相关论文: An optimal entropic uncertainty relation in a two-…

Heisenberg's uncertainty principle implies that if one party (Alice) prepares a system and randomly measures one of two incompatible observables, then another party (Bob) cannot perfectly predict the measurement outcomes. This implication…

We improve the entropic uncertainty relations for position and momentum coarse-grained measurements. We derive the continuous, coarse-grained counterparts of the discrete uncertainty relations based on the concept of majorization. The…

We classify and analyze the stability of all relative equilibria for the two-body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrinsic Riemannian data of the problem.

This note examines the implications of randomly selecting vectors from an infinite-dimensional Hilbert space on linear independence, assuming that for all $k$, the first $k$ vectors follow an absolutely continuous law with respect to a…

Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied…

This paper is concerned with all tests for continuous-variable entanglement that arise from linear combinations of second moments or variances of canonical coordinates, as they are commonly used in experiments to detect entanglement. All…

We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that…

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum…

We present a significantly improved scheme of entanglement detection inspired by local uncertainty relations for a system consisting of two qubits. Developing the underlying idea of local uncertainty relations, namely correlations, we…

An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…

We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be…

The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved…

We investigate the uncertainty principle for two successive projective measurements in terms of R\'enyi entropy based on a single quantum system. Our results cover a large family of the entropy (including the Shannon entropy) uncertainty…

The uncertainty principle, which bounds the uncertainties involved in obtaining precise outcomes for two complementary variables defining a quantum particle, is a crucial aspect in quantum mechanics. Recently, the uncertainty principle in…

We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…

We discuss the detection of entanglement in interacting quantum spin systems. First, thermodynamic Hamiltonian-based witnesses are computed for a general class of one-dimensional spin-1/2 models. Second, we introduce optimal bipartite…

We extend a class of recently derived thermodynamic uncertainty relations to vector-valued observables. In contrast to the scalar-valued observables examined previously, this multidimensional thermodynamic uncertainty relation provides a…

We study universal uncertainty relations and present a method called joint probability distribution diagram to improve the majorization bounds constructed independently in [Phys. Rev. Lett. 111, 230401 (2013)] and [J. Phys. A. 46, 272002…

We study the relative position of three subspaces in a separable infinite-dimensional Hilbert space. In the finite-dimensional case, Brenner described the general position of three subspaces completely. We extend it to a certain class of…

Generalized uncertainty relations may depend not only on the commutator relation of two observables considered, but also on mutual correlations, in particular, on entanglement. The equivalence between the uncertainty relation and Bohr's…