Benchmarking photon number resolving detectors

Deterministic Preparation of Optical Squeezed Cat and Gottesman-Kitaev-Preskill States

Large-amplitude squeezed cat states and high-quality Gottesman-Kitaev-Preskill (GKP) states are essential for effective quantum error correction, yet their optical preparation has been hindered by challenges such as low success probabilities, small amplitudes, and insufficient squeezing. Addressing these limitations, our research introduces scalable optical schemes for the deterministic preparation of large-amplitude squeezed cat states from photon-number states. Fock states have the benefit of producing consistent cat states across all measurement outcomes and intrinsically provides a degree of squeezing. Notably, these squeezed cat states facilitate the deterministic generation of high-quality approximate GKP states via "breeding," showing that GKP error correction in optics is technically feasible in near-term experiments. Our schemes allow fault-tolerant quantum computation through the use of GKP error correction.

Estimation of the number of single-photon emitters for multiple fluorophores with the same spectral signature

Fluorescence microscopy is of vital importance for understanding biological function. However, most fluorescence experiments are only qualitative inasmuch as the absolute number of fluorescent particles can often not be determined. Additionally, conventional approaches to measuring fluorescence intensity cannot distinguish between two or more fluorophores that are excited and emit in the same spectral window, as only the total intensity in a spectral window can be obtained. Here we show that, by using photon number resolving experiments, we are able to determine the number of emitters and their probability of emission for a number of different species, all with the same measured spectral signature. We illustrate our ideas by showing the determination of the number of emitters per species and the probability of photon collection from that species, for one, two and three otherwise unresolvable fluorophores. The convolution binomial model is presented to represent the counted photons emitted by multiple species. Then, the expectation-maximization (EM) algorithm is used to match the measured photon counts to the expected convolution binomial distribution function. In applying the EM algorithm, to leverage the problem of being trapped in a sub-optimal solution, the moment method is introduced to yield an initial guess for the EM algorithm. Additionally, the associated Cramér-Rao lower bound is derived and compared with the simulation results.

Non-Gaussian quantum state generation by multi-photon subtraction at the telecommunication wavelength

In the field of continuous-variable quantum information processing, non-Gaussian states with negative values of the Wigner function are crucial for the development of a fault-tolerant universal quantum computer. While several non-Gaussian states have been generated experimentally, none have been created using ultrashort optical wave packets, which are necessary for high-speed quantum computation, in the telecommunication wavelength band where mature optical communication technology is available. In this paper, we present the generation of non-Gaussian states on wave packets with a short 8-ps duration in the 1545.32 nm telecommunication wavelength band using photon subtraction up to three photons. We used a low-loss, quasi-single spatial mode waveguide optical parametric amplifier, a superconducting transition edge sensor, and a phase-locked pulsed homodyne measurement system to observe negative values of the Wigner function without loss correction up to three-photon subtraction. These results can be extended to the generation of more complicated non-Gaussian states and are a key technology in the pursuit of high-speed optical quantum computation.

Taming numerical errors in simulations of continuous variable non-Gaussian state preparation

Numerical simulation of continuous variable quantum state preparation is a necessary tool for optimization of existing quantum information processing protocols. A powerful instrument for such simulation is the numerical computation in the Fock state representation. It unavoidably uses an approximation of the infinite-dimensional Fock space by finite complex vector spaces implementable with classical digital computers. In this approximation we analyze the accuracy of several currently available methods for computation of the truncated coherent displacement operator. To overcome their limitations we propose an alternative with improved accuracy based on the standard matrix exponential. We then employ the method in analysis of non-Gaussian state preparation scheme based on coherent displacement of a two mode squeezed vacuum with subsequent photon counting measurement. We compare different detection mechanisms, including avalanche photodiodes, their cascades, and photon number resolving detectors in the context of engineering non-linearly squeezed cubic states and construction of qubit-like superpositions between vacuum and single photon states.

En route to nanoscopic quantum optical imaging: counting emitters with photon-number-resolving detectors

The fundamental understanding of biological pathways requires minimally invasive nanoscopic optical resolution imaging. Many approaches to high-resolution imaging rely on localization of single emitters, such as fluorescent molecules or quantum dots. Additionally, the exact determination of the number of such emitters in an imaging volume is essential for a number of applications; however, in standard intensity-based microscopy it is not possible to determine the number of individual emitters within a diffraction limited spot without initial knowledge of system parameters. Here we explore how quantum measurements of the emitted photons using photon number resolving detectors can be used to address this challenging task. In the proposed new approach, the problem of counting emitters reduces to the task of determining differences between the emitted photon distribution and the Poisson limit. We show that quantum measurements of the number of photons emitted from an ensemble of emitters enable the determination of both the number of emitters and the probability of emission. This method can be applied for any type of single-photon emitters. The scaling laws of this new approach are presented by the Cramer-Rao Lower Bounds, and this technique has great potential in quantum optical imaging with nanoscopic resolution.

High-speed photon-number-resolving detection via a GHz-gated SiPM

Silicon photomultipliers (SiPMs) constitute a promising candidate for photon-number-resolving (PNR) detection via spatial multiplexing, which offer advantages like high integration and low cost. Up to date, there has been continuous endeavor in boosting the PNR performances, particularly on the resolved photon numbers and operation speed. Here, we demonstrate a GHz-gated SiPM in the Geiger mode, which allows to quench the photon-induced avalanche signal within 1 ns. Specifically, the capacitive response of the SiPM has been effectively suppressed by combining the low-pass filtering and self-differencing technique, which facilitates a high-fidelity extraction of the avalanche pulse with a reduced error rate. Consequently, high-speed PNR detection has been manifested in resolving up to 14 photons for laser pulses at a repetition rate of 40 MHz. The presented high-speed PNR detector may open up new possibilities to implement applications such as large-dynamic-range optical sensing, high-capacity optical communication, and multi-photon quantum optics.

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.

Detector self-tomography

We present an intuitive model of detector self-tomography. Two identical realizations of the detector are illuminated by an entangled state that connects the joint statistics in a way in which each detector sees the other as a kind of mirror reflection. A suitable analysis of the statistics reveals the possibility of fully characterizing the detector. We apply this idea to Bell-type experiments, revealing their nonclassical nature.