Related papers: Entropic uncertainty relations from equiangular ti…
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
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…
We report on experimental studies on entanglement quantification and verification based on uncertainty relations for systems consisting of two qubits. The new proposed measure is shown to be invariant under local unitary transformations, by…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
We give an exact solution to the nonlinear optimization problem of approximating a Hermitian matrix by positive semi-definite matrices. Our algorithm was then used to judge whether a quantum state is entangled or not. We show that the exact…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
Quantum reference frames have attracted renewed interest recently, as their exploration is relevant and instructive in many areas of quantum theory. Among the different types, position and time reference frames have captivated special…
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…
The effects of any quantum measurement can be described by a collection of measurement operators {M_m} acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the…
A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete POVMs and mutually unbiased bases. Additionally, it provides a natural…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
We take a tour of a set of equiangular lines in eight-dimensional Hilbert space. This structure defines an informationally complete measurement, that is, a way to represent all quantum states of three-qubit systems as probability…
Quantum uncertainty relations impose fundamental limits on the joint knowledge that can be acquired from complementary observables: perfect knowledge of a quantum state in one basis implies maximal indetermination in all other mutually…
Genuine multipartite entanglement is crucial for quantum information and related technologies but quantifying it has been a long-standing challenge. Most proposed measures do not meet the ``genuine'' requirement, making them unsuitable for…
Determining the measurement uncertainty region is a difficult problem for generic sets of observables. For this reason the literature on exact measurement uncertainty regions is focused on symmetric sets of observables, where the symmetries…
The uncertainty principle, which bounds the uncertainties involved in obtaining precise outcomes for two complementary variables defining a quantum particle, is a crucial aspect in quantum mechanics. Recently, the uncertainty principle in…
The present Thesis covers the subject of the characterization of entangled states by recourse to entropic measures, as well as the description of entanglement related to several issues in quantum mechanics, such as the speed of a quantum…
Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu $et\ al.$…