Coherent Distributed Source Simulation as Multipartite Quantum State Splitting
Part Of
IEEE International Symposium on Information Theory - Proceedings
Start Page
1221
End Page
1226
ISBN (of the container)
979-835038284-6
Date Issued
2024-07-07
Author(s)
Ian George
Abstract
Recently, Cheng et al generalized quantum state splitting (QSS) to the multipartite setting for applications in quantum network information theory. Furthermore, Cheng and Gao recently noted that unipartite convex splitting reduces to soft covering for classical-quantum states. Soft covering is a common primitive in (classical, network) information theory that does not seem to need an extension to the multipartite setting, e.g. when establishing rates for many party distributed source simulation (DSS). This suggests a gap in our understanding of how these tasks are related. In this work we clarify this relation. We first identify “incoherent” QSS without entanglement assistance with DSS in the bipartite setting. Motivated by this, we identify “coherent” DSS as a special case of multipartite QSS. We then establish a one-shot rate region for multipartite QSS in terms of smooth multipartite mutual information quantities, which in turn implies a one-shot rate region for coherent DSS. Lastly, we establish a strong asymptotic equipartition property for mutual information quantities to establish a strong converse rate region for multipartite QSS and coherent DSS.
Event(s)
2024 IEEE International Symposium on Information Theory (ISIT)
SDGs
Publisher
IEEE
Type
conference paper