Photon-number-resolving (PNR) detectors are essential for photonic quantum computing, where a single measurement outcome must reliably herald a specific quantum state. However, detector fidelity is conventionally evaluated using ensemble-averaged statistics obtained from many measurements, which can remain high even when individual photon-number assignments are frequently misidentified. Here we introduce a universal single-shot fidelity that directly quantifies the probability of correctly identifying a photon number in a single measurement. The framework combines an efficiency-based POVM with a resolution-driven confusion matrix derived from the detector response, allowing photon loss and photon-number misidentification to be treated separately and then recombined into a single operational metric. This distinction reveals two fundamentally different limitations. Detection-efficiency loss represents an unrecoverable hardware constraint, whereas resolution-driven misidentification can be reduced by introducing a rejection region, trading generation rate for confidence. Because the metric is defined independently of detector architecture, it enables direct comparison between energy-resolving detectors such as transition-edge sensors and multiplexed click-based detectors on the same footing. Applying the framework to calibration data from three distinct detector architectures, we demonstrate quantitative comparison across photon-number regimes relevant to both discrete-variable and continuous-variable photonic quantum computing. The resulting benchmark provides a common operational metric for evaluating photon-number-resolving detectors and connecting detector performance to photonic quantum-computing requirements.
Photon-number-resolving (PNR) detectors are essential for photonic quantum computing, where a single measurement outcome must reliably herald a specific quantum state. However, detector fidelity is conventionally evaluated using ensemble-averaged statistics obtained from many measurements, which can remain high even when individual photon-number assignments are frequently misidentified. Here we introduce a universal single-shot fidelity that directly quantifies the probability of correctly identifying a photon number in a single measurement. The framework combines an efficiency-based POVM with a resolution-driven confusion matrix derived from the detector response, allowing photon loss and photon-number misidentification to be treated separately and then recombined into a single operational metric. This distinction reveals two fundamentally different limitations. Detection-efficiency loss represents an unrecoverable hardware constraint, whereas resolution-driven misidentification can be reduced by introducing a rejection region, trading generation rate for confidence. Because the metric is defined independently of detector architecture, it enables direct comparison between energy-resolving detectors such as transition-edge sensors and multiplexed click-based detectors on the same footing. Applying the framework to calibration data from three distinct detector architectures, we demonstrate quantitative comparison across photon-number regimes relevant to both discrete-variable and continuous-variable photonic quantum computing. The resulting benchmark provides a common operational metric for evaluating photon-number-resolving detectors and connecting detector performance to photonic quantum-computing requirements.
Photon-number-resolving (PNR) detectors are essential components of photonic quantum technologies, yet thus far, no practical metric exists to certify how many photons they can genuinely resolve in a single measurement. Here we introduce an operational framework for quantifying the capability of a PNR detector to distinguish between different numbers of photons, i.e. its genuine resolution. In turn, we develop a practical and scalable protocol for certifying the genuine resolution of a detector, which is based on coherent state probes. We apply the method to a 28-pixel photon-number-resolving superconducting nanowire single-photon detector (PNR-SNSPD) and certify genuine four-outcome resolution. Our work highlights the critical requirements in terms of detector efficiency towards achieving high genuine resolution. This approach provides an operational benchmark for PNR detectors and fills a crucial gap in the characterization of photonic quantum devices.
We analyze the performance of photon-number-resolving (PNR) detectors and introduce a figure of merit for the accuracy of such detectors. This figure of merit is the (worst-case) probability that the photon-number-resolving detector correctly predicts the input photon number. Simulations of various PNR detectors based on multiplexed single-photon ``click detectors'' is performed. We conclude that the required quantum efficiency is very high in order to achieve even moderate (up to a handful) photon resolution, we derive the required quantum efficiency as a function of the the maximal photon number one wants to resolve, and we show that the number of click detectors required grows quadratically with the maximal number of photons resolvable.
Single-photon detectors are ubiquitous and integral components of photonic quantum cryptography, communication, and computation. Many applications, however, require not only detecting the presence of any photons, but distinguishing the number present with a single shot. Here, we implement a single-shot, high-fidelity photon number-resolving detector of up to 15 microwave photons in a cavity-qubit circuit QED platform. This detector functions by measuring a series of generalized parity operators, which make up the bits in the binary decomposition of the photon number. Our protocol consists of successive, independent measurements of each bit by entangling the ancilla with the cavity, then reading out and resetting the ancilla. Photon loss and ancilla readout errors can flip one or more bits, causing nontrivial errors in the outcome, but these errors have a traceable form, which can be captured in a simple hidden Markov model. Relying on the independence of each bit measurement, we mitigate biases in ensembles of measurements, showing good agreement with the predictions of the model. The mitigation improves the average total variation distance error of Fock states from 13.5--1.1. We also show that the mitigation is efficiently scalable to an M-mode system provided that the errors are independent and sufficiently small. Our work motivates the development of new algorithms that utilize single-shot, high-fidelity PNR detectors.
Abstract Photon number resolving (PNR) measurements are beneficial or even necessary for many applications in quantum optics. Unfortunately, PNR detectors are usually large, slow, expensive, and difficult to operate. However, if the input signal is multiplexed, photon ‘click’ detectors, that lack an intrinsic PNR capability, can still be used to realize photon number resolution. Here, we investigate the operation of a single click detector, together with a storage line with tunable outcoupling. Using adaptive feedback to adjust the storage outcoupling rate, the dynamic range of the detector can in certain situations be extended by up to an order of magnitude relative to a purely passive setup. An adaptive approach can thus allow for photon number variance below the quantum shot noise limit under a wider range of conditions than using a passive multiplexing approach. This can enable applications in quantum enhanced metrology and quantum computing.
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.
High Resolution Image Download MS PowerPoint Slide Efficiently distinguishing photon numbers is a crucial yet challenging technology for various quantum information and quantum metrology applications. While superconducting transition edge sensors offer good photon-number-resolving (PNR) capabilities, they are hampered by low detection speed, timing jitter, and complex cooling and readout requirements. In this work, we present a significant advancement toward achieving high-fidelity PNR single-photon detectors by combing high efficiency superconducting nanowire single-photon detector and spatial multiplexing technology. The unique twin-layer configuration of superconducting nanowire atop a dielectric mirror ensures the near-unity detection efficiency. The segmented design, where each section is shunted by a resistor, enables spatial multiplexing, establishing a mapping relationship between pulse amplitude and registered photons. The fabricated detector exhibits impressive performance metrics, including a single-photon system detection efficiency (SDE) of ∼98% at a dark count rate of 20 cps and photon-number resolution capability up to 32. Further characterization through detector tomography reveals high fidelities for two-, three-, and four-photon events, approximately 87%, 73%, and 40% respectively. Moreover, the detector operates at a high count rate of 41 MHz at 3 dB-SDE, with a low timing jitter of as low as 40 ps. With its near-unity efficiency, high photon-number resolution, low dark count rate, fast detection speed, and superior timing resolution, we expect significant interest in these detectors, promising substantial benefits for weak light detection and optical quantum information applications.