Related papers: Uncertainty Relations for coarse-grained measureme…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
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 central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum…
We investigate the product form uncertainty relations of variances for $n\,(n\geq 3)$ quantum observables. In particular, tight uncertainty relations satisfied by three observables has been derived, which is shown to be better than the ones…
In the Copenhagen interpretation the Heisenberg uncertainty relation is interpreted as the mathematical expression of the concept of complementarity, quantifying the mutual disturbance necessarily taking place in a simultaneous or joint…
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…
The concept of quantum coherence and its possible use as a resource are currently the subject of active researches. Uncertainty and complementarity relations for quantum coherence allow one to study its changes with respect to other…
Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
In its original formulation, Heisenberg's uncertainty principle describes a trade-off relation between the error of a quantum measurement and the thereby induced disturbance on the measured object. However, this relation is not valid in…
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…
As a very fundamental principle in quantum physics, uncertainty principle has been studied intensively via various uncertainty inequalities. Based on the information measure introduced by Brukner and Zeilinger in [Phys. Rev. Lett. 83, 3354…
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…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
We derive a fine-grained uncertainty relation for the measurement of two incompatible observables on a single quantum system of continuous variables, and show that continuous variable systems are more uncertain than discrete variable…
The existence of incompatible measurements, epitomized by Heisenberg's uncertainty principle, is one of the distinctive features of quantum theory. So far, quantum incompatibility has been studied for measurements that test the preparation…
The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…
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…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…