Quantum Broadcast Channel Simulation via Multipartite Convex Splitting

arXiv (Cornell University)

Abstract

We show that the communication cost of quantum broadcast channel simulation under free entanglement assistance between the sender and the receivers is asymptotically characterized by an efficiently computable single-letter formula in terms of the channel's multipartite mutual information. Our core contribution is a new one-shot achievability result for multipartite quantum state splitting via multipartite convex splitting. As part of this, we face a general instance of the quantum joint typicality problem with arbitrarily overlapping marginals. The crucial technical ingredient to sidestep this difficulty is a conceptually novel multipartite mean-zero decomposition lemma, together with employing recently introduced complex interpolation techniques for sandwiched Rényi divergences. Moreover, we establish an exponential convergence of the simulation error when the communication costs are within the interior of the capacity region. As the costs approach the boundary of the capacity region moderately quickly, we show that the error still vanishes asymptotically.

Authors 3

1. Hao–Chung Cheng

   National Taiwan University · Foxconn (Taiwan)

   Affiliation as printed

   Department of Electrical Engineering and Graduate Institute of Communication Engineering , National Taiwan University , Taipei 106 , Taiwan (R.O.C.)

   Hon Hai (Foxconn) Quantum Computing Center , New Taipei City 236 , Taiwan (R.O.C.)

2. Gao Li
3. Mario Berta Aachen Institute for Quantum Information

   RWTH Aachen University · National Center for Theoretical Sciences

   Affiliation as printed

   Institute for Quantum Information , RWTH Aachen University , Aachen , Germany

   Physics Division , National Center for Theoretical Sciences , Taipei 10617 , Taiwan (R.O.C.)