Related papers: On the Formulas for Quantum Mean Values for a Comp…
We derive an analytical formula for the covariance $\mathrm{Cov}(A,B)$ of two smooth linear statistics $A=\sum_i a(\lambda_i)$ and $B=\sum_i b(\lambda_i)$ to leading order for $N\to\infty$, where $\{\lambda_i\}$ are the $N$ real eigenvalues…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…
In this paper, we present a general theory of finite quantum measurements, for which we assume that the state space of the measured system is a finite dimensional Hilbert space and that the possible outcomes of a measurement is a finite set…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
Generalized quantum statistics, such as paraboson and parafermion statistics, are characterized by triple relations which are related to Lie (super)algebras of type B. The correspondence of the Fock spaces of parabosons, parafermions as…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
For an arbitrary preparation, quantum mechanical descriptions refer to the complementary contexts set by incompatible measurements. We argue that an arbitrary preparation, therefore, should be described with respect to such a context by its…
In many physical applications, bound states and/or resonances are observed, which raises the question whether these states are elementary or composite. Here we elaborate on several methods for calculating the compositeness $X$ of bound…
The observables associated with a quantum system $S$ form a non-commutative algebra ${\mathcal A}_S$. It is assumed that a density matrix $\rho$ can be determined from the expectation values of observables. But $\mathcal A_S$ admits inner…
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…
We define generalized bialgebras and Hopf algebras and on this basis we introduce quantum categories and quantum groupoids. The quantization of the category of linear (super)spaces is constructed. We establish a criterion for the classical…
We consider the problem of estimating the Fr\'echet and conditional Fr\'echet mean from data taking values in separable metric spaces. Unlike Euclidean spaces, where well-established methods are available, there is no practical estimator…
The eigenvalue statistics of quantum ideal gases with single particle energies $e_n=n^\alpha$ are studied. A recursion relation for the partition function allows to calculate the mean density of states from the asymptotic expansion for the…
We use representation theory to write a formula for the magnetisation of the quantum Heisenberg ferromagnet. The core new result is a spectral decomposition of the function $\alpha_k 2^{\alpha_1+\dotsb+\alpha_n}$ where $\alpha_k$ is the…
We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…
Informationally complete measurements allow the estimation of expectation values of any operator on a quantum system, by changing only the data-processing of the measurement outcomes. In particular, an informationally complete measurement…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
To elucidate ideal measurements, one must explain how individual events emerge from quantum theory which deals with statistical ensembles, and how different may end up with different final states. This so-called "measurement problem" is…
A quantum statistical model of nuclear multifragmentation is proposed. The recurrence equation method used within the canonical ensemble makes the model solvable and transparent to physical assumptions and allows to get results without…