Distributed State Preparation with Zero Communication
Abstract: As quantum networks begin to be implemented, a theoretical understanding of their capabilities and limitations becomes of increasing practical interest. We consider a near-term network where a ‘hub node’ can send classical and/or quantum states to two (or more) nodes that exchange no messages. The goal is for the non-communicative nodes to prepare a target joint state to some tolerated non-zero error using the hub’s signal and local operations (LO). In this network setting, any separable state can be prepared to arbitrarily small error if the hub distributes sufficient shared randomness (SR). We establish bounds on the needed shared randomness in the one-shot setting that also recovers known asymptotic results. In contrast, an entangled state cannot be converted to a different one to arbitrary error using only LO and SR (LOSR). We establish a simple optimization program for the minimal error for entangled pure state transformations under LOSR. These results characterize our hub network’s capabilities and limitations while also allowing us to explore the relationship between correlation and (non)-separability.
Based On:
arXiv: 2301.04301
arXiv: 2301.04735
