Hansenne, Kiara
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Publication Access status: Metadata only , Covariance-Matrix-Based Criteria for Network Entanglement(2023); Quantum networks offer a realistic and practical scheme for generating multipArticle entanglement and implementing multipArticle quantum communication protocols. However, the correlations that can be generated in networks with quantum sources and local operations are not yet well understood. Covariance matrices, which are powerful tools in entanglement theory, have been also applied to the network scenario. We present simple proofs for the decomposition of such matrices into the sum of positive semi-definite block matrices and, based on that, develop analytical and computable necessary criteria for preparing states in quantum networks. These criteria can be applied to networks where nodes share at most one source, such as all bipartite networks.Source Type:Article3 - Some of the metrics are blocked by yourconsent settings
Publication Access status: Open Access , Exploring quantum information theory through graphs and networks(2024)In this manuscript, we explore different aspects of quantum information using graph theory as a principal tool. The research presented in this thesis addresses fundamental questions in quantum information theory, such as uncertainty relations and quantum entanglement, as well as practical applications such as certification of quantum systems. First, we define and analyse the anticommutativity graph associated with a set of observables. This approach allows us to relate the expectation values of these observables to the Lovász number of their anticommutativity graph, a well-known graph invariant. More specificity, the Lovász number provides an upper bound on the sum of the squares of the expectation values. This relationship enables us to derive uncertainty relations for any set of dichotomic observables. These can be transformed into witnesses to detect entanglement, including in PPT entangled states. Second, we address the problem of measurement scheduling for marginal state tomography, i.e., finding measurement settings that allow for the reconstruction of marginal states of a quantum system. We demonstrate that, for Pauli tomography, this problem can be mapped to a specific instance of the graph-theoretical problem of edge clique covering. Using this mapping, we show for instance that, for two-body marginal tomography of planar qubit topologies, nine Pauli settings are necessary and sufficient, regardless of the numbers of qubits in the system. Furthermore, we establish that with general local projective measurements, 3^k measurement settings are sufficient to reconstruct all k-body marginal states of a multi-qubit system. We report an experimental demonstration of the applicability of the measurement settings derived in our work. Lastly, we develop necessary criteria for network entanglement, revealing that many graph states, as well as permutationally symmetric states, cannot be prepared in network structures without the usage of classical communication. We then propose a certification protocol for the topology of quantum networks, which has later been implemented experimentally.Source Type:Doctoral Thesis336 277 - Some of the metrics are blocked by yourconsent settings
Publication Access status: Open Access , Symmetries in quantum networks lead to no-go theorems for entanglement distribution and to verification techniquesQuantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that entangled quantum states with a bosonic or fermionic symmetry can not be generated in networks; moreover, cluster and graph states are not accessible. Our methods can be used to design certification methods for the functionality of specific links in a network and have implications for the design of future network structures.Source Type:Article191 86
