Related papers: Entropic uncertainty relations from equiangular ti…

We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum…

We use operators from generalized equiangular measurements to construct positive maps. Their positivity follows from the inequality for indices of coincidence corresponding to few equiangular tight frames. These maps give rise to…

We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…

Entanglement is widely regarded as an essential resource for a number of tasks and can in some cases be quantified by figures of merit related to those tasks. In quantum metrology, this is showcased by the connections between the quantum…

The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…

We ask which is the best strategy to reveal uncertainty relations between comple- mentary observables of a continuous variable system for coarse-grained measurements. This leads to the derivation of new uncertainty relations for…

As the fundamental tool in quantum information science, the uncertainty principle is essential for manifesting nonclassical properties of quantum systems. Plenty of efforts on the uncertainty principle with two observables have been…

Measurements with randomly chosen settings determine many important properties of quantum states without the need for a shared reference frame or calibration. They naturally emerge in the context of quantum communication and quantum…

Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic…

Entanglement-enhanced quantum metrology explores the utilization of quantum entanglement to enhance measurement precision. When particles in a probe are prepared into a quantum entangled state, they collectively accumulate information about…

We show how entanglement can be used to improve the estimation of an unknown transformation. Using entanglement is always of benefit, in improving either the precision or the stability of the measurement. Examples relevant for applications…

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.…

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…

Quantum coherence is an essential ingredient in quantum information processing and plays a central role in emergent fields such as nanoscale thermodynamics and quantum biology. However, our understanding and quantitative characterization of…

Characterizing entanglement in all but the simplest case of a two qubit pure state is a hard problem, even understanding the relevant experimental quantities that are related to entanglement is difficult. It may not be necessary, however,…

Entanglement entropies calculated in the framework of quantum field theory on classical, flat or curved, spacetimes are known to show an intriguing area law in four dimensions, but they are also notorious for their quadratic ultraviolet…

We study the mathematical structure of superoperators describing quantum measurements, including the \emph{entangling measurement}--the generalization of the standard quantum measurement that results in entanglement between the measurable…

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…

Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite dimensional subspaces. Hence, entanglement is a finite dimensional property. A generalization for multipartite…

We study several interesting examples of Biangular Tight Frames (BTFs) - basis-like sets of unit vectors admitting exactly two distinct frame angles (ie, pairwise absolute inner products) - and examine their relationships with Equiangular…