Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels

Understand

We establish several upper bounds on the energy-constrained quantum and private capacities of all single-mode phase-insensitive bosonic Gaussian channels.

• The first upper bound, which we call the "data-processing bound," is the simplest and is obtained by decomposing a phase-insensitive channel as a pure-loss channel followed by a quantum-limited amplifier channel.
• We prove that the data-processing bound can be at most 1.45 bits larger than a known lower bound on these capacities of the phase-insensitive Gaussian channel.
• We discuss another data-processing upper bound as well.