相关论文: Canonical divergence for flat $\alpha$-connections…
One of the basic observations of the classical world is that physical entities are real and can be distinguished from each other. However, within quantum theory, the idea of physical realism is not well established. A framework to analyse…
An isomorphism between two hermitian unitals is proved, and used to treat isomorphisms of classical groups that are related to the isomorphism between certain simple real Lie algebras of types A and D (and rank 3).
In this paper, we use the canonical connection instead of Levi-Civita connection to study the smooth maps between almost Hermitian manifolds, especially, the pseudoholomorphic ones. By using the Bochner formulas, we obtian the…
We show that a bi-flat F-structure $(\nabla,\circ,e,\nabla^*,*,E)$ on a manifold $M$ defines a differential bicomplex $(d_{\nabla},d_{E\circ\nabla^*})$ on forms with value on the tangent sheaf of the manifold. Moreover, the sequence of…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
In this article, we prove that the quantum $f$-divergence between two normal states on a semifinite von~Neumann algebra is equal to the classical $f$-divergence between two corresponding classical states, which are called Nussbaum-Szko{\l}a…
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
Let $M$ be a closed oriented Riemannian manifold of dimension $2 \leq d \leq 7$, and let $\rho \in H^{d - 1}(M, \mathbb R)$ have unit norm. We construct a lamination $\lambda_\rho$ whose leaves are exactly the minimal hypersurfaces which…
Let $\varphi:\mathbb{R}\rightarrow \mathbb{R}$ be a continuously differentiable function on an interval $J\subset\mathbb{R}$ and let $\boldsymbol{\alpha}=(\alpha_1,\alpha_2)$ be a point with algebraically conjugate coordinates such that the…
We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere,…
In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information…
We present a classification of the complete, simply connected, contact metric $(\kappa,\mu)$-spaces as homogeneous contact metric manifolds, by studying the base space of their canonical fibration. According to the value of the Boeckx…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
The term "Layers of classicality" in the context of quantum measurements, was introduced in [T. Heinosaari, Phys. Rev. A 93, 042118 (2016)]. The strongest layer among these consists of the sets of observables that can be broadcast and the…
Deviations from classical physics when distant quantum systems become correlated are interesting both fundamentally and operationally. There exist situations where the correlations enable collaborative tasks that are impossible within the…
Given a Banach algebra $ \mathcal{A} $ and a continuous homomorphism $\sigma$ on it, the notion of $\sigma$-biflatness for $ \mathcal{A} $ is introduced. This is a generalization of biflatness and it is shown that they are distinct. The…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
Several recent studies have concerned the faith of classical symmetries in quantum space-time. In particular, it appears likely that quantum (discretized, noncommutative,...) versions of Minkowski space-time would not enjoy the classical…
The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and…