We show that prior information, such as that a quantum state is sparse in a known mathematical basis, enables algorithmic reconstruction of an initial three-photon state from two-photon coincidence measurements, thereby achieving quantum super-resolution.
The field of quantum information has been growing fast over the past decade. Optical quantum computation, based on the concepts of KLM and cluster states, has witnessed experimental realizations of larger and more complex systems in terms of photon number. Quantum optical systems, which offer long coherence times and easy manipulation of single qubits, allow us to probe quantum properties of the light itself and of the physical systems around it. Recently, a linear scheme for quantum computing, relying on the bosonic nature of particles, has been proposed and realized experimentally with photons. The ability to efficiently measure superpositions of quantum states consisting of several photons is essential to the characterization of such systems. In fact, the entire field of quantum information completely relies on the ability to recover quantum states from measurements. However, the characterization of quantum states requires many measurements, and often necessitates complicated measurements schemes; for example, characterizing qubits requires measurements. Here, we utilize structure, inherent to physically interesting quantum states of light, in order to reduce the complexity in the recovery of a quantum state. In particular, we devise a method enabling the recovery of three-photon quantum states from only two-fold correlation measurements in a single setting. The ability to take two-fold coincidences instead of three-fold offers the recovery of the quantum states in far less measurements and in a considerably higher SNR, because detection of two-photon events is much more likely than that of three-photon ones. The concept suggested here paves the way to further ideas on structure-based super resolution in quantum state tomography, such as recovering a quantum state in an unknown basis in a single setup and recovering the state of several photons without number resolving detectors.
Quantum information processing has emerged as a transformative technology with significant potential across diverse fields, including image processing and data analysis. This paper presents a novel approach to super-resolution computation leveraging the unique properties of quantum information – specifically, superposition and entanglement – to achieve significantly improved results compared to classical methods. We propose a new algorithm that utilizes a quantum-enhanced measurement process to precisely determine pixel values, ultimately leading to enhanced image reconstruction and data interpretation. The core claim of this work is the design of a quantum-informed super-resolution algorithm that surpasses current state-of-the-art performance, particularly in scenarios demanding high-fidelity image reconstruction. This research explores the potential of quantum entanglement and superposition to address challenges inherent in traditional super-resolution techniques. We will detail the underlying mathematical framework, provide a simplified implementation, and discuss the theoretical implications of this approach.
Quantum entanglement, a peculiar phenomenon where two or more particles become linked and share the same fate, has captivated researchers across various fields, and its potential applications are rapidly expanding. This paper explores the utilization of quantum entanglement to develop a novel approach to super-resolution computation, aiming to surpass the limitations of current image processing techniques. We propose a method that leverages the unique properties of entangled states to achieve precise reconstruction of low-resolution images. The core mechanism centers around establishing a "quantum information jump" through entanglement, allowing for detailed analysis and reconstruction of subtle image features. This paper details the proposed algorithm, its underlying principles, and initial experimental validation demonstrating its potential for surpassing traditional methods.
Quantum imaging emerged quite recently as a breakthrough technology of overcoming the diffraction limit in microscopy and enhancement of optical resolution without the necessity to use hard radiation or perform scanning in the near field [1] , [2] . Both, the quantum imaging itself and the more “classical” techniques inspired by it (for example, super-resolution optical fluctuations imaging – SOFI [3] ), rely on detection and analysis of photon (intensity) correlations. Typically, it is believed that the more correlated illuminating light is used and the higher order of the correlations is measured, the larger super-resolution can be achieved. That conclusion is based on efficient narrowing of the point-spread function, which, however, does not necessarily imply better resolution as the ability to reconstruct smaller features of the investigated object successfully.