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New sum and product uncertainty relations, containing variances of three or four observables, but not containing explicitly their covariances, are derived. One of consequences is the new inequality, giving a nonzero lower bound for the product of two variances in the case of zero mean value of the commutator between the related operators. Moreover, explicit examples show that in some cases this new bound can be better than the known Robertson--Schrodinger one.
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 relations are e
We formulate the conditional-variance uncertainty relations for general qubit systems and arbitrary observables via the inferred uncertainty relations. We find that the lower bounds of these conditional-variance uncertainty relations can be written i
A new lower boundary for the product of variances of two observables is obtained in the case, when these observables are entangled with the third one. This boundary can be higher than the Robertson--Schrodinger one. The special case of the two-dimens
Being one of the centroidal concepts in quantum theory, the fundamental constraint imposed by Heisenberg uncertainty relations has always been a subject of immense attention and challenging in the context of joint measurements of general quantum mech
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 is semidefi