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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 operators. Compared to the known bound introduced in Phys.Rev.A.100,022116(2019), the unitary uncertainty relations bound with our method is tighter, to a certain extent. Meanwhile, some examples are given in the paper to illustrate our conclusions.
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-
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
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
Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from estimation theory,
The non-zero value of Planck constant $hbar$ underlies the emergence of several inequalities that must be satisfied in the quantum realm, the most prominent one being the Heisenberg Uncertainty Principle. Among these inequalities, the Bekenstein boun