We establish the classical capacity of optical quantum channels as a sharp transition between two regimes-one which is an error-free regime for communication rates below the capacity, and the other in which the probability of correctly decoding a classical message converges exponentially fast to zero if the communication rate exceeds the classical capacity. This result is obtained by proving a strong converse theorem for the classical capacity of all phase-insensitive bosonic Gaussian channels, a well-established model of optical quantum communication channels, such as lossy optical fibers, amplifier and free-space communication. The theorem holds under a particular photonnumber occupation constraint, which we describe in detail in the paper. Our result bolsters the understanding of the classical capacity of these channels and opens the path to applications, such as proving the security of noisy quantum storage models of cryptography with optical links.
Index Termschannel capacity, Gaussian quantum channels, optical communication channels, photon number constraint, strong converse theorem I. INTRODUCTION One of the most fundamental tasks in quantum information theory is to determine the ultimate limits on achievable data transmission rates for a noisy communication channel. The classical capacity is defined as the maximum rate at which it is possible to send classical data over a quantum channel such that the error probability decreases to zero in the limit of many independent uses of the channel [1], [2]. As such, the classical capacity serves as a distinctive bound on our ability to faithfully recover classical information sent over the channel.The above definition of the classical capacity states that (a) for any rate below capacity, one can communicate with vanishing error probability in the limit of many channel uses and (b) there cannot exist such a communication scheme in the limit of many channel uses whenever the rate exceeds the capacity. However, strictly speaking, for any rate R above capacity, the above definition leaves open the possibility for one to increase the communication rate R by allowing for some error ε > 0. Leaving room for the possibility of such a trade-off between the rate R and the error ε is the characteristic of a "weak converse,"