The quantization of light is the basis for quantum optics and has led to the observation of a multitude of genuine quantum effects which cannot be explained by classical physics. Yet, there exist different views when we refer to the distinct quantum character of light as opposed to classical fields. A major impact on how we describe photonic states is caused by the detection method we use for the quantum state characterization. In the theoretical modelling measuring light always means the recording of photon statistics of some kind, though the way we interpret the results is quite different and depends mainly on the intensity of actual detected light. If we use conventional photodiodes and monitor bright light, we attribute the detected statistics to quadrature measurements in a phase space representation, or—in other words—we identify the quantum state by studying its uncertainties of its field amplitude and phase properties which correspond to conjugate quantum observables. For multi-photon states with very low intensity we have to employ avalanche photodiodes (APDs) to be able to see any signal, but photon number resolution seems difficult in this regime. Recent developments allow one to ascertain information about the photon statistics from APD measurements opening up new routes for characterizing photonic states. In this article we review the different methods for modern quantum state metrology where we include theoretical aspects as well as the description of the state-of-the-art technology for measuring photon statistics.
The quantization of light is the basis for quantum optics and has led to the observation of a multitude of genuine quantum effects which cannot be explained by classical physics. Yet, there exist different views when we refer to the distinct quantum character of light as opposed to classical fields. A major impact on how we describe photonic states is caused by the detection method we use for the quantum state characterization. In the theoretical modelling measuring light always means the recording of photon statistics of some kind, though the way we interpret the results is quite different and depends mainly on the intensity of actual detected light. If we use conventional photodiodes and monitor bright light, we attribute the detected statistics to quadrature measurements in a phase space representation, or—in other words—we identify the quantum state by studying its uncertainties of its field amplitude and phase properties which correspond to conjugate quantum observables. For multi-photon states with very low intensity we have to employ avalanche photodiodes (APDs) to be able to see any signal, but photon number resolution seems difficult in this regime. Recent developments allow one to ascertain information about the photon statistics from APD measurements opening up new routes for characterizing photonic states. In this article we review the different methods for modern quantum state metrology where we include theoretical aspects as well as the description of the state-of-the-art technology for measuring photon statistics.
Non-classical light is both easily encoded with quantum information and robust against decoherence, making it a key resource that enables many quantum information applications including quantum computing, quantum communication, and quantum metrology. We present a wide range of experimental and theoretical research toward the generation, detection, characterization, and storage of non-classical states of light with an eye toward quantum information applications. To provide a basis for the rest of the work, we begin by discussing theoretically the role of photon number statistics in optical quantum information and the use of second-order optical coherence to characterize non-classical light. Building on that, we present an original tool for the difficult problem of reconstructing the underlying mode distribution of multi-mode optical fields using simple measurements of higher-order optical coherence. We then move on to the problem of generating and storing single photons. We do this in a solid-state medium, a rare-earth ion-doped crystal, with a long-lived spin transition ideal for storing quantum information. We experimentally demonstrate the feasibility of this concept by showing correlations between the optical fields that herald storage and retrieval of collective excitations. This scheme can be used for the two important and distinct applications of generating single photons on-demand and storing quantum information and entanglement. The detection of non-classical light is a task as important as its generation. To this end, we study detectors with near unity detection efficiency and photon number resolution for use in quantum-enabled metrology. We use such a detector to experimentally demonstrate compression of spatial fringes and investigate the possibility of improving measurement resolution with classical and non-classical light. Finally, we report a set of experiments using photon number statistics to characterize classical and non-classical light. We measure suppression of unwanted multi-photon emission in a heralded single photon source based on four-wave mixing in microstructure optical fiber. And we, for the first time, experimentally demonstrate reconstruction of multi-mode classical and non-classical light from measured photon number statistics.
The technologies utilizing quantum states of light have been in the spotlight for the last two decades. In this regard, quantum metrology, quantum imaging, quantum-optical communication are some of the important applications that exploit fascinating quantum properties like quantum superposition, quantum correlations, and nonclassical photon statistics. However, the state-of-art technologies operating at the single-photon level are not robust enough to truly realize a reliable quantum-photonic technology. In Chapter 1, I present a historical account of photon-based technologies. Furthermore, I discuss recent efforts and encouraging developments in the field of quantum-photonic technologies, and major challenges for the experimental realization of reliable quantum technologies utilizing photons, setting up a stage for unveiling our smart methodologies to cope with them. Similarly, in Chapter 2, I review the fundamental concepts such as states of light, spatial modes of light, and machine learning. In Chapter 3 of this dissertation, I present a theoretical work on a nonlinear quantum metrology scheme, showing a sub-shot-noise limited phase estimation using the displaced-squeezed light and on/off detection. Furthermore, I discuss a camera-based squeezed-light detection technique that can be a smart and time-efficient alternative to conventional balanced-homodyne detection. In Chapter 4, I discuss our efforts to incorporate artificial intelligence in a quest to improve the efficiency of discriminating thermal light sources from coherent light sources. The conventional identification technique requires a large number of measurements. We utilize artificial neural networks to dramatically reduce the number of measurements required to distinguish thermal light and coherent light. In Chapter 5, I present a communication protocol that utilizes the spatial modes of light. Despite being valuable resources for a wide variety of quantum technologies, spatial modes of light are extremely vulnerable to random phase fluctuations. The conventional techniques to cope with these challenges are relatively inefficient. We utilize convolutional neural networks to perform the spatial mode correction of single photons, resulting in a near-unity fidelity of correction. I wrap up my dissertation in Chapter 6 by summarizing the historical context of quantum technologies, challenging problems facing state-of-art quantum technologies, and the importance of our efforts to introduce artificial intelligence in photonic technologies.
Generation and measurement of quantum states of the electromagnetic field represent a hot and widely discussed topic in the Physics community, since optical states are useful not only in fundamental experiments but also in several applications in the fields of Quantum Optics and Quantum Information (Bouwmeester et al., 2000). In fact, optical radiation is endowed with relevant characteristics as it travels at maximum possible speed, it is almost unaffected by the interaction with the environment, which in many cases represents an unavoidable decoherence source, and it can be integrated in optoelectronic circuits to implement quantum computing protocols (Sansoni et al., 2010). The possibility of using optical fields in applicative protocols depends on the capability of generating and manipulating optical states that are robust with respect to losses (i.e. that contain a sizeable number of photons) and that can be produced and measured at high rate. For all these reasons, mesoscopic pulsed optical states containing few tens of photons per pulse seem to be the ideal candidates for applications to quantum communication protocols in which each pulse must be addressed individually. Moreover, the problem of generating suitable pulsed states must be considered together with the question of their measurement and characterization. In fact, nowadays we have many types of pulsed-light sources at our disposal, each of them characterized by different pulse durations (from few fs up to few ns), different pulse-repetition rates (from few Hz to 100 MHz) and a wide range of energies per pulse (from few nJ to several J). However, not all these pulsed light can be easily measured. In the mesoscopic intensity regime, for example, detectors endowed with photon-number resolution are required so as to determine shot-by-shot photon numbers or, at least, to characterize some features of the optical states. In fact, full characterization of the optical state, obtained e.g. by evaluating its Wigner function, can be achieved with optical homodyne tomography (OHT) (Raymer, 1997), a technique that over the years has proved its effectiveness in reconstructing both classical and quantum states, even if further optimizations are needed in the case of pulsed fields (Zavatta et al., 2006). Direct detection schemes are an alternative to OHT in all the cases in which knowing the statistics of detected photons is sufficient to characterize the signal state, as demonstrated in the pioneering work of Arecchi (Arecchi, 1965). Obviously, the implementation of a direct detection scheme requires a proper choice of the detector, the development of a calibration 11
Reconstruction of photon statistics of optical states provides fundamental information on the nature of any optical field and finds various relevant applications. Nevertheless, no detector that can accurately discriminate the number of incident photons is available, whereas reconstruction by quantum tomography is not an easily implementable technique suited for a diffuse use. Even if on/off detectors, as usual avalanche photodiodes operating in Geiger mode, seem useless as photocounters, recently it was shown that reconstruction of photon statistics is possible by considering variable quantum efficiency. We have experimentally demonstrated the potential of this technique by reconstructing photon statistics for various optical fields both in the cw and pulsed regime ranging from heralded photon states to multi-thermal and coherent ones. In this paper, after having introduced the method, a review of the results obtained for the mono-partite case is given and the extension to bi-partite case is presented in detail.
Quantum states are ultimately responsible for numerous counterintuitive phenomena that defy classical intuition. As the development of quantum technologies accelerates, our ability to harness these quantum resources becomes essential. This review addresses a fundamental question. How do we quantify the quantumness of a state, and which specific traits distinguish it from its classical counterparts? We examine quantumness through both theoretical and operational lenses, providing a clear framework for state characterization. Ultimately, we demonstrate that certifying quantumness is not just a theoretical exercise. It is a practical necessity for identifying, and realizing quantum advantage in real-world applications.
Non-classical correlations in optical beams offer an unprecedented opportunity for surpassing the conventional limits of sensitivity and resolution in optical measurements and imaging, especially, but not only, when low photon flux, down to the single photon, is measured. We review the principles of quantum imaging and sensing techniques that exploit sub-Poissonian photon statistics and non-classical photon number correlation, presenting some state-of-the-art achievements in the field. These quantum photonics protocols have the potential to trigger major steps in many applications, such as microscopy and biophotonics, and represent an important opportunity for a new deal in radiometry and photometry.