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A statistically feasible data post-processing method for the conventional qubit state tomography is studied from an information geometrical point of view. It is shown that the space $(-1,1)^3$ of the Stokes parameters $(\xi_1, \xi_2,\xi_3)$…
Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and…
A new algorithmic framework is presented for holographic phase retrieval via maximum likelihood optimization, which allows for practical and robust image reconstruction. This framework is especially well-suited for holographic coherent…
The dynamical likelihood method for analysis of high energy collider events is reformulated. The method is to reconstruct the elementary parton state from observed quantities. The basic assumption is that each of final state partons…
Multimode Gaussian states are a versatile resource for quantum information technologies and have been realized across a wide range of physical platforms. Recent progress in the large-scale generation of such states provides a key ingredient…
We construct a probabilistic quantum cloning machine by a general unitary-reduction operation. With a postselection of the measurement results, the machine yields faithful copies of the input states. It is shown that the states secretly…
We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy…
We propose a general methodology for efficient statistical reconstruction of a quantum state through collection and analysis of photon counting statistics. Our approach includes both strict quantitative criteria for adequacy and…
Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…
Quantum state tomography, a process that reconstructs a quantum state from measurements on an ensemble of identically prepared copies, plays a crucial role in benchmarking quantum devices. However, brute-force approaches to quantum state…
Reconstructing the full quantum state of a many-body system requires the estimation of a number of parameters that grows exponentially with system size. Nevertheless, there are situations in which one is only interested in a subset of these…
Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic…
In standard optical tomographic methods, the off-diagonal elements of a density matrix $\rho$ are measured indirectly. Thus, the reconstruction of $\rho$, even if it is based on linear inversion, typically magnifies small errors in the…
Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…
We study the possibility of performing quantum state reconstruction from a measurement record that is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of a single random unitary map,…
We address the problem of image reconstruction from incomplete measurements, encompassing both upsampling and inpainting, within a learning-based framework. Conventional supervised approaches require fully sampled ground truth data, while…
Modern technology for producing extremely bright and coherent X-ray laser pulses provides the possibility to acquire a large number of diffraction patterns from individual biological nanoparticles, including proteins, viruses, and DNA.…
In quantum tomography, a quantum state or process is estimated from the results of measurements on many identically prepared systems. Tomography can never identify the state or process exactly. Any point estimate is necessarily "wrong" --…
Quantum information has been drawing a wealth of research in recent years, shedding light on questions at the heart of quantum mechanics, as well as advancing fields such as complexity theory, cryptography, key distribution, and chemistry.…
We study the physical implementation of an optimal tomographic reconstruction scheme for the case of determining the state of a multi-qubit system, where trapped ions are used for defining qubits. The protocol is based on the use of…