Related papers: Information geometry of density matrices and state…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
A discrimination problem consists of $N$ linearly independent pure quantum states $\Phi=\{\ket{\phi_i}\}$ and the corresponding occurrence probabilities $\eta=\{\eta_i\}$. To any such problem we associate, up to a permutation over the…
Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…
We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value. In this scenario, new notions of informationally complete POVMs emerge, which…
A quantum system's state is identified with a density matrix. Though their probabilistic interpretation is rooted in ensemble theory, density matrices embody a known shortcoming. They do not completely express an ensemble's physical…
The density ratio of two probability distributions is one of the fundamental tools in mathematical and computational statistics and machine learning, and it has a variety of known applications. Therefore, density ratio estimation from…
The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in…
For a quantum system, a density matrix rho that is not pure can arise, via averaging, from a distribution mu of its wave function, a normalized vector belonging to its Hilbert space H. While rho itself does not determine a unique mu,…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
A phenomenological method based on the natural orbital representation is applied to construct the ground state one-body density matrix which describes correctly both density and momentum distributions in $^{4}He$, $^{16}O$ and $^{40}Ca$…
An algorithm to calculate the density of states, based on the well-known Wang-Landau method, is introduced. Independent random walks are performed in different restricted ranges of energy, and the resultant density of states is modified by…
We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure…
It is known that on a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive densities that is invariant under the action of the diffeomorphism group, is of the form $$…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
Eigenvalues of a density matrix characterize well the quantum state's properties, such as coherence and entanglement. We propose a simple method to determine all the eigenvalues of an unknown density matrix of a finite-dimensional system in…
We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: Hilbert-Schmidt measure, Bures (statistical) measure, the measures induced by…
Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled…
In this paper I show that any $m$th-degree polynomial function of the elements of the density matrix $\rho$ can be determined by finding the expectation value of an observable on $m$ copies of $\rho$, without performing state tomography.…
Ensembles of random density matrices determined by various probability measures are analysed. A simple and efficient algorithm to generate at random density matrices distributed according to the Bures measure is proposed. This procedure may…