Related papers: Classifying Entanglement by Algebraic Geometry

We show that the bipartite separability of a pure qubit state hinges critically on the combinatorial structure of its computational-basis support. Using Boolean cube geometry, we introduce a taxonomy that distinguishes support-guaranteed…

Quantum information theory is a rapidly growing area of math and physics that combines two independent theories, quantum mechanics and information theory. Quantum entanglement is a concept that was first proposed in the EPR paradox. In…

Quantum entanglement plays a pivotal role in quantum information processing. Quantifying quantum entanglement is a challenging and essential research area within the field. This manuscript explores the relationships between bipartite…

Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…

Entanglement is the key resource for quantum technologies and is at the root of exciting many-body phenomena. However, quantifying the entanglement between two parts of a real-world quantum system is challenging when it interacts with its…

Entanglement is often regarded as an inherently quantum feature. We show that this does not have to be the case: under restricted operational access, classical correlations can appear nonseparable when expressed in the formalism of quantum…

Using an inductive approach to classify multipartite entangled states under stochastic local operations and classical communication introduced recently by the authors [Phys. Rev. A 74, 052336 (2006)], we give the complete classification of…

The quantum entanglement as one of very important resources has been widely used in quantum information processing. In this work, we present a new kind of genuine multipartite entanglement. It is derived from special geometric feature of…

Quantifying genuine entanglement is a crucial task in quantum information theory.In this work, we give an approach of constituting genuine $m$-partite entanglement measures from any bipartite entanglement and any $k$-partite entanglement…

The restrictions that nature places on the distribution of correlations in a multipartite quantum system play fundamental roles in the evolution of such systems, and yield vital insights into the design of protocols for the quantum control…

We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an $N$-qubit symmetric state onto a bipartite symmetric state of higher local dimension. We show that this mapping preserves…

We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group actions in the space of states. In…

We claim that both multipartiteness and localization of subsystems of compound quantum systems are of an essentially relative nature crucially depending on the set of operationalistically available states. In a more general setting, to…

Entangled systems in experiments may be lost or offline in distributed quantum information processing. This inspires a general problem to characterize quantum operations which result in breaking of entanglement or not. Our goal in this work…

Understanding the nature of multipartite entanglement is a central mission of quantum information theory. To this end, we investigate the question of tripartite entanglement convertibility. We find that there exists no easy criterion to…

Despite the fundamental importance of quantum entanglement in many-body systems, our understanding is mostly limited to bipartite situations. Indeed, even defining appropriate notions of multipartite entanglement is a significant challenge…

We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…

Entanglement is the cornerstone of quantum communication, yet conventional detection relies solely on local measurements. In this work, we present a unified theoretical and experimental framework demonstrating that one-way local operations…

We review supervised learning and deep neural network design for learning membership on algebraic varieties. We demonstrate that these trained artificial neural networks can predict the entanglement type for quantum states. We give examples…

Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have…