Quantum detector tomography of a time-multiplexed superconducting nanowire single-photon detector at telecom wavelengths

Extending the quantum tomography of a quasi-photon-number-resolving detector

The ability to discriminate the number of photons in a radiation field has a critical role in the implementation of quantum optical technologies. True photon-number-resolving detectors are rare and complex devices, while a quasi-photon-number-resolving detector (qPNRD) is a practical alternative for real-world applications. Our qPNRD is composed of a fiber demultiplexer and individual non-photon-number-resolving detectors. We perform quantum tomography on our qPNRD based on the positive operator-valued measure and extend the analysis using the Bayesian formalism to uncover how the measurement influences knowledge of the measured photon probability distribution.

Reliable Optimization of Arbitrary Functions over Quantum Measurements

As the connection between classical and quantum worlds, quantum measurements play a unique role in the era of quantum information processing. Given an arbitrary function of quantum measurements, how to obtain its optimal value is often considered as a basic yet important problem in various applications. Typical examples include but are not limited to optimizing the likelihood functions in quantum measurement tomography, searching the Bell parameters in Bell-test experiments, and calculating the capacities of quantum channels. In this work, we propose reliable algorithms for optimizing arbitrary functions over the space of quantum measurements by combining the so-called Gilbert's algorithm for convex optimization with certain gradient algorithms. With extensive applications, we demonstrate the efficacy of our algorithms with both convex and nonconvex functions.

Reducing g(2)(0) of a parametric down-conversion source via photon-number resolution with superconducting nanowire detectors

Multiphoton contributions pose a significant challenge for the realisation of heralded single-photon sources (HSPS) based on nonlinear processes. In this work, we improve the quality of single photons generated in this way by harnessing the photon-number resolving (PNR) capabilities of commercial superconducting nanowire single-photon detectors (SNSPDs). We report a 13 ± 0.4% reduction of g⁽²⁾(τ = 0), even with a collection efficiency in the photon source of only 29.6%. Our work demonstrates the first application of the PNR capabilities of SNSPDs and shows improvement in the quality of an HSPS with widely available technology.

Quantum detector tomography of a superconducting nanostrip photon-number-resolving detector

Superconducting nanostrip photon detectors have been used as single-photon detectors, which can discriminate only photons' presence or absence. It has recently been found that they can discriminate the number of photons by analyzing the output signal waveform, and they are expected to be used in various fields, especially in optical-quantum-information processing. Here, we improve the photon-number-resolving performance for light with a high-average photon number by pattern matching of the output signal waveform. Furthermore, we estimate the positive-operator-valued measure of the detector by a quantum detector tomography. The result shows that the device has photon-number-resolving performance up to five photons without any multiplexing or arraying, indicating that it is useful as a photon-number-resolving detector.

Direct Experimental Certification of Quantum Non-Gaussian Character and Wigner Function Negativity of Single-Photon Detectors

Highly nonclassical character of optical quantum detectors, such as single-photon detectors, is essential for preparation of quantum states of light and a vast majority of applications in quantum metrology and quantum information processing. Therefore, it is both fundamentally interesting and practically relevant to investigate the nonclassical features of optical quantum measurements. Here we propose and experimentally demonstrate a procedure for direct certification of quantum non-Gaussianity and Wigner function negativity, two crucial nonclassicality levels, of photonic quantum detectors. Remarkably, we characterize the highly nonclassical properties of the detector by probing it with only two classical thermal states and a vacuum state. We experimentally demonstrate the quantum non-Gaussianity of a single-photon avalanche diode even under the presence of background noise, and we also certify the negativity of the Wigner function of this detector. Our results open the way for direct benchmarking of photonic quantum detectors with a few measurements on classical states.

Quantum detector tomography of a 2×2 multi-pixel array of superconducting nanowire single photon detectors

We demonstrate quantum detector tomography of a commercial 2×2 array of superconducting nanowire single photon detectors. We show that detector-specific figures of merit including efficiency, dark-count and cross-talk probabilities can be directly extracted, without recourse to the underlying detector physics. These figures of merit are directly identified from just four elements of the reconstructed positive operator valued measure (POVM) of the device. We show that the values for efficiency and dark-count probability extracted by detector tomography show excellent agreement with independent measurements of these quantities, and we provide an intuitive operational definition for cross-talk probability. Finally, we show that parameters required for the reconstruction must be carefully chosen to avoid oversmoothing the data.

Experimental Quantification of Coherence of a Tunable Quantum Detector

Quantum coherence is a fundamental resource that quantum technologies exploit to achieve performance beyond that of classical devices. A necessary prerequisite to achieve this advantage is the ability of measurement devices to detect coherence from the measurement statistics. Based on a recently developed resource theory of quantum operations, here we quantify experimentally the ability of a typical quantum-optical detector, the weak-field homodyne detector, to detect coherence. We derive an improved algorithm for quantum detector tomography and apply it to reconstruct the positive-operator-valued measures of the detector in different configurations. The reconstructed positive-operator-valued measures are then employed to evaluate how well the detector can detect coherence using two computable measures. As the first experimental investigation of quantum measurements from a resource theoretical perspective, our work sheds new light on the rigorous evaluation of the performance of a quantum measurement apparatus.

Resolving Photon Numbers Using a Superconducting Nanowire with Impedance-Matching Taper

Time- and number-resolved photon detection is crucial for quantum information processing. Existing photon-number-resolving (PNR) detectors usually suffer from limited timing and dark-count performance or require complex fabrication and operation. Here, we demonstrate a PNR detector at telecommunication wavelengths based on a single superconducting nanowire with an integrated impedance-matching taper. The taper provides a kΩ load impedance to the nanowire, making the detector's output amplitude sensitive to the number of photon-induced hotspots. The prototyping device was able to resolve up to four absorbed photons with 16.1 ps timing jitter and <2 c.p.s. device dark count rate. Its exceptional distinction between single- and two-photon responses is ideal for high-fidelity coincidence counting and allowed us to directly observe bunching of photon pairs from a single output port of a Hong-Ou-Mandel interferometer. This detector architecture may provide a practical solution to applications that require high timing resolution and few-photon discrimination.

Tomography of a Feedback Measurement with Photon Detection

Quantum measurement is essential to both the foundations and practical applications of quantum information science. Among many possible models of quantum measurement, feedback measurements that dynamically update their physical structure are highly interesting due to their flexibility, which enables a wide range of measurements that might otherwise be hard to implement. Here we investigate by detector tomography a measurement consisting of a displacement operation combined with photon detection followed by a real time feedback operation. We design the measurement in order to discriminate the superposition of vacuum and single photon states-the single-rail qubit-and find that it can discriminate the superposition states with a certainty of 96%. Such a feedback-controlled photon counter will facilitate the realization of quantum information protocols with single-rail qubits as well as the nonlocality test of certain entangled states.

Photon-number-resolving segmented detectors based on single-photon avalanche-photodiodes

We investigate the feasibility and performance of photon-number-resolved photodetection employing single-photon avalanche photodiodes (SPADs) with low dark counts. While the main idea, to split n photons into m detection modes with a vanishing probability of more than one photon per mode, is not new, we investigate here a important variant of this situation where SPADs are side-coupled to the same waveguide rather than terminally coupled to a propagation tree. This prevents the nonideal SPAD quantum efficiency from contributing to photon loss. We propose a concrete SPAD segmented waveguide detector based on a vertical directional coupler design, and characterize its performance by evaluating the purities of Positive-Operator-Valued Measures (POVMs) in terms of number of SPADs, photon loss, dark counts, and electrical cross-talk.

Characterization of entangling properties of quantum measurement via two-mode quantum detector tomography using coherent state probes

Entangled measurement is a crucial tool in quantum technology. We propose a new entanglement measure of multi-mode detection, which estimates the amount of entanglement that can be created in a measurement. To illustrate the proposed measure, we perform quantum tomography of a two-mode detector that is comprised of two superconducting nanowire single photon detectors. Our method utilizes coherent states as probe states, which can be easily prepared with accuracy. Our work shows that a separable state such as a coherent state is enough to characterize a potentially entangled detector. We investigate the entangling capability of the detector in various settings. Our proposed measure verifies that the detector makes an entangled measurement under certain conditions, and reveals the nature of the entangling properties of the detector. Since the precise characterization of a detector is essential for applications in quantum information technology, the experimental reconstruction of detector properties along with the proposed measure will be key features in future quantum information processing.

Accurate Detection of Arbitrary Photon Statistics

We report a measurement workflow free of systematic errors consisting of a reconfigurable photon-number-resolving detector, custom electronic circuitry, and faithful data-processing algorithm. We achieve an unprecedented accurate measurement of various photon-number distributions going beyond the number of detection channels with an average fidelity of 0.998, where the error is primarily caused by the sources themselves. Mean numbers of photons cover values up to 20 and faithful autocorrelation measurements range from g^{(2)}=6×10^{-3} to 2. We successfully detect chaotic, classical, nonclassical, non-Gaussian, and negative-Wigner-function light. Our results open new paths for optical technologies by providing full access to the photon-number information without the necessity of detector tomography.

Quantum Calibration of Photon-Number-Resolving Detectors Based on Multi-pixel Photon Counters

In this paper, we reconstructed the positive operator-valued measure (POVM) of a photon-number-resolving detector (PNRD) based on a multi-pixel photon counter (MPPC) by means of quantum detector tomography (QDT) at 791 nm and 523 nm, respectively. MPPC is a kind of spatial-multiplexing PNRD with a silicon avalanche photodiode (Si-APD) array as the photon receiver. Experimentally, the quantum characteristics of MPPC were calibrated at 2 MHz at two different wavelengths. The POVM elements were given by QDT. The fidelity of the reconstructed POVM elements is higher than 99.96%, which testifies that the QDT is reliable to calibrate MPPC at different wavelengths. With QDT and associated Wigner functions, the quantum properties of MPPC can be calibrated more directly and accurately in contrast with those conventional methods of modeling detectors.

Explicit formulas for photon number discrimination with on/off detectors

Discriminating between Fock states with a high degree of accuracy is a desirable feature for modern applications of optical quantum information processing. A well-known alternative to sophisticated photon number discriminating detectors is to split the field among a number of simple on/off detectors and infer the desired quantity from the measurement results. In this work we find an explicit analytical expression of the detection probability for any number of input photons, any number of on/off detectors, and we include quantum efficiency and a false count probability. This allows us to explicitly invert the conditional probability using Bayes' theorem and express the number of photons that we had at the input in the most unbiased way possible with ready-to-use formulas. We conclude with some examples.

Quantum witness of high-speed low-noise single-photon detection

We demonstrate high-speed and low-noise near-infrared single-photon detection by using a capacitance balancing circuit to achieve a high spike noise suppression for an InGaAs/InP avalanche photodiode. The single-photon detector could operate at a tunable gate repetition rate from 10 to 60 MHz. A peak detection efficiency of 34% has been achieved with a dark count rate of 9 × 10⁻³ per gate when the detection window was set to 1 ns. Additionally, quantum detector tomography has also been performed at 60 MHz of repetition rate and for the detection window of 1 ns, enabling to witness the quantum features of the detector with the help of a negative Wigner function. By varying the bias voltage of the detector, we further demonstrated a transition from the full-quantum to semi-classical regime.

Position-Dependent Local Detection Efficiency in a Nanowire Superconducting Single-Photon Detector

We probe the local detection efficiency in a nanowire superconducting single-photon detector along the cross-section of the wire with a far subwavelength resolution. We experimentally find a strong variation in the local detection efficiency of the device. We demonstrate that this effect explains previously observed variations in NbN detector efficiency as a function of device geometry.

Local mapping of detector response for reliable quantum state estimation

Improved measurement techniques are central to technological development and foundational scientific exploration. Quantum physics relies on detectors sensitive to non-classical features of systems, enabling precise tests of physical laws and quantum-enhanced technologies including precision measurement and secure communications. Accurate detector response calibration for quantum-scale inputs is key to future research and development in these cognate areas. To address this requirement, quantum detector tomography has been recently introduced. However, this technique becomes increasingly challenging as the complexity of the detector response and input space grow in a number of measurement outcomes and required probe states, leading to further demands on experiments and data analysis. Here we present an experimental implementation of a versatile, alternative characterization technique to address many-outcome quantum detectors that limits the input calibration region and does not involve numerical post processing. To demonstrate the applicability of this approach, the calibrated detector is subsequently used to estimate non-classical photon number states.

The successful realization of quantum information protocols relies on characterization of quantum states and measurements. Here, Cooper et al. experimentally demonstrate a technique enabling calibration of a detector with a sizeable number of outcomes using a limited amount of resources.