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arXiv:2102.08419 · Physical Review Applied

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 Sep 10, 2021• 5 citations
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Abstract

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.

DOI
10.1103/physrevapplied.16.034020

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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.
Quantum key distribution (QKD) has a prospect to realize unconditional secure communication. However, many real system problems should be solved. Transmitters security is an important part of QKD security. And measuring photon number distribution could help improve it. This measurement is also useful for measuring unknown sources or testing newly designed sources. In this article, a method to measure the photon number distribution of pulses using non-photon-number-resolving detectors is proposed. Numerical simulation is conducted to test this scheme and performs well. Experiment on Poisson source is also used to test this method.
Characterization of photon statistics of a light source is one of the most basic tools in quantum optics. Existing methods rely on an implicit and unverifiable assumption that the source never emits too many photons to stay within the measuring range of the detectors. As a result, they fail to fulfill the demand arising from emerging applications of quantum information such as quantum cryptography. Here, we propose a characterization method using a conventional Hanbury-Brown-Twiss setup to produce rigorous bounds on emission probabilities of low photon numbers from an unknown source. As an application, we show that our characterization method can be used for a practical light source in a quantum key distribution protocol to forsake the commonly used a priori assumption without significant change in efficiency. Our versatile and flexible formula for rigorous bounds will make an essential contribution to the optics toolbox in the era of quantum information.
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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.
Optical homodyne detection has been widely used in continuous-variable (CV) quantum information processing for measuring field quadrature. In this paper we explore the possibility of operating a conjugate homodyne detection system in ``photon counting'' mode to implement discrete-variable (DV) quantum key distribution (QKD). A conjugate homodyne detection system, which consists of a beam splitter followed by two optical homodyne detectors, can simultaneously measure a pair of conjugate quadratures XXX and PPP of the incoming quantum state. In classical electrodynamics, X2+P2{X}^{2}+{P}^{2}X2+P2 is proportional to the energy (the photon number) of the input light. In quantum optics, XXX and PPP do not commute and thus the above photon-number measurement is intrinsically noisy. This implies that a blind application of standard security proofs of QKD could result in pessimistic performance. We overcome this obstacle by taking advantage of two special features of the proposed detection scheme. First, the fundamental detection noise associated with vacuum fluctuations cannot be manipulated by an external adversary. Second, the ability to reconstruct the photon number distribution at the receiver's end can place additional constraints on possible attacks from the adversary. As an example, we study the security of the BB84 QKD using conjugate homodyne detection and evaluate its performance through numerical simulations. This study may open the door to a family of QKD protocols, complementary to the well-established DV-QKD based on single-photon detection and CV-QKD based on coherent detection.