Description

Book Synopsis
Characterizing entanglement is an important issue in quantum information, as it is considered to be a resource for many applications such as quantum key distribution or quantum metrology. One useful tool to detect and quantify entanglement are witness operators. A standard way to construct them is based on the fidelity of pure states and mathematically relies on the Schmidt decomposition of vectors. In this book a method to build entanglement witnesses using the Schmidt decomposition of operators is presented. One can show that these are strictly stronger than the fidelity witnesses. Moreover, the concept can be generalized easily to the multipartite case, and one may use it to quantify the dimensionality of entanglement. Finally, this scheme will be used to provide two algorithms that can be combined to improve given witnesses for multiparticle entanglement.



Table of Contents
Introduction.- Physical and mathematical background.- OSD witnesses for bipartite states.- The OSD witness for the multipartite case.- Schmidt number witnesses.- Conclusion and outlook.

Characterizing Multiparticle Entanglement Using

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    A Paperback / softback by Sophia Denker

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      Publisher: Springer Fachmedien Wiesbaden
      Publication Date: 04/01/2024
      ISBN13: 9783658432027, 978-3658432027
      ISBN10: 3658432020
      Also in:
      Quantum physics

      Description

      Book Synopsis
      Characterizing entanglement is an important issue in quantum information, as it is considered to be a resource for many applications such as quantum key distribution or quantum metrology. One useful tool to detect and quantify entanglement are witness operators. A standard way to construct them is based on the fidelity of pure states and mathematically relies on the Schmidt decomposition of vectors. In this book a method to build entanglement witnesses using the Schmidt decomposition of operators is presented. One can show that these are strictly stronger than the fidelity witnesses. Moreover, the concept can be generalized easily to the multipartite case, and one may use it to quantify the dimensionality of entanglement. Finally, this scheme will be used to provide two algorithms that can be combined to improve given witnesses for multiparticle entanglement.



      Table of Contents
      Introduction.- Physical and mathematical background.- OSD witnesses for bipartite states.- The OSD witness for the multipartite case.- Schmidt number witnesses.- Conclusion and outlook.

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