Related papers: Uncertainty principle with quantum Fisher informat…
Quantum mechanics gives a new breakthrough to the field of parameter estimation. In the realm of quantum metrology, the precision of parameter estimation is limited by the quantum Fisher information. We introduce the measures of partial…
Uncertainty relations represent a foundational principle in quantum mechanics, imposing inherent limits on the precision with which \textit{mechanically} conjugate variables such as position and momentum can be simultaneously determined.…
We add non-linear and state-dependent terms to quantum field theory. We show that the resulting low-energy theory, non-linear quantum mechanics, is causal, preserves probability and permits a consistent description of the process of…
A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…
We present a systematic procedure to obtain all necessary and sufficient (quantum) constraints on the expectation values for any set of qudit's operators. These constraints---arise form Hermiticity, normalization, and positivity of a…
The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either…
Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…
We prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in…
We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all…
This paper is generally concerned with understanding how the uncertainty principle arises in formulations of quantum mechanics, such as the decoherent histories approach, whose central goal is the assignment of probabilities to histories.…
The goal of this paper is to calculate exactly the average of uncertainty-product of two bounded observables and to establish its typicality over the whole set of finite dimensional quantum pure states. Here we use the uniform ensembles of…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…
Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
When you measure an observable, A, in Quantum Mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some non-commuting observable, B. The standard Uncertainty Relation puts a lower bound on…
This paper presents a robust performance analysis result for a class of uncertain quantum systems containing sector bounded nonlinearities arising from perturbations to the system Hamiltonian. An LMI condition is given for calculating a…
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
The quantum Fisher information is a Riemannian metric, defined on the state space of a quantum system, which is symmetric and decreasing under stochastic mappings. Contrary to the classical case such a metric is not unique. We complete the…