Related papers: Optimal quantum tomography of permutationally inva…
We describe an optimized, self-correcting procedure for the Bayesian inference of pure quantum states. By analyzing the history of measurement outcomes at each step, the procedure returns the most likely pure state, as well as the optimal…
We discuss quantitatively the complementarity of information transmitted by a quantum system prepared in a basis state in one out of several different mutually unbiased bases (MUBs). We obtain upper bounds on the information available to a…
The article undertakes the problem of pure state estimation from projective measurements based on photon counting. Two generic frames for qubit tomography are considered -- one composed of the elements of the SIC-POVM and the other defined…
Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few…
Quantum coherence is a key resource in quantum information processing scenarios, and quantifying coherence is an important task for both quantum foundation and quantum technology. However, until now, all most of coherence measures are…
Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple…
Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting…
We construct an informationally complete set of mutually unbiased - like bases for N ququarts. These bases are used in an explicit tomographic protocol which performance is analyzed by estimating quadratic errors and compared to other…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
From a practical perspective it is advantageous to develop methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of mutually unbiased bases (MUBs) needed to…
Tomographic reconstruction of the many-body quantum state of a scalable qubit system is of paramount importance in quantum computing technologies. However, conventional approaches which use tomographically orthogonal base measurements…
We present optimal and minimal measurements on identical copies of an unknown state of a qubit when the quality of measuring strategies is quantified with the gain of information (Kullback of probability distributions). We also show that…
We study the discrimination of N mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value. After considering the discrimination…
Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…
It is shown that, despite strong nonlinearity, entanglement of formation of two-qubit state can be measured without prior state reconstruction. Collective measurements on small number of copies are provided that allow to determine quantum…
The present short review article illustrates the latest theoretical developments on quantum tomography, regarding general optimization methods for both data-processing and setup. The basic theoretical tool is the informationally complete…
This short note highlights the most prominent mathematical problems and physical questions associated with the existence of the maximum sets of mutually unbiased bases (MUBs) in the Hilbert space of a given dimension
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…
Reconstructing quantum states is an important task for various emerging quantum technologies. The process of reconstructing the density matrix of a quantum state is known as quantum state tomography. Conventionally, tomography of arbitrary…