Semidefinite programming strong converse bounds for classical capacity

Understand

We investigate the classical communication over quantum channels when assisted by no-signaling (NS) and positive-partial-transpose-preserving (PPT) codes, for which both the optimal success probability of a given transmission rate and the one-shot $\epsilon$-error capacity are formalized as semidefinite programs (SDPs).

• Based on this, we obtain improved SDP finite blocklength converse bounds of general quantum channels for entanglement-assisted codes and unassisted codes.
• Furthermore, we derive two SDP strong converse bounds for the classical capacity of general quantum channels: for any code with a rate exceeding either of the two bounds of the channel, the success probability vanishes exponentially fast as the number of channel uses increases.
• In particular, applying our efficiently computable bounds, we derive an improved upper bound on the classical capacity of the amplitude damping channel.