Related papers: On definition of quantum tomography via the Sobole…
We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.
We calculate the Wigner (quasi)probability distribution function of the quantum optical elliptical vortex (QEV), generated by coupling squeezed vacuum states of two modes. The coupling between the two modes is performed by using beam…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
The problem of quantum particle moving in Dirac delta potential with instant changing well depth is studied by using formalism of tomographic representation of quantum mechanics.The bound state tomogram is given in terms of error…
Wigner function tomography is indispensable for characterizing quantum states, but its commonly used version, balanced homodyne detection, suffers from several weaknesses. First, it requires efficient detection, which is critical for…
Consistent quantum formalism based on the localized basis of the Wannirer functions in Heisenberg and Schrodinger pictures to describe propagation of electromagnetic field in a three dimensional media including diffraction is presented. In…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
We study different techniques that allow us to gain complete knowledge about an unknown quantum state, e.g. to perform full tomography of this state. We focus on two apparently simple cases, full tomography of one and two qubit systems. We…
The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical…
The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical…
Quantifying and verifying the control level in preparing a quantum state are central challenges in building quantum devices. The quantum state is characterized from experimental measurements, using a procedure known as tomography, which…
We study high dimensional integration in the quantum model of computation. We develop quantum algorithms for integration of functions from Sobolev classes $W^r_p([0,1]^d)$ and analyze their convergence rates. We also prove lower bounds…
We present the first complete optimization of quantum tomography, for states, POVMs, and various classes of transformations, for arbitrary prior ensemble and arbitrary representation, giving corresponding feasible experimental schemes.
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…
We introduce an efficient method to reconstruct the Wigner function of many-mode continuous variable systems. It is based on convex optimization with semidefinite programs, and also includes a version of the maximum entropy principle, in…
All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This paper develops coherent and comprehensive methodologies and mathematical models to describe Fourier…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. This quantity is properly defined only for states that possess a positive Wigner function, which we name…
This article outlines a novel interpretation of quantum theory: the Q-based interpretation. The core idea underlying this interpretation, recently suggested for quantum field theories by Drummond and Reid [2020], is to interpret the phase…
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…