相关论文: How to mix a density matrix

Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…

The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…

A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…

This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…

This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…

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 consider ensembles of $N \times N$ Hermitian Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. Assuming sufficient regularity for the probability density…

It has previously been hypothesized, and supported with some experimental evidence, that deeper representations, when well trained, tend to do a better job at disentangling the underlying factors of variation. We study the following related…

Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…

In this survey the possible approaches to the description of the evolution of states of quantum many-particle systems by means of the possible modifications of the density operator which kernel known as density matrix are considered. In…

We show that two chosen ensembles of spin states, which are differently prepared but are described by the same density matrix in quantum mechanics, do not fully share the same measurable characteristics. One characteristic on which they…

We find that the mixed maximally entangled states exist and prove that the form of the mixed maximally entangled states is unique in terms of the entanglement of formation. Moreover, even if the entanglement is quantified by other…

For a mixed quantum state with density matrix $\rho$ there are infinitely many ensembles of pure quantum states, which average to $\rho$. Starting from Laplace principle of insufficient reason (not to give \emph{a priori} preference to any…

Mixed states of a quantum system, represented by density operators, can be decomposed as a statistical mixture of pure states in a number of ways where each decomposition can be viewed as a different preparation recipe. However the fact…

Estimation of quantum states is one of the most important steps in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not…

Contrary to previous claims, it is shown that, for an ensemble of either single-particle systems or multi-particle systems, the realistic interpretation of a superposition state that mathematically describes the ensemble does not imply that…

The generic linear evolution of the density matrix of a system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear…

We introduce a measure of the compatibility between quantum states--the likelihood that two density matrices describe the same object. Our measure is motivated by two elementary requirements, which lead to a natural definition. We list some…

We give a generalization of the random matrix ensembles, including all lassical ensembles. Then we derive the joint density function of the generalized ensemble by one simple formula, which give a direct and unified way to compute the…

In this note I will present a subtle interplay between density matrices and the knowledge about their preparation, and I will argue that there is a need to consider a new type of quantum state, in between pure states and density matrices.