Zero-Added-Loss Multiplexing (ZALM)

• Zero-Added-Loss Multiplexing (ZALM) is a quantum entanglement architecture that uses passive spectral or temporal multiplexing to scale heralded entanglement generation without incurring additional loss.
• It leverages engineered multi-mode photon-pair sources, partial Bell-state measurements, and cross-island heralding to achieve quasi-deterministic, high-fidelity entanglement across multiple channels.
• Performance benchmarks demonstrate that ZALM delivers orders-of-magnitude improvements in entanglement rates and fidelity while reducing hardware complexity for integration with quantum networks and memories.

Zero-Added-Loss Multiplexing (ZALM) is a physical-layer entanglement distribution and multiplexing architecture that enables quasi-deterministic, high-fidelity entanglement generation by leveraging carefully engineered multi-mode sources and heralding techniques. ZALM’s central innovation is the use of passive spectral or temporal multiplexing structures—such as domain-engineered spontaneous parametric down-conversion (SPDC) sources, demultiplexers, and heralded Bell-state measurements—that enable scaling of heralded entanglement rates without introducing additional loss per multiplexed mode. The architecture enables dramatic performance improvements over both conventional single-mode entanglement sources and actively switched multiplexing approaches, establishing unprecedented end-to-end rates suitable for advanced quantum networking applications (Shapiro et al., 19 Jul 2025, Horgan et al., 29 Oct 2025, Chen et al., 2022).

1. Fundamental Principles and Physical Model

ZALM leverages multi-mode photon-pair sources, typically engineered χ^2 crystals or waveguides, to generate many disjoint, spectrally (or temporally) factorable “islands” or channels. The joint biphoton wave function for N_I spectral islands is

$$\Psi(\omega_s, \omega_i) = \sum_{n=1}^{N_I} \phi_n(\omega_s - \omega_{S_n}) \psi_n(\omega_i - \omega_{I_n}),$$

with orthonormal, nonoverlapping functions $\phi_n$, $\psi_n$. For each island $n$ and polarization $P \in \{H, V\}$, the output state is a two-mode squeezed vacuum (TMSV), tensor-product over polarizations. The photon-pair statistics per island and per polarization are characterized by

$$P_m = \frac{(G-1)^m}{G^{m+1}},\quad G = \cosh^2(r),\; G-1 = \sinh^2(r),$$

with $\langle m \rangle = G-1$ the mean photon-pair number per island per pulse (Shapiro et al., 19 Jul 2025).

By applying a partial Bell-state measurement (BSM) to the idler modes (comprising a 50:50 beamsplitter, PBSs, and spectral demultiplexers feeding partially number-resolving SPDs), the protocol heralds the presence and identity of entangled signal photons with no switch-related insertion loss, since all multiplexed channels are routed passively to their outputs (Campbell et al., 10 Apr 2024, Chen et al., 2022).

2. Heralding, Multiplexing Strategies, and Scaling

The critical advance of ZALM is the ability to achieve scalable entanglement distribution rates without increased photon loss as the number of channels increases. The probability of a correct herald per island, accounting for detector efficiency $\eta_T$, is

$$P(\mathcal{H}_n) = \frac{4 [\eta_T (G-1)]^2}{[\eta_T(G-1) + 1]^6}.$$

For same-island heralding (H and V from the same island), the total herald probability is

$$P_{\text{true}} = \frac{1}{2} \left[1 - (1 - P(\mathcal{H}_n))^{N_I}\right].$$

A central design innovation is incorporating cross-island heralding (SPCI)—allowing combinations where H and V are detected from different islands—leading to an

$$P_{\text{true}} \approx \frac{1}{2} N_I^2 P(\mathcal{H}_n) \quad (G-1 \ll 1),$$

which gives quadratic scaling ($N_I^2$) of the heralding rate in the weak squeezing regime required for high-fidelity operation under realistic losses (Shapiro et al., 19 Jul 2025). This enables high entanglement delivery rates using fewer channels and detectors compared to earlier ZALM schemes that scaled linearly in $N_I$ (Shapiro et al., 19 Jul 2025, Chen et al., 2022).

3. Loss Modeling, Bell-State Fidelity, and Trade-Offs

Loss in both the idler/Bell-state measurement arm ($\eta_T$) and the signal/receiver arm ($\eta_R$) can be modeled analytically using characteristic-function methods. For only BSM-arm loss ($\eta_R=1$), the post-heralded signal state has

$\mathcal{F} = 1,$

whereas the Bell-state fraction—probability the post-herald state is in the two-qubit Bell subspace—is

$$N_S = \frac{\eta_T(G-1) + 1}{G},\quad \mathcal{B} = \frac{N_S^6}{2 - N_S^2}.$$

To maintain $\mathcal{B} \geq 0.99$ with $\eta_T = 0.9$, low mean photon number per mode ($G-1 \approx 0.0129$) is required.

When including propagation loss to the receivers ($\eta_R < 1$), the outgoing signal-mode characteristic function is modified, and the Bell-state fidelity remains optimized for $G-1$ chosen obeying $\mathcal{F} \geq 0.99$. Under realistic satellite or fiber $\eta_R$ (e.g., 0.01 for 100 km fiber), high heralding rates ($>P_{\text{true}}\geq0.25$) are achievable with $N_I\sim28$–62 and corresponding reductions in total hardware overhead (Shapiro et al., 19 Jul 2025).

Key trade-offs center on the usable pump power (controlled by $G-1$), detector efficiency, the number of islands (channels), and the acceptable Bell-state fidelity—highlighting the importance of matching heralding rates to memory and network requirements (Shapiro et al., 19 Jul 2025, Shapiro et al., 19 Jun 2024).

4. Practical Architectures and Quantum Memory Integration

A canonical ZALM source employs two SPDC elements (often in Sagnac or waveguide configurations), whose idler and signal outputs are spectrally demultiplexed by dense wavelength division multiplexing (DWDM). Idlers are measured in the partial BSM, while the signal photons, after a programmable delay, are routed—using classically fed-forward herald information and potentially active polarization or spectral mode gates—to the appropriate quantum memory channel (Horgan et al., 29 Oct 2025, Shapiro et al., 19 Jun 2024).

The frequency and bandwidth of each heralded photon are matched to the quantum memory via active spectral conversion and bandwidth compression (e.g., using a $\chi^{(2)}$ ring resonator or push–pull Duan–Kimble cavities), ensuring high purity memory loading. The necessity for a near-separable joint spectral amplitude in each channel is emphasized for achieving high memory loading fidelities ($>99\%$), which are preserved if the mode conversion is ideal (Shapiro et al., 19 Jun 2024, Chen et al., 2022).

A key advantage is the “zero-added-loss” aspect: as each spectral mode is routed passively (not through an N:1 active optical switch), there is no scaling of loss with the number of channels, in contrast to active-multiplexing alternatives (Campbell et al., 10 Apr 2024).

5. Time-Bin and Spectral Shearing Protocols

ZALM can also be realized in a time-bin encoding using deterministic spectral shearing. Pulsed SPDC sources partition broadband emission into frequency bins, with heralded events mapped back to a single reference bin by an electro-optic phase modulator implementing a unitary shear

$$\hat S(\Delta\omega) = \exp(-i \Delta\omega \hat t).$$

This operation is shown experimentally to impart no differential phase to the time-bins if the modulation waveform is correctly aligned. The net result is $n$-fold multiplexing, with the heralding efficiency and photon transmission loss per signal remaining independent of $n$ (Chapman et al., 19 Dec 2025).

The overall success probability per pulse becomes $P_{\text{succ}} \approx n P_p \eta_H$ for $n$ channels and low per-channel pair production probability $P_p$. This enables multiplexed, lossless scaling of heralded entanglement sources suitable for fiber and free-space quantum repeater architectures (Chapman et al., 19 Dec 2025).

6. Simulation, Performance Benchmarks, and Codesign

Comprehensive simulation of ZALM sources is performed using discrete-event network simulators (e.g., NetSquid + QSI interfaces), with realistic models for SPDC emission, filtering, interference, delays, polarization gates, and fiber attenuation. Key performance metrics include the entangled-bit rate per use ($R$), fidelity ($F$), and their dependencies on SPDC bandwidth, channel number, link loss, detector efficiency, and emission probability (Horgan et al., 29 Oct 2025).

Performance evaluation shows that, for identical pump and total detection rates, ZALM delivers orders-of-magnitude improvement in end-to-end entanglement rates and maintains $F\gtrsim0.99$ even in high-loss regimes, outperforming legacy approaches by more than five orders of magnitude (Shapiro et al., 19 Jul 2025). Codesign guidelines emphasize matching SPDC bandwidth to memory bandwidth, careful DWDM grid selection, optimal feedforward timing, and the use of photon-number-resolving detectors for maximal heralding yield (Horgan et al., 29 Oct 2025).

7. Generalizations: Beyond Photonic Quantum Networks

Zero-Added-Loss Multiplexing has direct analogs in classical and quantum relay networks, including the successive relaying protocol with repetition coding for wireless networks (0705.3261). In this context, ZALM’s principle is realized by a carefully timed handoff schedule, which recovers multiplexing loss present in conventional half-duplex systems. The multiplexing gain recovers to the direct-link value (up to a vanishing $1/(L+1)$ penalty as the relay block size $L$ increases), while retaining significant diversity—providing “zero added loss” even in network settings outside photonic quantum communication (0705.3261).

ZALM has also been shown to enhance alternative entanglement distribution protocols, such as those exploiting separable states for entanglement via correlation transfer, by maximizing the multiplexing efficiency under varying channel and memory noise conditions (Campbell et al., 10 Apr 2024).

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References:

• (Shapiro et al., 19 Jul 2025) High-fidelity, quasi-deterministic entanglement generation using phase-matched spectral islands in a zero-added-loss multiplexing architecture
• (Horgan et al., 29 Oct 2025) A Zero Added Loss Multiplexing (ZALM) Source Simulation
• (Shapiro et al., 19 Jun 2024) Entanglement source and quantum memory analysis for zero added-loss multiplexing
• (Chen et al., 2022) Zero-Added-Loss Entangled Photon Multiplexing for Ground- and Space-Based Quantum Networks
• (Chapman et al., 19 Dec 2025) Zero-added-loss entanglement multiplexing using time-bin spectral shearing
• (0705.3261) Recovering Multiplexing Loss Through Successive Relaying Using Repetition Coding
• (Campbell et al., 10 Apr 2024) Entanglement distribution through separable states via a zero-added-loss photon multiplexing inspired protocol