相关论文: Correlation coefficients and the Robertson-Schroed…
The thermodynamic uncertainty relation sets the minimal bound of the cost-precision trade-off relation for dissipative processes. Examining the dynamics of an internally coupled system that is driven by a constant thermodynamic force, we…
This paper studies multipartite observables formed from sums of local self-adjoint contractions on tensor product Hilbert spaces. The square of such a sum has a parity structure: after decomposing each local product into commutator and…
We consider so-called univariate unlinked (sometimes ``decoupled,'' or ``shuffled'') regression when the unknown regression curve is monotone. In standard monotone regression, one observes a pair $(X,Y)$ where a response $Y$ is linked to a…
The Pearson correlation, correlation ratio, and maximal correlation have been well-studied in the literature. In this paper, we study the conditional versions of these quantities. We extend the most important properties of the unconditional…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary…
We present uncertainty relations based on Wigner--Yanase--Dyson skew information with quantum memory. Uncertainty inequalities both in product and summation forms are derived. \mbox{It is} shown that the lower bounds contain two terms: one…
Having the quantum correlations in a general bipartite state in mind, the information accessible by simultaneous measurement on both subsystems is shown never to exceed the information accessible by measurement on one subsystem, which, in…
The quantification of the "measurement uncertainty" aspect of Heisenberg's Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two…
A numerical illustration of a universally valid Heisenberg uncertainty relation, which was proposed recently, is presented by using the experimental data on spin-measurements by J. Erhart, et al.[ Nature Phys. {\bf 8}, 185 (2012)]. This…
Pearson's r, the most widely-used correlation coefficient, is traditionally regarded as exclusively capturing linear dependence, leading to its discouragement in contexts involving nonlinear relationships. However, recent research…
We ask which is the best strategy to reveal uncertainty relations between comple- mentary observables of a continuous variable system for coarse-grained measurements. This leads to the derivation of new uncertainty relations for…
We analyze entropic uncertainty relations in a finite dimensional Hilbert space and derive several strong bounds for the sum of two entropies obtained in projective measurements with respect to any two orthogonal bases. We improve the…
Seemingly unrelated regression models generalize linear regression models by considering multiple regression equations that are linked by contemporaneously correlated disturbances. Robust inference for seemingly unrelated regression models…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
Based on his extension of the classical argument of Einstein, Podolsky and Rosen, Schr\"odinger observed that, in certain quantum states associated with pairs of particles that can be far away from one another, the result of the measurement…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
The uncertainty principle lies at the heart of quantum mechanics, as it describes the fundamental trade-off between the precision of position and momentum measurements. In this work, we study the quantum particle in the Boltzmann states and…
Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…
A multimode uncertainty relation (generalising the Robertson-Schroedinger relation) is derived as a necessary constraint on the second moments of n pairs of canonical operators. In turn, necessary conditions for the separability of…