Classical capacity of bosonic broadcast communication and a new minimum output entropy conj.pdf

a r X i v : 0 7 0 6 .3 4 1 6 v 1 [ q u a n t - p h ] 2 2 J u n 2 0 0 7 Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture Saikat Guha, Jeffrey H. Shapiro, and Baris I. Erkmen Massachusetts Institute of Technology, Research Laboratory of Electronics, Cambridge, Massachusetts 02139 USA Previous work on the classical information capacities of bosonic channels has established the capacity of the single-user pure-loss channel, bounded the capacity of the single-user thermal-noise channel, and bounded the capacity region of the multiple-access channel. The latter is a multi-user scenario in which several transmitters seek to simultaneously and independently communicate to a single receiver. We study the capacity region of the bosonic broadcast channel, in which a single transmitter seeks to simultaneously and independently communicate to two different receivers. It is known that the tightest available lower bound on the capacity of the single-user thermal-noise channel is that channel’s capacity if, as conjectured, the minimum von Neumann entropy at the output of a bosonic channel with additive thermal noise occurs for coherent-state inputs. Evidence in support of this minimum output entropy conjecture has been accumulated, but a rigorous proof has not been obtained. In this paper, we propose a new minimum output entropy conjecture that, if proved to be correct, will establish that the capacity region of the bosonic broadcast channel equals the inner bound achieved using a coherent-state encoding and optimum detection. We provide some evidence that supports this new conjecture, but again a full proof is not available. PACS numbers: 03.67.Hk, 89.70.+c, 42.79.Sz I. INTRODUCTION The past decade has seen several advances in evalu- ating classical information capacities of several impor- tant quantum communication channels [1]–[5]. Despite these advances [1], exact capacity results are not known for many important and prac