Related papers: Adaptive estimation of qubits by symmetry measurem…
We consider the problem of determining the weights of a quantum ensemble. That is to say, given a quantum system that is in a set of possible known states according to an unknown probability law, we give strategies to estimate the…
The quantum variables that can be accessed directly by experiments are described by observables. Therefore, physical parameters can only be evaluated indirectly, via estimations based on experimental measurement results. I show that the…
We present the optimal scheme for estimating a pure qubit state by means of local measurements on N identical copies. We give explicit examples for low N. For large N, we show that the fidelity saturates the collective measurement bound up…
The evolution of the quantum state of a system upon measurement results in state update. In this work, we investigate the characterization of updated states of multi-partite entangled qubit states with non-destructive weak measurements,…
By quantum calibration we name an experimental procedure apt to completely characterize an unknown measurement apparatus by comparing it with other calibrated apparatuses. Here we show how to achieve the calibration of an arbitrary…
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
We discuss the problem of estimating a general (mixed) qubit state. We give the optimal guess that can be inferred from any given set of measurements. For collective measurements and for a large number $N$ of copies, we show that the error…
Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases…
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 propose a classification of measurement apparatuses based on their reliability and accessibility. Our notion of reliability parameterises the possibility of getting unexpected wrong results when using the apparatus in a given time…
Quantum computing is a growing field where the information is processed by two-levels quantum states known as qubits. Current physical realizations of qubits require a careful calibration, composed by different experiments, due to noise and…
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…
We exhibit measurements for optimal state estimation which have a finite number of outcomes. This is achieved by a connection between finite optimal measurements and Gauss quadratures. The example we consider to illustrate this connection…
We study the convergence properties of state estimates of an oscillating qubit being monitored by a sequence of \textit{discrete}, unsharp measurements. Our method derives a differential equation determining the evolution of the estimation…
We address the problem of information completeness of quantum measuremets in connection to quantum state tomography and with particular concern to quantum symplectic tomography. We put forward some non-trivial situations where…
Measurements of quantum systems can be used to generate classical data that is truly unpredictable for every observer. However, this true randomness needs to be discriminated from randomness due to ignorance or lack of control of the…
Quantum measurements, alongside quantum states and processes, form a cornerstone of quantum information processing. However, unlike states and processes, their efficient characterisation remains relatively unexplored. We resolve this…
We report our theoretical and experimental investigations into errors in quantum state estimation, putting a special emphasis on their asymptotic behavior. Tomographic measurements and maximum likelihood estimation are used for estimating…
Syndrome measurements made in quantum error correction contain more information than is typically used. We show that the statistics of data from syndrome measurements can be used to do the following: (i) estimation of parameters of an error…
We propose a quantum device that can approximate any projective measurement on a qubit. The desired measurement basis is selected by the quantum state of a "program register". The device is optimized with respect to maximal average fidelity…