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In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and…
In this paper, we use certain norm inequalities to obtain new uncertain relations based on the Wigner-Yanase skew information. First for an arbitrary finite number of observables we derive an uncertainty relation outperforming previous…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…
A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should use when doing any calculation using the entangled wave function of the pair. This new…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the…
We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the…
We show that for fermion states, measurements of any two finite outcome particle quantum numbers (e.g.\ spin) are not constrained by a minimum total uncertainty. We begin by defining uncertainties in terms of the outputs of a measurement…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…
Bell's inequalities are defined by sums of correlations involving non-commuting observables in each of the two systems. Violations of Bell's inequalities are only possible because the precision of any joint measurement of these observables…
Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger…
We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…
Conventional quantum uncertainty relations (URs) contain dispersions of two observables. Generalized URs are known which contain three or more dispersions. They are derived here starting with suitable generalized Cauchy inequalities. It is…
Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs…
It is shown that the well-defined unbiased measurement or disturbance of a dynamical variable is not maintained for the precise measurement of the conjugate variable, independently of uncertainty relations. The conditionally valid…
We propose an uncertainty-complementarity balance relation and build quantitative connections among non-locality, complementarity, and uncertainty. Our balance relation, which is formulated in a theory-independent manner, states that for…
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…