Connections between operator systems and the problem of local quantum state discrimination
The interplay between locality and entanglement is fundamental in Quantum Information Theory, and the problem of extracting classical information from a bipartite system is at the heart of many protocols. The set of possible quantum operations under the restriction of Local Quantum Operations and Classical Communications (LOCC) is notoriously unwieldy to describe mathematically. Simpler is the set of one-way communication protocols, in which Alice can send classical information to Bob but he cannot send information to her. Our recent work shows how operator structures such as operator systems, operator algebras, and Hilbert $C^*$-modules arise naturally in the one-way LOCC setting, and we make use of these structures to derive new results and bounds in the study of one-way LOCC.
Joint work with David Kribs, Comfort Mintah, and Rajesh Pereira