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Quantum measurement is a fundamental cornerstone of experimental quantum computations. The main issues in current quantum measurement strategies are the high number of measurement rounds to determine a global optimal measurement output and…
We study the simultaneous estimation of multiple phases as a discretised model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each…
The estimation of quantum entropies and distance measures, such as von Neumann entropy, R\'{e}nyi entropy, Tsallis entropy, trace distance, and fidelity-induced distances such as the Bures distance, has been a key area of research in…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
In this thesis, we present optimization tools for different problems in quantum information theory. First, we introduce an algorithm for quantum estate estimation. The algorithm consists of orthogonal projections on intersecting…
The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in…
The report presents a general approach for estimating quantum information technologies by means of fuzzy quantum measurements. The developed methods are used for precision reconstruction of quantum states under conditions of significant…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
We develop a quantum process tomography method, which variationally reconstruct the map of a process, using noisy and incomplete information about the dynamics. The new method encompasses the most common quantum process tomography schemes.…
Quantum sensors are among the most promising quantum technologies, allowing to attain the ultimate precision limit for parameter estimation. In order to achieve this, it is required to fully control and optimize what constitutes the…
Liquid state nuclear magnetic resonance (NMR) techniques have produced some spectacular successes in the construction of small quantum computers, and NMR is currently by far the leading technology for quantum computation. There are,…
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.
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
We propose a high efficiency tomographic scheme to reconstruct an unknown quantum state of the qubits by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the…
A central task in medical imaging is the reconstruction of an image or function from data collected by medical devices (e.g., CT, MRI, and PET scanners). We provide quantum algorithms for image reconstruction with exponential speedup over…
Quantum state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements does, as a rule, not yield a unique result. We derive a reconstruction scheme where both the likelihood and the von…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
This is the draft version of a review paper which is going to appear in "Advances in Imaging and Electron Physics"
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary `cluster' problems to exploit the locality of the correlated physics. In this work we critically review approaches to…