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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Recovery of classical images and nontomographic quantum state reconstruction

Celso L. Ladera

Published Jul 19, 1999• 0 citations
Publisher

Abstract

Quantum tomography, as being recently used in atomic optics and quantum optics for quantum state recovery, has been developed in analogue fashion to the standard method of classical computer tomography. Unfortunately, it is only possible to handle a limited number of cases with such methods. Advanced non-tomographic quantum state reconstruction is now being developed as an alternative to achieve reconstruction for arbitrary potential functions. It has now become feasible, in turn, to apply the new method, again in analogue fashion, for the reconstruction of classical images.

DOI
10.1117/12.354781

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Quantum tomography, as being recently used in atomic optics and quantum optics for quantum state recovery, has been developed in analogue fashion to the standard method of classical computer tomography. Unfortunately, it is only possible to handle a limited number of cases with such methods. Advanced non-tomographic quantum state reconstruction is now being developed as an alternative to achieve reconstruction for arbitrary potential functions. It has now become feasible, in turn, to apply the new method, again in analogue fashion, for the reconstruction of classical images.
Quantum computing has emerged as a transformative paradigm, capable of tackling complex computational problems that are infeasible for classical methods within a practical timeframe. At the core of this advancement lies the concept of quantum supremacy, which signifies the ability of quantum processors to surpass classical systems in specific tasks. In the context of tomographic image reconstruction, quantum optimization algorithms enable faster processing and clearer imaging than conventional methods. This study further substantiates quantum supremacy by reducing the required projection angles for tomographic reconstruction while enhancing robustness against image artifacts. Notably, our experiments demonstrated that the proposed algorithm accurately reconstructed tomographic images without artifacts, even when up to 50% error was introduced into the sinogram to induce ring artifacts. Furthermore, it achieved precise reconstructions using only 50% of the projection angles from the original sinogram spanning 0° to 180°. These findings highlight the potential of quantum algorithms to revolutionize tomographic imaging by enabling efficient and accurate reconstructions under challenging conditions, paving the way for broader applications in medical imaging, material science, and advanced tomography systems as quantum computing technologies continue to advance.
Quantum state tomography (QST) refers to any method that allows one to reconstruct the accurate representation of a quantum system based on data obtainable from an experiment. In this paper, we concentrate on theoretical methods of quantum tomography, but some significant experimental results are also presented. Due to a considerable body of literature and intensive ongoing research activity in the field of QST, this overview is restricted to presenting selected ideas, methods, and results. First, we discuss tomography of pure states by distinguishing two aspects—complex vector reconstruction and wavefunction measurement. Then, we move on to the Wigner function reconstruction. Finally, the core section of the article is devoted to the stroboscopic tomography, which provides the optimal criteria for state recovery by including the dynamics in the scheme. Throughout the paper, we pay particular attention to photonic tomography, since multiple protocols in quantum optics require well-defined states of light.
We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging known as Computer Aided Tomography. We explain how this method can be taken over to quantum mechanics, where it leads to a description of the quantum state in terms of the Wigner function which, although may take on negative values, plays the role of the probability density in phase space in classical physics. We explain another approach to quantum state reconstruction based on the notion of Mutually Unbiased Bases, and indicate the relation between these two approaches. Both are for a continuous, infinite-dimensional Hilbert space. We then study the finite-dimensional case and show how the second method, based on Mutually Unbiased Bases, can be used for state reconstruction.