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Efficiently characterizing large quantum states and processes is a central yet notoriously challenging task in quantum information science, as conventional tomography methods typically require resources that grow exponentially with system…
Quantum state tomography suffers from the measurement effort increasing exponentially with the number of qubits. Here, we demonstrate permutationally invariant tomography for which, contrary to conventional tomography, all resources scale…
Associated with the use of conventional integrated parton densities are kinematic approximations on parton momenta which result in unphysical differential distributions for final-state particles. We argue that it is important to reformulate…
The relation of the Wigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics…
A common misconception is that decoherence gives the eigenstates that we observe to be fairly definite about a subsystem (e.g., approximate eigenstates of position) as the elements of the Schmidt basis in which the density matrix of the…
In this study the determinant of the average quadratic error matrix is used as the measure of state estimation efficiency. This quantity is easily computable in some cases, so it gives us a reasonable tool to find optimal measurement setup…
We argue that there is an intrinsic noise on measurements of the equation of state parameter $w=p/\rho$ from large-scale structure around us. The presence of the large-scale structure leads to an ambiguity in the definition of the…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
We examine the full counting statistics of quantum dots, which display super-Poissonian shot noise. By an extension to a generic situation with many excited states we identify the underlying transport process. The statistics is a sum of…
We express the probabilistic character associated to the wave function by treating it as a stochastic variable. This is accomplished by means of a stochastic equation for the wave function whose noise changes the phase of the wave function…
A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix…
The present era of quantum processors with hundreds to thousands of noisy qubits has sparked interest in understanding the computational power of these devices and how to leverage it to solve practically relevant problems. For applications…
Quantum state tomography (QST) is an essential technique for characterizing quantum states. However, practical implementations of QST are significantly challenged by factors such as shot noise, attenuation, and Raman scattering, especially…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate) tests of hypotheses on an unknown value of the parameter…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
Phase estimation in quantum interferometry is a major scenario where the quantum advantage is significantly revealed. Recently, the optimal finite-dimensional probe states (OFPSs) for phase estimation in two-mode quantum interferometry have…
The eigenvalue statistics of quantum ideal gases with single particle energies $e_n=n^\alpha$ are studied. A recursion relation for the partition function allows to calculate the mean density of states from the asymptotic expansion for the…
The density matrix of a two-level system (spin, atom) is usually determined by measuring the three non-commuting components of the Pauli vector. This density matrix can also be obtained via the measurement data of two commuting variables,…