Related papers: Uncertainty relations based on state-dependent nor…
The uncertainty relation for continuous variables due to Byalinicki-Birula and Mycielski expresses the complementarity between two $n$-uples of canonically conjugate variables $(x_1,x_2,\cdots x_n)$ and $(p_1,p_2,\cdots p_n)$ in terms of…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
Constructive techniques to establish state-independent uncertainty relations for the sum of variances of arbitrary two observables are presented. We investigate the range of simultaneously attainable pairs of variances, which can be applied…
Uncertainty principle is one of the fundamental principles of quantum mechanics. Exploring such uncertainty relations in pre- and postselected (PPS) systems, where weak measurements on post-selected states have been used as a powerful tool…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty…
We show how the Schroedinger Uncertainty Relation for a pair of observables can be deduced using the Cauchy-Schwarz inequality plus successive applications of the commutation relation involving the two observables. Our derivation differs…
The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the…
We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability vectors in terms of…
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 prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable…
Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a novel lower bound on the entropy sum for general pairs of observables in…
We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…
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…
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
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…
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…
We derive uncertainty relation inequalities according to the mutually unbiased measurements. Based on the calculation of the index of coincidence of probability distribution given by $d+1$ MUMs on any density operator $\rho$ in…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…