Quantum Broadcast Channel Simulation via Multipartite Convex Splitting

Communications in Mathematical Physics, vol. 406, pp. 36

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. Mario Berta corresponding Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

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

2. Hao–Chung Cheng corresponding

   National Taiwan University · Foxconn (Taiwan) · National Center for Theoretical Sciences · National Center for Theoretical Sciences, Physics Division

   Affiliation as printed

   Center for Quantum Science and Engineering, National Taiwan University, Taipei, 106319 Taiwan

   Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University, Taipei 106319, Taiwan

   Department of Mathematics, National Taiwan University, Taipei, 106319 Taiwan

   Hon Hai (Foxconn) Quantum Computing Center, New Taipei City, 236, Taiwan

   Physics Division, National Center for Theoretical Sciences, Taipei, 106319 Taiwan

   Center for Quantum Science and Engineering, National Taiwan University, Taipei, 106319, Taiwan

   Department of Mathematics, National Taiwan University, Taipei, 106319, Taiwan

   Physics Division, National Center for Theoretical Sciences, Taipei, 106319, Taiwan

3. Li Gao corresponding

   Wuhan University

   Affiliation as printed

   School of Mathematics and Statistics, Wuhan University, Wuhan, 430072 China

   School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China