相关论文: Metric and classical fidelity uncertainty relation…
We generalize the concept of mutually unbiased bases (MUB) to measurements which are not necessarily described by rank one projectors. As such, these measurements can be a useful tool to study the long standing problem of the existence of…
Recent developments in gravitational path integrals indicate that the nonperturbative physical Hilbert space of a closed universe is one-dimensional within each superselection sector. This raises a basic puzzle: how can a unique…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
This paper introduces a methodology based on Euclidean information theory to investigate local properties of secure communication over discrete memoryless wiretap channels. We formulate a constrained optimization problem that maximizes a…
Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from…
Boundedness properties of operators associated with non-degenerate symmetric $\alpha$-stable, $\alpha \in (1,2)$, probability measures on $\mathbb{R}^d$ are investigated on appropriate, Euclidean or otherwise, $L^p$-spaces, $p \in…
Embedding data into vector spaces is a very popular strategy of pattern recognition methods. When distances between embeddings are quantized, performance metrics become ambiguous. In this paper, we present an analysis of the ambiguity…
We demonstrate that the local nonfreeness, an unbiased measure of correlation between electrons at a single lattice site, can be computed as the mutual information between local natural spin orbitals. This leads us to prove a general…
The standard state-dependent Heisenberg-Robertson uncertainly-relation lower bound fails to capture the quintessential incompatibility of observables as the bound can be zero for some states. To remedy this problem, we establish a class of…
Building upon a recent analysis of the measurement process in Hamiltonian mechanics, this article investigates the Bayesian epistemology of classical physics -- the landscape of accessible probability distributions over phase space. I prove…
We establish a connection between distributionally robust optimization (DRO) and classical robust statistics. We demonstrate that this connection arises naturally in the context of estimation under data corruption, where the goal is to…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…
It is well known that, due to the uncertainty principle, the Planck constant sets a resolution boundary in phase space and the resulting trade-off in resolution between incompatible measurements has been thoroughly investigated. It is also…
Quantifying differences between probability distributions is fundamental to statistics and machine learning, primarily for comparing statistical uncertainty. In contrast, epistemic uncertainty -- due to incomplete knowledge -- requires…
We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the…
We investigate the fine-grained uncertainty relations for qubit system by measurements corresponding respectively to two and three spin operators. Then we derive the general bound for a combination of two probabilities of projective…
Our investigation of the results of the neutron spin experiment by Ehhart et al. demonstrates that their results cannot be understood in accordance with common sense. For example, their results obtained with different measurement errors are…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of…