Optimal filtering and generation of entangled photons for quantum applications in the presence of noise

TL;DR

This work tackles the challenge of noise filtering in multiphoton quantum applications by coupling a quantitative JSA-filtering model with experimental demonstrations of coexisting C-band entangled photons and classical data over long fiber links. It highlights a fundamental trade-off between noise rejection and single-mode purity through the filter heralding efficiency (FHE) and introduces the pair-symmetric heralding efficiency (PSHE). By comparing filter shapes, bandwidths, and pump parameters, the study derives conditions under which maximum coincidence-to-accidental ratios (CAR) are achieved and shows how imperfect PSHE degrades performance in realistic noisy environments. The results have practical implications for scalable quantum networks, including compatibility with erbium-doped quantum memories, and point to design strategies—such as flat-top filtering and mode-selective or coherent filtering—to optimize high-fidelity, high-rate multiphoton operations in the presence of SpRS noise.

Abstract

Filtering is commonly used in quantum optics to reject noise photons, and also to enable interference between independent photons. However, filtering the joint spectrum of photon pairs can reduce the inherent coincidence probability or loss-independent heralding efficiency. Here, we investigate filtering for multiphoton applications based on entanglement and interference (e.g., quantum teleportation). We multiplex C-band entangled photons and C-band classical communications into the same long-distance fibers, which enables scalable low-loss quantum networking but requires filtering of spontaneous Raman scattering noise from classical light. Using tunable-bandwidth filters, low-jitter detectors, and polarization filters, we co-propagate time-bin-entangled photons at wavelengths compatible with erbium-ion quantum memories (1536.5 nm) and 10-Gbps C-band classical data over 25 km/25 km of standard fiber. Narrow filtering enables mW-level C-band power, which exceeds comparable studies by roughly an order of magnitude and could feasibly support Tbps classical rates. We evaluate how performance depends on pump and filter bandwidths, multipair emission, filter shapes, loss, phase matching, and how quantum information is measured. We find a trade-off between improving noise impact and single-mode purity and discuss mitigation methods toward optimal multiphoton applications. Importantly, these results apply to noise in free space and in quantum devices (sources, frequency converters, switches, detectors, etc.) and provide insight on filter-induced degradation of single-photon purity and rates even in noise-free environments.

Figures (10)

• Figure 1: (a) Conceptual diagram for polarization, frequency, and time filtering around photon pairs in the presence of background noise photons. (b) Effect of filtering a source's joint spectral correlations on the number of photons within the signal ($\mu_s$) and idler ($\mu_i$) filter passbands, which lead to single-photon counts, and their overlap ($\mu_{\rm both}$), which leads to true coincidence counts. When $\mu_{s/i} > \mu_{\rm both}$, not all detected photons will yield true coincidences. (c) Experimental diagram. Single-pulse or time-bin entangled photon pairs generated by type-II SPDC at degenerate wavelengths (1536.5 nm) are distributed over two 25-km single-mode fibers to co-propagate with 10-Gbps C-band classical signals (1547.72 nm), which generates strong spontaneous Raman scattering (SpRS) noise. We filter SpRS and SPDC photons using tunable bandwidth filters (32 pm to 600 pm). Polarization is filtered using a fiber polarizing beam splitter (FPBS) and an electronic fiber polarization controllers (E-FPCs) to actively correct time-dependent polarization rotations. Temporal filtering is applied in post-processing of the counts from low-jitter superconducting nanowire single-photon detectors (SNSPDs) and a time-to-digital converter (TDC). Michelson interferometers (INTERF) are inserted for time-bin experiments to perform measurements along the time-bin Bloch sphere Takesue2008_TimeBinTomography.
• Figure 2: (a) Measured JSI of the type-II SPDC photon pair source. (b) Heralding efficiencies as a function of filter bandwidth $\Delta \lambda$. (c) CAR as a function of $\mu_s$ for $\Delta \lambda \Delta T =300\,\rm pm \times 300 \rm ps$ or $\Delta \lambda \Delta T =50\,\rm pm \times 1800\,\rm ps$, which have different FHEs but the same background count probability since $\Delta \lambda \Delta T$ is fixed. The classical power is adjusted to receive $P_R = -27$ dBm after each 25-km fiber. The solid lines show the prediction based on our model. Even when each case has the same single-detector SNR (purple), the two-fold CAR for $\Delta \lambda=50\,$pm is notably lower compared to $\Delta \lambda=300\,$pm
• Figure 3: CAR as a function of the spectral filter bandwidth (BW) at the signal/idler receivers $\Delta \lambda_{s,i}$ for a fixed SPDC pump power whilst each C-band classical source transmits $P_0 = -12.5$ dBm into each 25-km/25-km fibers. The black line shows the simulation for an ideal system, and the blue line shows the results accounting for $\delta_{j}(\Delta \lambda_{j})<1$. The inset shows the results within the range of $\Delta \lambda_{j}$= 20 pm to 100 pm.
• Figure 4: Results for distributing 1536.5-nm time-bin entangled photons over 25-km/25-km fibers with a co-propagating 10-Gbps C-band (1547.72 nm) classical data signal in each fiber. The filtering is set to $\Delta \lambda=50$ pm and $\Delta T =200$ ps for each photon. (a) Histogram of single counts relative to the clock for signal time bin photons, SpRS noise, and total counts at the output of Alice's interferometer when the classical launch power is $P_0=-4.8$ dBm. (b) Entanglement visibility in the $X$ and $Z$ bases versus $P_0$. The color-coded solid lines show the predictions given our experimental parameters. The dashed lines are simulations when optimizing parameters such as ideal PSHE ($\delta_{\rm PS} = 1$), source loss ($\eta_{c} = 1$), or optimization of the entangled pair source's pump power at each $P_0$. The black horizontal lines show the limits for QKD and verifying nonlocality. (c) Two-photon interference fringe when $P_0=-4.8$ dBm, where $V_X = 89.6 \pm 1.6$%.
• Figure 5: (a) CAR as a function of filter bandwidth for either Gaussian or flat-top filter shapes when $P_0=-12.5$ dBm. The dashed lines show the results excluding background noise. The SPDC source is adjusted to keep a constant $\mu_s(\Delta \lambda) = 0.005$. (b) Signal and idler filter heralding efficiencies for flat-top (red) and Gaussian (blue) filters and spectral purity for flat-top (solid line) and Gaussian (dashed line) filters.