Fundamental Limits of Classical and Quantum Imaging

Relating to magnified image formation systems, we consider two processes in this work: quantum and classical incoherent imaging. There are similarities and differences between them. A similarity is that the optical transfer functions (OTFs) of both systems are obtained by calculating a correlation function. Concerning the differences, only two were found. The first difference is that, unlike classical incoherent imaging, quantum imaging with photon pairs generated by spontaneous parametric down-conversion is sensitive to the phase in the function which describes the object. The second difference is that the OTF of the quantum imaging system is a cross-correlation function of the OTFs of the signal and idler arms, while the OTF of the classical incoherent imaging system is an autocorrelation of the only pupil function existing in this case. We explore experimentally the second difference. We report the observation of a highly resolved image produced by a quantum light source in a setup where an incoherent light source is unable to spatially resolve the image of the object. The spatial resolution of the image is studied in a situation where the size of the object is magnified at the image.

One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. Even though we still have questions in regard to fundamental issues of the entangled quantum systems, quantum entanglement has started to play important roles in practical applications. Quantum imaging is one of the hot topics. Quantum imaging has many interesting features which are useful for different applications. For example, quantum imaging can be nonlocal, which is useful for secure two-dimensional information transfer. Quantum imaging can reach a much higher spatial resolution comparing with classical imaging, even beyond the diffraction limit, which is useful for lithography and other microsystem fabrication technology. It is not a violation of the uncertainty principle, however, a quantum mechanical multi-particle phenomenon.

Properties of quantum states have disclosed new technologies, ranging from quantum information to quantum metrology. Among them a recent research field is quantum imaging, addressed to overcome limits of classical imaging by exploiting spatial properties of quantum states of light . In particular quantum correlations between twin beams represent a fundamental resource for these studies. One of the most interesting proposed scheme exploits spatial quantum correlations between parametric down conversion light beams for realizing sub-shot-noise imaging of the weak absorbing objects, leading ideally to a noise-free imaging. Here we present the first experimental realisation of this scheme, showing its capability to reach a larger signal to noise ratio (SNR) with respect to classical imaging methods. This work represents the starting point of this quantum technology that can have relevant applications, especially whenever there is a need of a low photon flux illumination (e.g. as with certain biological samples).

We explore the use of nonlinear optical methods for important applications in quantum information science. One example is the use nonlinear optical methods in the context of “quantum imaging.” We describe some of the conceptual possibilities afforded by the marriage of quantum and classical imaging methods, and we describe recent work that illustrates some of these features. We also address the complementary issue of how advanced imaging protocols can allow one to utilize and manipulate the enormous information content residing in the transvers structure of a quantum light field.

Quantum imaging utilizing entangled photon pairs takes advantage of their strong quantum correlations to surpass the limitations of classical imaging techniques in terms of spatial resolution and signal-to-noise ratio. However, due to the low brightness of entangled photon sources, an enormous amount number of intensity images (\(\sim 10^7\)) is required for imaging, posing a challenge for practical implementation. In this study, we propose the use of a BiBO crystal for generating entangled photons to enhance the efficiency of quantum imaging. A BiBO crystal has large nonlinear optical coefficient, so it has been expected to serve as a high-brightness entangled photon source. However, a BiBO crystal has never been applied to quantum imaging because it's relatively recently discovered. Here, we investigate the potential of a BiBO crystal as a light source for high-efficiency quantum imaging by performing parallel intensity correlation measurements and implementing quantum image distillation as an example in comparison with the commonly used a BBO crystal. As a result, we achieved a tenfold reduction in measurement time of the conventional method and a significant improvement in imaging efficiency.

Quantum image computing has attracted attention due to its vast storage capacity and faster image data processing, leveraging unique properties such as parallelism, superposition, and entanglement, surpassing classical computers. Although classical computing power has grown substantially over the last decade, its rate of improvement has slowed, struggling to meet the demands of massive datasets. Several approaches have emerged for encoding and compressing classical images on quantum processors. However, a significant limitation is the complexity of preparing the quantum state, which translates pixel coordinates into corresponding quantum circuits. Current approaches for representing large-scale images require higher quantum resources, such as qubits and connection gates, presenting significant hurdles. This article aims to overview the pixel intensity and state preparation circuits requiring fewer quantum resources and explore effective compression techniques for medium and high-resolution images. It also conducts a comprehensive study of quantum image representation and compression techniques, categorizing methods by grayscale and color image types and evaluating their strengths and weaknesses. Moreover, the efficacy of each model’s compression can guide future research toward efficient circuit designs for medium- to high-resolution images. Furthermore, it is a valuable reference for advancing quantum image processing research by providing a systematic framework for evaluating quantum image compression and representation algorithms.

Quantum imaging can beat classical resolution limits, imposed by the diffraction of light. In particular, it is known that one can reduce the image blurring and increase the achievable resolution by illuminating an object by entangled light and measuring coincidences of photons. If an n-photon entangled state is used and the nth-order correlation function is measured, the point-spread function (PSF) effectively becomes sqrt{n} times narrower relatively to classical coherent imaging. Quite surprisingly, measuring n-photon correlations is not the best choice if an n-photon entangled state is available. We show that for measuring (n − 1)-photon coincidences (thus, ignoring one of the available photons), PSF can be made even narrower. This observation paves a way for a strong conditional resolution enhancement by registering one of the photons outside the imaging area. We analyze the conditions necessary for the resolution increase and propose a practical scheme, suitable for observation and exploitation of the effect.

Quantum imaging with undetected photons is recently appeared promising brunch of quantum optics. Due to properties of photon pairs (signal and idler), generated via spontaneous down-conversion (SPDC) process and phenomenon of induced coherence, one can obtain phase or intensity image of object without detecting of the photon, interacting with it. The theoretical treatment and limitations of such a system with an only crystal and increased brightness are given.

Quantum imaging is an advanced method for microscopy and investigating the optical properties of materials or biomedical samples with high accuracy, low noise, and minimal photo-damage. Previously, we proposed a quantum imaging technique where variations in polarization angle due to reflection or transmission enhanced image contrast in the second-order autocorrelation function at zero delay, g²(0). However, the observed image resolution was insufficient. In this study, we optimized the coincidence window to better distinguish photon statistics and used an objective lens to focus the entangled photon beams, improving image quality. Although effective for various samples, this method has limitations for samples exhibiting polarization disturbances such as photon scattering. Nevertheless, it demonstrates superior imaging performance under noisy conditions and low illumination, offering potential for high-quality quantum imaging applications.

Coincidence, or ghost, imaging is a technique that uses two correlated optical fields to form an image of an object. In this work we identify aspects of coincidence imaging which can be performed with classically correlated light sources and aspects which require quantum entanglement. We find that entangled photons allow high-contrast, high-resolution imaging to be performed at any distance from the light source. We demonstrate this fact by forming ghost images in the near and far fields of an entangled photon source, noting that the product of the resolutions of these images is a factor of 3 better than that which is allowed by classical diffraction theory.

By applying information theoretic concepts to analog-to-digital convertor (ADC) design, we have created a mathematical framework from which the fundamental limit for the resolution-bandwidth product of any ADC may be derived. We found the surprising result that the limiting resolution of any ADC is proportional to oversampling-ratio (OSR), as opposed to widely-held belief that the resolution is proportional to \(log_2(OSR)\), a dramatic increase in the achievable resolution. This result, which resembles Shannon’s well-known result for the capacity of a communication channel, represents a paradigm shift in our understanding of data conversion methods and provides encouragement that new methods may be found. Furthermore, to achieve this theoretical limit, the internal analog modulator (or filter) of an ADC should be a chaotic system, so that both small as well as large changes in the input signal cause large (but bounded) deterministic changes at the output of the modulator - analogous to the “Butterfly effect”. This led us to discover a new class of ADCs, which we call TurboADC’s, that can trade off resolution for bandwidth on the fly, keeping their product equal to the fundamental information theoretic limit. These designs impose modest requirements on the analog front-end resources and power at the expense of greater complexity in the back-end decoder. A discrete-time TurboADC proposed here is a hybrid of a 1st order Delta-Sigma modulator and a Cyclic ADC, with the best features of both designs - oversampling, noise shaping, and simplicity from the Sigma-delta ADC approach and fast half-interval searching from Cyclic ADC’s. Simulations of the proposed TurboADC confirm our finding that the resolution of an ADC may approach fundamental limit of OSR bits within the baseband.

The resolution ofa classical imaging system is limited by diffraction.This limit can be overcome, for example, by implementing various formsof localization microscopy in which the center of a fluorescence distributionis estimated to an accuracy scaling with the square root of the numberof detected photons, . In quantumimaging the object can be illuminatedusing correlated photon-pairs, leading early work to suggest thata improvement could be obtainedas a resultof averaging the position of N = 2 events. However,similar to quantum lithography, which relies upon quantum illuminationusing entangled photon-pairs and two-photon absorption, the minimumresolvable feature size is reduced by a factor of 2, not just . Quantum imaging schemes canalso leadto a factor of 2 improvement. By using a similar source of correlatedphoton-pairs to illuminate an object, a single-photon sensitive camerato detect the photon-pairs, and an image processing algorithm to recordand sum the bisector positions of the transmitted photon-pairs, werealize a similar factor of ×2 improvement in image resolution,surpassing that of most earlier quantum imaging work.

We propose a continuous variable quantum state tomography protocol of electrons which result from the ionization of atoms or molecules by the absorption of extreme ultraviolet light pulses. Our protocol is benchmarked against a direct calculation of the quantum state of photoelectrons ejected from helium and argon in the vicinity of a Fano resonance. In the latter case, we furthermore distill ion-photoelectron entanglement due to spin-orbit splitting. This opens routes toward the investigation of quantum coherence and entanglement properties on the ultrafast timescale.

Qubit readout is commonly performed by thresholding a collection of analog detector signals to obtain a sequence of single-shot bit values. The intrinsic irreversibility of the mapping from analog to digital signals discards soft information associated with an aposteriori confidence that can be assigned to each bit value when a detector is well characterized. Accounting for soft information, we show significant improvements in enhanced state detection with the quantum repetition code as well as quantum state or parameter estimation. These advantages persist in spite of non-Gaussian features of realistic readout models, experimentally relevant small numbers of qubits, and finite encoding errors. These results show useful and achievable advantages for a wide range of current experiments on quantum state tomography, parameter estimation, and qubit readout.

Quantum tomography is an important tool for obtaining information about the quantum state from experimental data. In this study, we conduct a comparative analysis of various quantum tomography protocols, including protocols based on highly symmetric sets of state vectors, on mutually unbiased bases (MUB), and two-level transformations. Using the universal distribution for the fidelity of quantum state tomography, we estimate the fidelity and efficiency of quantum measurements for qudits of various dimensions as applied to a set of random states uniformly distributed over the Haar measure.