PPT-assisted capacities of bosonic Gaussian channels

Abstract: We determine the exact quantum communication and entanglement-distribution capacities of three fundamental bosonic channels, namely thermal loss, thermal amplification and additive Gaussian noise, assisted by operations that completely preserve positive partial transpose (PPT). These operations are more powerful than local operations and classical communication (LOCC), but cannot generate distillable entanglement on their own. For thermal loss, the unconstrained capacity coincides with the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound throughout the non-entanglement-breaking regime. The corresponding upper bounds are also attained for thermal amplification and additive noise. We extend these results to energy-constrained communication, establishing exact capacities for all three channels at every prescribed mean input energy. Our results solve a class of bosonic capacity problems under PPT assistance and establish exact benchmarks for determining whether the same communication rates can be achieved via LOCC alone.