Related papers: Classifying Entanglement by Algebraic Geometry
In quantum systems with infinitely many degrees of freedom, states can be infinitely entangled across a pair of subsystems, but are there different forms of infinite entanglement? To understand entanglement in such systems, we use a…
Quantum entanglement is the cornerstone of quantum technology and enables quantum devices to outperform classical systems in terms of performance. However, detecting entanglement in high-dimensional systems remains a significant challenge…
Entanglement is one of important resources for quantum communication tasks. Most of results are focused on qubit entanglement. Our goal in this work is to characterize the multipartite high-dimensional entanglement. We firstly derive an…
The study of multipartite entanglement is not only interesting but also important due to its wide application in quantum information processing. However, the complicated structure of the Hilbert space for many parties makes multipartite…
Multipartite entanglement is of important resources for quantum communication and quantum computation. Our goal in this paper is to characterize general multipartite entangled states according to shallow quantum circuits. We firstly prove…
Quantifying entanglement is vital to understand entanglement as a resource in quantum information processing, and many entanglement measures have been suggested for this purpose. When mathematically defining an entanglement measure, we…
We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…
Variational quantum algorithms have emerged as a powerful tool for harnessing the potential of near-term quantum devices to address complex challenges across quantum science and technology. Yet, the robust and scalable quantification of…
A classification of multipartite entanglement in qubit systems is introduced for pure and mixed states. The classification is based on the robustness of the said entanglement against partial trace operation. Then we use current machine…
Quantum entanglement plays a crucial role in quantum information processing tasks and quantum mechanics, hence quantifying unknown entanglement is a fundamental task. However, this is also challenging, as entanglement cannot be measured by…
Neural networks have emerged as a promising paradigm for quantum information processing, yet they confront the challenge of generating training datasets with sufficient size and rich diversity, which is particularly acute when dealing with…
Large-scale quantum networks, necessary for distributed quantum information processing, are posited to have quantum entangled systems between distant network nodes. The extent and quality of distributed entanglement in a quantum network,…
We introduce algebriac sets in the products of complex projective spaces for multipartite mixed states, which are independent of their eigenvalues and only measure the "position" of their eigenvectors, as their non-local invariants (ie.…
From the consideration of measuring bipartite mixed states by separable pure states, we introduce algebraic sets in complex projective spaces for bipartite mixed states as the degenerating locus of the measurement. These algebraic sets are…
Quantum entanglement is a defining signature and resource of quantum theory, but its standard definition presupposes a globally fixed decomposition into subsystems. We develop a geometric framework that detects when such a decomposition…
Although the foundations of quantum and classical physics are much different, it is often difficult to pinpoint which features of a particular system are intrinsically "quantum". Perhapse, the most clear-cut distinction between "classical"…
We present a practical classification scheme for the four-partite entangled states under stochastic local operations and classical communication (SLOCC). By transforming a four-partite state into a triple-state set composed of two…
Entanglement is an important resource that allows quantum technologies to go beyond the classically possible. There are many ways quantum systems can be entangled, ranging from the archetypal two-qubit case to more exotic scenarios of…
In this thesis, we investigate two different aspects of entanglement and classical communication in distributed quantum computation (DQC). In the first part, we analyze implementable computation over a given quantum network resource by…
Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully…