ﻻ يوجد ملخص باللغة العربية
In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are fine-grained compared with the well-known Cauchy-Schwarz inequality, our framework naturally improves the results based on the latter. As such, the unitary uncertainty relations based on our method outperform the best known bound introduced in [Phys. Rev. Lett. 120, 230402 (2018)] to some extent. Explicit examples of unitary uncertainty relations are provided to back our claims.
We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is saturated by e
We derive the lower bound of uncertainty relations of two unitary operators for a class of states based on the geometric-arithmetic inequality and Cauchy-Schwarz inequality. Furthermore, we propose a set of uncertainty relations for three unitary ope
In spite of enormous theoretical and experimental progresses in quantum uncertainty relations, the experimental investigation of most current, and universal formalism of uncertainty relations, namely majorization uncertainty relations (MURs), has not
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by Heisenberg. Here w
New uncertainty relations for n observables are established. The relations take the invariant form of inequalities between the characteristic coefficients of order r, r = 1,2,...,n, of the uncertainty matrix and the matrix of mean commutators of the