Related papers: Uncertainty regions of observables and state-indep…
Quantifying quantum mechanical uncertainty is vital for the increasing number of experiments that reach the uncertainty limited regime. We present a method for computing tight variance uncertainty relations, i.e., the optimal…
Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…
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…
The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of…
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…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
The standard state-dependent Heisenberg-Robertson uncertainly-relation lower bound fails to capture the quintessential incompatibility of observables as the bound can be zero for some states. To remedy this problem, we establish a class of…
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…
Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…
Given two or more non-commuting observables, it is generally not possible to simultaneously assign precise values to each. This quantum mechanical uncertainty principle is widely understood to be encapsulated by some form of uncertainty…
We present a significantly improved scheme of entanglement detection inspired by local uncertainty relations for a system consisting of two qubits. Developing the underlying idea of local uncertainty relations, namely correlations, we…
We prove a few novel state-dependent uncertainty relations for product as well the sum of variances of two incompatible observables. These uncertainty relations are shown to be tighter than the Roberson-Schr\"odinger uncertainty relation…
Entanglement is not only the resource that fuels many quantum technologies but also plays a key role for some of the most profound open questions of fundamental physics. Experiments controlling quantum systems at the single quantum level…
The efficient experimental verification of entanglement requires an identification of the essential physical properties that distinguish entangled states from non-entangled states. Since the most characteristic feature of entanglement is…
We present the generalized state-dependent entropic uncertainty relations in multiple measurements setting, and the optimal lower bound is obtained by considering different measurement sequences. We then apply this uncertainty relation to…
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 derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a…
The well-known Robertson-Schr\"odinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…