Related papers: Classifying Entanglement by Algebraic Geometry
Entanglement is a well known fundamental resource in quantum information. Here the following question is addressed : which are the deeper roots of entanglement that may help in its better understanding and use ? The answer is that one can…
Entanglement is unanimously recognized as the key communication resource of the Quantum Internet. Yet, the possibility of implementing novel network functionalities by exploiting the marvels of entanglement has been poorly investigated so…
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.…
In this paper, we investigate the hierarchical structure of the $n$-partite quantum states. We present a whole set of hierarchical quantifications as a method of characterizing quantum states, which go beyond genuine multipartite…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
Scaling the number of entangled nodes in a quantum network is a challenge with significant implications for quantum computing, clock synchronisation, secure communications, and quantum sensing. In a quantum network, photons interact with…
The ability to generate bipartite entanglement in quantum computing technologies is widely regarded as pivotal. However, the role of genuinely multipartite entanglement is much less understood than bipartite entanglement, particularly in…
Multipartite entanglement constitutes one of the key resources in quantum information processing. We exploit correlation tensor norms to develop a framework for its experimental detection without the need for shared frames of reference. By…
We explore the question of using an entangled state as a universal resource for implementing quantum measurements by local operations and classical communication (LOCC). We show that for most systems consisting of three or more subsystems,…
Entanglement is a central resource in quantum information and quantum technologies, yet its characterization remains challenging due to both theoretical complexity and measurement requirements. Machine learning has emerged as a promising…
This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert…
This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction.…
Stochastic local operations and classical communication (SLOCC), also called local filtering operations, are a convenient, useful set of quantum operations in grasping essential properties of entanglement. We give a quick overview about the…
The states in the three-qubit GHZ SLOCC class can exhibit diverse entanglement patterns, as they may have no entanglement in any reduced subsystems, or show entanglement across one, two, or all three bipartite cuts. Significant research has…
We focus on determining the separability of an unknown bipartite quantum state $\rho$ by invoking a sufficiently large subset of all possible entanglement witnesses given the expected value of each element of a set of mutually orthogonal…
We consider the problem of operator-valued kernel learning and investigate the possibility of going beyond the well-known separable kernels. Borrowing tools and concepts from the field of quantum computing, such as partial trace and…
As information carriers for fault-tolerant quantum computing, systems composed of anyons exhibit non-tensor product state spaces due to their distinctive fusion rules, leading to fundamentally different entanglement properties from…
It is well known that the classification of pure multiparticle entangled states according to stochastic local operations leads to a natural classification of mixed states in terms of convex sets. We present a simple algorithmic procedure to…
In this paper I will investigate geometrical structures of multipartite quantum systems based on complex projective varieties. These varieties are important in characterization of quantum entangled states. In particular I will establish…