Related papers: Probing multipartite entanglement through persiste…
We study the entanglement properties of quantum hypergraph states of $n$ qubits, focusing on multipartite entanglement. We compute multipartite entanglement for hypergraph states with a single hyperedge of maximum cardinality, for…
Although quantum entanglement has already been verified experimentally and applied in quantum computing, quantum sensing and quantum networks, most of the existing measures cannot characterize the entanglement faithfully. In this work, by…
Entanglement is a striking feature of quantum mechanics, and it has a key property called unextendibility. In this paper, we present a framework for quantifying and investigating the unextendibility of general bipartite quantum states.…
Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…
Datasets often possess an intrinsic multiscale structure with meaningful descriptions at different levels of coarseness. Such datasets are naturally described as multi-resolution clusterings, i.e., not necessarily hierarchical sequences of…
We study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field. Our method is based on a decomposition of the persistent homology. We demonstrate that, under fairly general…
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…
We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…
Characterizing the intricate structure of entanglement in quantum many-body systems remains a central challenge, as standard measures often obscure underlying geometric details. In this Letter, we introduce a powerful framework, termed…
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.…
Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…
Tools of Topological Data Analysis provide stable summaries encapsulating the shape of the considered data. Persistent homology, the most standard and well studied data summary, suffers a number of limitations; its computations are hard to…
Quantum many-body systems display an extraordinary degree of complexity, yet many of their features are universal: they depend not on microscopic details, but on a few fundamental physical aspects such as symmetries. A central challenge is…
Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations within the framework of combinatorial dynamical systems -- a…
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…
We present two results which combined enable one to reliably detect multimode, multipartite entanglement in the presence of measurement errors. The first result leads to a method to compute the best (approximated) physical covariance matrix…
In this paper, we derive a simple method for separating topological noise from topological features using a novel measure for comparing persistence barcodes called persistent entropy.
Organising the space of entanglement structures of a multipartite quantum system is a much more challenging task than its bipartite version: while the local unitary (LU) orbit of a bipartite pure state can be conveniently characterized by…
Experimental detection of entanglement certainly disturbs the underlying shared state. It is possible that the entanglement content of the system is lost in the process of its detection. This observation has led to the study of sequential…
Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…