Related papers: Probing the geometry of correlation matrices with …
In the standard geometric approach, the entanglement of a pure state is $\sin^2\theta$, where $\theta$ is the angle between the entangled state and the closest separable state of products of normalised qubit states. We consider here a…
This thesis is an attempt to enhance understanding of the following questions A- Given a multipartite quantum state (possibly mixed), how to find out whether it is entangled or separable? (Detection of entanglement.) B- Given an entangled…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…
We introduce a novel geometric approach to characterize entanglement relations in large quantum systems. Our approach is inspired by Schumacher's singlet state triangle inequality, which used an entropic-based distance to capture the…
Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a…
We investigate monogamy of correlations and entropy inequalities in the Bloch representation. Here, both can be understood as direct relations between different correlation tensor elements and thus appear intimately related. To that end we…
The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…
While the structure of entangled quantum states is relatively well understood, the characterization of entangled measurements, especially in multipartite and high-dimensional settings, remains far less developed. In this work, we introduce…
We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states…
An arbitrarily dense discretisation of the Bloch sphere of complex Hilbert states is constructed, where points correspond to bit strings of fixed finite length. Number-theoretic properties of trigonometric functions (not part of the…
We show that the expectation value of squared correlations measured along random local directions is an identifier of quantum entanglement in pure states which can be directly experimentally assessed if two copies of the state were…
The set of all qubit states that can be steered to by measurements on a correlated qubit is predicted to form an ellipsoid---called the quantum steering ellipsoid---in the Bloch ball. This ellipsoid provides a simple visual characterisation…
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, already present in a number of settings [A. Shimony, Ann. NY.…
We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state…
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.…
Based on the generalized Bloch representation, we study the separability and entanglement of arbitrary dimensional multipartite quantum states. Some sufficient and some necessary criteria are presented. For certain states, these criteria…
If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present…
Entanglement is a unique feature of quantum mechanics. In coupled systems of light and matter, entanglement manifests itself in the linear superposition of multipartite quantum states (e.g., parametrized by the multiple spatial, spectral,…