Upper bounds on the private capacity for bosonic Gaussian channels

Understand

Recently, there have been considerable progresses on the bounds of various quantum channel capacities for bosonic Gaussian channels.

• Especially, several upper bounds for the classical capacity and the quantum capacity on the bosonic Gaussian channels, via a technique known as quantum entropy power inequality, have been shed light on understanding the mysterious quantum-channel-capacity problems.
• However, upper bounds for the private capacity on quantum channels are still missing for the study on certain universal upper bounds.
• Here, we derive upper bounds on the private capacity for bosonic Gaussian channels involving a general Gaussian-noise case through the conditional quantum entropy power inequality.