Related papers: Sum uncertainty relations for arbitrary $N$ incomp…
Uncertainty is a fundamental and important concept in quantum mechanics. In this work, using the technique in matrix theory, we propose an uncertainty relation of four observables and show that the uncertainty constant is tight. It is…
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…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
We derive entropic uncertainty relations for successive generalized measurements by using general descriptions of quantum measurement within two {distinctive operational} scenarios. In the first scenario, by merging {two successive…
Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present…
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 introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
Bounded uncertainty relations provide the minimum value of the uncertainty assuming some additional information on the state. We derive analytically an uncertainty relation bounded by a pair of constraints, those of purity and Gaussianity.…
In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
In this paper, we compute uncertainty relations for non-commutative space and obtain a better lower bound than the standard one obtained from Heisenberg's uncertainty relation. We also derive the reverse uncertainty relation for product and…
Uncertainty principle is one of the most essential features in quantum mechanics and plays profound roles in quantum information processing. We establish tighter summation form uncertainty relations based on metric-adjusted skew information…
Bell nonlocality and uncertainty relations are distinct features of quantum theory from classical physics. Bell nonlocality concerns the correlation strength among local observables on different quantum particles, whereas the uncertainty…
Although progress has been made recently in defining nontrivial uncertainty limits for the SU(2) group, a description of the intermediate states bound by these limits remains lacking. In this paper we enumerate possible uncertainty…
A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and…
Uncertainty relations play a significant role in drawing a line between classical physics and quantum physics. Since the introduction by Heisenberg, these relations have been considerably explored. However, the effect of quantum…
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…
Often, one would like to determine some observable A, but can only measure some (hopefully related) observable M. This can arise, for example, in quantum eavesdropping, or when the research lab budget isn't large enough for that 100%…
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…
We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds is typically complicated, and efficient procedures are known only for a handful of cases. In this paper we present procedures based…