and tighter environmental stabilization [2606.18840]. The CV quantum switch analysis assumes unconstrained quantum resources, synchronized clocks, and one-step switch memories; the same work explicitly identifies limited hardware, memory-fidelity decay, and longer switch-memory lifetimes as open issues [2209.08350]. The frequency-comb architecture scales in spectral resources but requires \(O(N^2)\) LO generation and is limited by modulator bandwidth and waveshaper spacing [2512.24718]. Thermal-state broadcasting removes hundreds of active modulators and QRNGs, but its multimode security analysis must track residual broadcast-induced correlations and finite-size penalties [2605.20077]. CV-QPON itself still lacks a dedicated multiuser finite-size theory for broadcast operation [2402.16044].

Network-level operation raises a second set of questions. Capacity-detection methods can certify or monitor the quantum capacity of CV channels and memories without full tomography, even in finite-use, correlated, and adversarial scenarios [2108.13348]. Dynamic global CVQKD studies, by contrast, model secret-key distribution as a spatiotemporal graph problem and use link capacity as a routing metric across fiber, satellite-to-ground, inter-satellite, and underwater segments [2502.11746]. Graph-state analyses add a complementary resource perspective in which star and diamond topologies have low squeezing rank and parallel-path routing can increase delivered entanglement [2108.08176]. This suggests a unified future direction in which CV access networks are co-designed across physical-layer cost, trust model, finite-size security, and dynamic routing, rather than treated as isolated QKD links.

Source: https://www.emergentmind.com/topics/continuous-variable-quantum-access-networks