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Quantum Information and Measurement (QIM)

Estimating the Photon-Number Distribution of Photonic Channels for Realistic Devices and Applications in Photonic Quantum Information Processing

Emilien Lavie, Ignatius William Primaatmaja, Wen Yu Kon, Chao Wang, Charles Ci Wen Lim

Published Jan 1, 2021• 1 citation
Publisher

Abstract

We present a framework based on linear estimation to reconstruct the input-output statistics of any unknown quantum photonic channel and we highlight two applications: Quantum Key Distribution and Time-Correlated Single Photon Counting with homo-dyne detectors.
DOI
10.1364/qim.2021.f2c.1

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Characterizing the input-output photon-number distribution of an unknown optical quantum channel is a worthwhile task for many applications in quantum information processing. Ideally, this would require deterministic photon-number sources and photon-number-resolving detectors, but these technologies are still work in progress. In this work, we propose a general method to rigorously bound the input-output photon-number distribution of an unknown optical channel using standard optical devices such as coherent light sources and non-photon-number-resolving detectors and homodyne detectors. To demonstrate the broad utility of our method, we consider the security analysis of practical quantum key distribution systems based on calibrated single-photon detectors and an experimental proposal to implement time-correlated single-photon counting technology using homodyne detectors instead of single-photon detectors.
In practice the most advanced field of quantum information science is quantum cryptography. The best known example of quantum cryptography is quantum key distribution (QKD) which offers an information-theoretically secure solution to the key exchange problem. There are QKD protocols which rely on a quantum channel that is able to transmit single photons. This can be implemented by using very low-power coherent light field, where values of bits are encoded into the polarization state of photons. Therefore, it is important to know the photon number distribution of the light source. In this paper we present the reconstruction of photon statistics for different pulsed light sources radiating at 850 nm (a common choice for free space quantum communication), using only a single on-off photon counting detector.
Quantum key distribution (QKD) theoretically offers unconditional security. Unfortunately, the gap between theory and practice threatens side-channel attacks on practical QKD systems. Many well-known QKD protocols use weak coherent laser pulses to encode the quantum information. These sources differ from ideal single photon sources and follow Poisson statistics. Many protocols, such as decoy state and coincidence detection protocols, rely on monitoring the photon statistics to detect any information leakage. The accurate measurement and characterization of photon statistics enable the detection of adversarial attacks and the estimation of secure key rates, strengthening the overall security of the QKD system. We have rigorously characterized our source to estimate the mean photon number employing multiple detectors for comparison against measurements made with a single detector. Furthermore, we have also studied intensity fluctuations to help identify and mitigate any potential information leakage due to state preparation flaws. We aim to bridge the gap between theory and practice to achieve information-theoretic security.
We introduce the direct linearity characterization of single-photon detectors and photon-number-resolving detectors. We discuss the supralinearity that goes beyond the current single-photon detection models. We also report on advanced detectors and sensors of statistical, vector, and correlation properties of light down to the single-photon level. The novel detection schemes harness complex optical networks, single-photon detector arrays, and deep learning. We present high-fidelity photon statistics estimation, resource-efficient polarization sensor, and quantum entanglement detector. We discuss the efficiency and scaling of the presented detection modalities.
Photon-number resolving detectors are a fundamental building-block of optical quantum information processing protocols. A loop detector, combined with appropriate statistical processing, can be used to convert a binary on/off photon counter into a photon-number-resolving detector. Here we describe the idea of a signature of photon-counts, which may be used to more robustly reconstruct the photon number distribution of a quantum state. The methodology is applied experimentally in a 9-port loop detector operating at a telecommunications wavelength and compared directly to the approach whereby only the number of photon-counts is used to reconstruct the input distribution. The signature approach is shown to be more robust against calibration errors, exhibit reduced statistical uncertainty, and reduced reliance on a-priori assumptions about the input state.