Positive operator-valued measure reconstruction of a beam-splitter tree-based photon-number-resolving detector

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.

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.

Testing the photon-number statistics of a quantum key distribution light source

A commonly held tenet is that lasers well above threshold emit photons in a coherent state, which follow Poissonian statistics when measured in photon number. This feature is often exploited to build quantum-based random number generators or to derive the secure key rate of quantum key distribution systems. Hence the photon number distribution of the light source can directly impact the randomness and the security distilled from such devices. Here, we propose a method based on measuring correlation functions to experimentally characterize a light source's photon statistics and use it in the estimation of a quantum key distribution system's key rate. This promises to be a useful tool for the certification of quantum-related technologies.

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.

Effect of dark counts on single-photon heralding with quasi-number-resolving detection schemes

We consider photon heralding with quasi-number-resolving detection schemes and account for detection efficiencies and dark count probabilities. With a straightforward formalism, we develop closed-form expressions for the heralding probability, photon number distribution of the resulting heralded state, and fidelity of this heralded state to a single-photon state. We calculate that this fidelity has a maximum as a function of the number of multiplexed detection modes and that, for experimental configurations in which the maximum is reached for quite a large number of detection modes, it can still be highly beneficial to multiplex fewer modes.

Temporal and spatial multiplexed infrared single-photon counter based on high-speed avalanche photodiode

We report on a high-speed temporal and spatial multiplexed single-photon counter with photon-number-resolving capability up to four photons. The infrared detector combines a fiber loop to split, delay and recombine optical pulses and a 200 MHz dual-channel single-photon detector based on InGaAs/InP avalanche photodiode. To fully characterize the photon-number-resolving capability, we perform quantum detector tomography and then reconstruct its positive-operator-valued measure and the associated Wigner functions. The result shows that, despite of the afterpulsing noise and limited system detection efficiency, this temporal and spatial multiplexed single-photon counter can already find applications for large repetition rate quantum information schemes.

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.