Related papers: Quantum tomography with random diagonal unitary ma…

Quantum process tomography (QPT) methods aim at identifying a given quantum process. The present paper focuses on the estimation of a unitary process. This class is of particular interest because quantum mechanics postulates that the…

We introduce a positive Hermitian operator, the Fisher operator, and use it to examine a measurement process incorporating unitary dynamics and complete measurements. We develop the idea of information complement, the minimization of which…

We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product…

In quantum information geometry, the curvature of von-Neumann entropy and relative entropy induce a natural metric on the space of mixed quantum states. Here we use this information metric to construct a random matrix ensemble for states…

Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically this increases the quantum Fisher information with respect to…

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 computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with…

Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…

We present a diffeomorphism-invariant formulation of differential entropy for Riemannian spaces, providing a fine-grained, coordinate-independent notion of quantum information for continuous variables in physical space. To this end, we…

How precisely can we estimate cosmological parameters by performing a quantum measurement on a cosmological quantum state? In quantum estimation theory the variance of an unbiased parameter estimator is bounded from below by the inverse of…

We reconstruct the explicit formalism of qubit quantum theory from elementary rules on an observer's information acquisition. Our approach is purely operational: we consider an observer O interrogating a system S with binary questions and…

Quantum learning (in metrology and machine learning) involves estimating unknown parameters from measurements of quantum states. The quantum Fisher information matrix can bound the average amount of information learnt about the unknown…

We use a meta-learning neural-network approach to analyse data from a measured quantum state. Once our neural network has been trained it can be used to efficiently sample measurements of the state in measurement bases not contained in the…

We analytically model a one-dimensional lattice with periodic impurities representing a photonic crystal from first principles. We then investigate bound states in the continuum by computing the transmission and reflection coefficients. It…

Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not…

This thesis is a compilation of research in relativistic quantum information theory, and research in quantum reference frames. The research in the former category provides a fundamental construction of quantum information theory of…

Quantum simulation using time evolution in phase estimation-based quantum algorithms can yield unbiased solutions of classically intractable models. However, long runtimes open such algorithms to decoherence. We show how measurement-based…

In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…

The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…

Quantum state tomography provides a fundamental framework for reconstructing quantum states. When the measurement data are not informationally complete, the observed statistics admit multiple compatible density matrices, making the…