相关论文: Monotone Riemannian metrics on density matrices wi…
Generalized metric spaces are obtained by weakening the requirements (e.g., symmetry) on the distance function and by allowing it to take values in structures (e.g., quantales) that are more general than the set of non-negative real…
We characterize the convexity of functions and the monotonicity of vector fields on metric measure spaces with Riemannian Ricci curvature bounded from below. Our result offers a new approach to deal with some rigidity theorems such as…
The contribution of this work is twofold. The first part deals with a Hilbert-space version of McCann's celebrated result on the existence and uniqueness of monotone measure-preserving maps: given two probability measures $\rm P$ and $\rm…
It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, that is that its integral is one and that the marginal properties are satisfied.…
The physical origin of spacetime discreteness remains a central open problem in quantum gravity, with most existing approaches relying on specific microscopic structures or model-dependent assumptions. In this letter, spacetime discreteness…
Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the…
The measurement problem is to explain why a system which is in a linear combination of states appears, upon measurement, to be in just one of those states. The solution given here is to first show that if one assumes linear, unitary, no…
Symmetries rigidly delimit the landscape of quantum matter. Recently uncovered spatially modulated symmetries, whose actions vary with position, enable excitations with restricted mobility, while Lieb-Schultz-Mattis (LSM) type anomalies…
The critical points of the total scalar curvature functional, restricted to closed $n$-dimensional manifolds with constant scalar curvature metrics and unit volume, are termed CPE metrics. In 1987, Arthur L. Besse conjectured that CPE…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
Let (E,D,P) be a flat vector bundle with a parabolic structure over a punctured Riemann surface, (M,g). We consider a deformation of the harmonic metric equation which we call the Poisson metric equation. This equation arises naturally as…
For the Riemannian space, built from the collective coordinates used within nuclear models, an additional interaction with the metric is investigated, using the collective equivalent to Einstein's curvature scalar. The coupling strength is…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
The measurability by means of continuous measurements, of an observable $\A(t_0)$, at an instant, and of a time averaged observable, $\bar \A=1/T\int \A(t')dt'$, is examined for linear and in particular for non-linear quantum mechanical…
The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…
The study of conditional $q$-entropies in composite quantum systems has recently been the focus of considerable interest, particularly in connection with the problem of separability. The $q$-entropies depend on the density matrix $\rho$…
Constant rescaling of a Riemannian metric appears in many computational settings, often through a global scale parameter that is introduced either explicitly or implicitly. Although this operation is elementary, its consequences are not…
Quantum electronics is significantly involved in the development of the field of quantum information processing. In this domain, the growth of Blind Quantum Source Separation and Blind Quantum Process Tomography has led, within the…
In this work we introduce the randomness which is truly quantum mechanical in nature arising as an act of measurement. For a composite classical system we have the joint entropy to quantify the randomness present in the total system and…