Twin beams from spontaneous parametric down-conversion (SPDC) enable sub-shot-noise transmission estimation, yet practical advantages are constrained by loss. We map joint photon-number-resolved (PNR) statistics to channel parameters using an exact, analytically solvable binomial-damping model for the lossy two-mode squeezed vacuum, removing the need for numerical master-equation integration. Benchmarking against an energy-matched coherent probe, we show the optimal linear estimator saturates the Cramer-Rao bound in closed form. For a fiber-coupled SPDC source interrogated with PNR superconducting nanowire detectors, we demonstrate that no quantum advantage survives at 14.7 to 23.5 dB signal loss and 14.8 dB idler loss. We conclude by providing a parameter-space design chart specifying the precise loss budget required for quantum-enhanced transmission estimation.
Twin beams from spontaneous parametric down-conversion (SPDC) enable sub-shot-noise transmission estimation, yet practical advantages are constrained by loss. We map joint photon-number-resolved (PNR) statistics to channel parameters using an exact, analytically solvable binomial-damping model for the lossy two-mode squeezed vacuum, removing the need for numerical master-equation integration. Benchmarking against an energy-matched coherent probe, we show the optimal linear estimator saturates the Cramer-Rao bound in closed form. For a fiber-coupled SPDC source interrogated with PNR superconducting nanowire detectors, we demonstrate that no quantum advantage survives at 14.7 to 23.5 dB signal loss and 14.8 dB idler loss. We conclude by providing a parameter-space design chart specifying the precise loss budget required for quantum-enhanced transmission estimation.
Twin beams from spontaneous parametric down-conversion (SPDC) enable sub-shot-noise transmission estimation, yet practical advantages are constrained by loss. We map joint photon-number-resolved (PNR) statistics to channel parameters using an exact, analytically solvable binomial-damping model for the lossy two-mode squeezed vacuum, removing the need for numerical master-equation integration. Benchmarking against an energy-matched coherent probe, we show the optimal linear estimator saturates the Cramer-Rao bound in closed form. For a fiber-coupled SPDC source interrogated with PNR superconducting nanowire detectors, we demonstrate that no quantum advantage survives at 14.7 to 23.5 dB signal loss and 14.8 dB idler loss. We conclude by providing a parameter-space design chart specifying the precise loss budget required for quantum-enhanced transmission estimation.
Quantum metrology plays a crucial role in characterizing and stabilizing optical channels in a quantum network, where precise estimation of loss is critical for loss-sensitive quantum protocols. Optical fiber channels are the primary medium for linking quantum nodes, where loss estimation with optical quantum states may enhance the precision compared to classical probes. In this study, we investigate the use of two-mode squeezed vacuum (TMSV) states, an optical quantum state generated via parametric down-conversion, and their detection with photon-number-resolving detectors for characterization of transmission loss. Theoretical analysis indicates that TMSV states exhibit higher Fisher information for transmission parameter estimation than coherent states, suggesting they are superior probes that can significantly enhance measurement precision. Our experimental results confirm that these TMSV states outperform coherent states in the context of loss estimation in an optical channel, achieving up to 3.9 dB higher Fisher information for transmissivity estimation without relying on post-selection measurements. This source can effectively probe transmission losses in optical fibers up to 35 km, maintaining a measurement precision advantage over coherent probe states. These findings underscore the potential of TMSV states to advance quantum metrology and improve the robustness of quantum network applications.
Tolerance to imperfections is a defining performance criterion for quantum sensors. The threshold for achieving a quantum advantage depends on the input state, sensor configuration, detection scheme, and, critically for optical platforms, photon loss. We consider a nonlinear interferometer in which two gain-optimized parametric nonlinear optical processes couple the state to the internal sensor and subsequently mix the reference and sensor beams. We demonstrate that measuring the full photon-number output statistics of this setup yields marked improvements in the loss threshold. Using photon-number-resolving detection (PNRD) based on transition-edge sensors (TESs), we experimentally reconstruct the joint photon-number statistics at the interferometer output. Subject to internal and external losses of approximately 25 % and 45 %, respectively -- and without any post-selection or loss correction -- we observe an unconditional violation of the shot-noise limit by 2.37±0.11 dB. This translates to a 44 % enhancement in estimation precision over conventional click-detection strategies. We verify this performance by evaluating the classical Fisher information against both an analytical model of the joint photon-number distribution and the raw measured statistics. Ultimately, our results demonstrate that combining nonlinear interferometry with PNRD unlocks metrological information fundamentally inaccessible to click detectors, establishing a clear path toward practical, quantum-enhanced sensing under realistic loss conditions.
We have developed a “digital twin” of the photon entanglement generation process to model the degradation of quantum entangled states produced via spontaneous parametric down-conversion (SPDC) when transmitted through lossy and noisy optical channels. These two-mode entangled states can exhibit entanglement in photon number, polarization, and spectral-temporal modes, making them valuable resources for quantum communication and information processing. Using a density matrix formalism, we perform numerical simulations to model the interaction of each mode with its environment, incorporating the effects of photon loss, incoherent noise processes, and intermodal correlations between polarization and frequency degrees of freedom. Purity and fidelity are key metrics used to quantify the mixedness and coherence of the transmitted state. The simulation results quantify the decoherence as noise and loss increase, highlighting the vulnerability of entanglement to environmental disturbances and the compounding impact of mode-dependent quantum correlations. This study provides insight into the performance limits of SPDC-based entangled photon sources and offers guidance for optimizing quantum systems operating under realistic conditions. The simulation platform serves as a predictive tool, enabling future integration with experimental control systems and benchmarking against measured entangled photon characteristics such as Hong-Ou-Mandel interference and polarization correlation visibility.
We study the sensitivity of phase estimation in a lossy Mach-Zehnder interferometer (MZI) using two general, and practical, resources generated by a laser and a nonlinear optical medium with passive optimal elements, which are readily available in the laboratory: One is a two-mode separable coherent and squeezed vacuum state at a beam splitter and the other is a two-mode squeezed vacuum state. In view of the ultimate precision given by quantum Fisher information, we show that the two-mode squeezed vacuum state can achieve a lower bound of estimation error than the coherent and squeezed vacuum state under a photon-loss channel. We further consider practical measurement schemes, homodyne detection and photon number resolving detection (PNRD), to characterize the accuracy of phase estimation in reality and find that the coherent and squeezed vacuum state largely achieves a lower bound than the two-mode squeezed vacuum in the lossy MZI while maintaining quantum enhancement over the shot-noise limit. By comparing homodyne detection and PNRD, we demonstrate that quadrature measurement with homodyne detection is more robust against photon loss than parity measurement with PNRD. We also show that double homodyne detection can provide a better tool for phase estimation than single homodyne detection against photon loss.
Abstract Estimating transmission or loss is at the heart of spectroscopy. To achieve the ultimate quantum resolution limit, one must use probe states with definite photon number and detectors capable of distinguishing the number of photons impinging thereon. In practice, one can outperform classical limits using two-mode squeezed light, which can be used to herald definite-photon-number probes, but the heralding is not guaranteed to produce the desired probes when there is loss in the heralding arm or its detector is imperfect. We show that this paradigm can be used to simultaneously measure distinct loss parameters in both modes of the squeezed light, with attainable quantum advantages. We demonstrate this protocol on Xanadu’s X8 chip, accessed via the cloud, building photon-number probability distributions from 106 shots and performing maximum likelihood estimation (MLE) on these distributions 103 independent times. Because pump light may be lost before the squeezing occurs, we also simultaneously estimate the actual input power, using the theory of nuisance parameters. MLE converges to estimate the transmission amplitudes in X8’s eight modes to be 0.392 02(6), 0.307 06(8), 0.369 37(6), 0.287 30(9), 0.382 06(6), 0.304 41(8), 0.372 29(6), and 0.286 21(8) and the squeezing parameters, which are proxies for effective input coherent-state amplitudes, their losses, and their nonlinear interaction times, to be 1.3000(2), 1.3238(3), 1.2666(2), and 1.3425(3); all of these uncertainties are within a factor of two of the quantum Cramér–Rao bound. This study provides crucial insight into the intersection of quantum multiparameter estimation theory, MLE convergence, and the characterization and performance of real quantum devices.