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.
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.
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.
The article surveys the state of the art in the design, development and application of devices for deterministically generating single photons on demand. Both the defined function and requisite form of such ‘single-photon’ sources are explained in detail. Their attributes and characteristics, in particular the photon-counting statistics of the light that they generate, are presented in conjunction with the experimental apparatus (most notably the Hanbury-Brown and Twiss interferometer) for measuring them. Promising applications of single-photon sources within quantum key distribution, quantum information processing, as well as metrology and fundamental tests of quantum mechanics, are described. The utility and relative advantages of single-photon sources vis-á-vis more conventional sources of light are explained in terms of application-specific requirements and the respective abilities of different sources to fulfil them. The article collects, classifies and sorts the most significant work towards realizing practical single-photon sources to date. Though emanating from a diverse set of technological disciplines, with different research and application objectives in mind, the relative advantages and drawbacks of each approach are assessed, to give the reader a broad yet coherent and critical review of a rapidly developing research front.
Abstract To guarantee the security of quantum key distribution (QKD), security proofs of QKD protocols have assumptions on the devices. Commonly used assumptions are, for example, each random bit information chosen by a sender to be precisely encoded on an optical emitted pulse and the photon-number probability distribution of the pulse to be exactly known. These typical assumptions imposed on light sources such as the above two are rather strong and would be hard to verify in practical QKD systems. The goal of the paper is to replace those strong assumptions on the light sources with weaker ones. In this paper, we adopt the differential-phase-shift (DPS) QKD protocol and drastically mitigate the requirements on light sources, while for the measurement unit, trusted and photon-number-resolving detectors are assumed. Specifically, we only assume the independence among emitted pulses, the independence of the vacuum emission probability from a chosen bit, and upper bounds on the tail distribution function of the total photon number in a single block of pulses for single, two and three photons. Remarkably, no other detailed characterizations, such as the amount of phase modulation, are required. Our security proof significantly relaxes demands for light sources, which paves a route to guarantee implementation security with simple verification of the devices.
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.
Photon statistics is a branch of physics that involves observing the behavior of single or a small number of photons and then aggregating the results through statistical averaging. This process is essential to obtain meaningful and reliable data, especially in quantum optics research. Photon statistics provides valuable information about correlations in the electromagnetic field and characteristics of the type of light being measured. For example, second-order correlation function obtained via Hanbury Brown and Twiss experiment is the fundamental way to differentiate between coherent, chaotic and quantum light. Moreover, extensive investigations into the quantum properties of light resulted in significant progress that allows for precise control of quantum optical systems and sets the stage for genuine quantum engineering. This progress extends to applications in confirming the generation of entangled photons and exploring their properties for various purposes. The non-classical correlation between the entangled photons has resulted in various quantum optical techniques that enable the practical implementation of conceptual experiments that probe the core principles of quantum theory. This enhanced control over quantum phenomena offers exciting opportunities to explore novel information-processing approaches, with the potential to revolutionize technologies rooted in quantum information science. Driven by the significance and pivotal role of photon statistics, our research pursuits were directed toward two specific domains: the characterization of nanolasers and the characterization of time-bin entangled photons. In the first segment, we delve into the realm of metallic coaxial nanolasers, renowned for their intriguing threshold-less lasing behavior. Through comprehensive photon statistics analysis, we seek to unravel the coherence properties inherent in these nanolasers. Our focus also lies on understanding the elusive threshold-less operation, which has remained a subject of debate and intrigue. To evaluate this unique lasing characteristic, we conduct rigorous second-order coherence measurements alongside time-resolved second-order correlation analyses. The second segment of this study ventures into the generation and characterization of high-dimensional time-bin entangled states, a critical resource for quantum technological applications. We simulate a synthetic photonic lattice by employing a coupled fiber-loop system to perform various quantum walk schemes to generate and process high-dimensional time-bin entangled states. Our investigation focuses on the quantum interference phenomena through detailed photon statistics analysis, with an emphasis on their applications across diverse quantum technologies. Through these two interconnected research endeavors, this thesis demonstrates the profound significance of photon statistics as a versatile tool, bridging classical and quantum realms, and paving the way for advancements in diverse applications, ranging from nanolasers to quantum technologies.