Lower Bounding the Secret Key Capacity of Bosonic Gaussian Channels via Optimal Gaussian Measurements

We find the maximum rate achievable in the private communication over a bosonic quantum channel with a fully Gaussian protocol based on optimal single-mode Gaussian measurements. This rate establishes a lower bound on the secret rate capacity of the channel. We focus on the class of phase-insensitive Gaussian channels. For the thermal-loss and thermal amplification channels, our results demonstrate the optimality, within the constraints of our analysis, of previously proposed protocols, while also providing a significantly simplified formula for their performance evaluation. For the added noise channel, our rate provides a better lower bound than any previously known.

💡 Research Summary

The paper addresses the long‑standing problem of determining tight lower bounds on the secret‑key capacity of bosonic Gaussian channels, which are central to continuous‑variable quantum communication and quantum key distribution (QKD). The authors consider an entanglement‑based picture: Alice prepares a two‑mode squeezed vacuum (TMSV) state, keeps one mode (A) and sends the other (B) through a Gaussian channel 𝔈. After the channel, Alice and Bob each perform a local single‑mode Gaussian measurement (POVM) on their respective modes, while one‑way classical communication is allowed. The achievable secret‑key rate R is bounded by the Holevo quantity χ between the measurement outcome and the remote party’s system. In the asymptotic limit of infinite TMSV energy (μ→∞) this bound is tight, i.e., R = χ.

The secret‑key capacity K of the channel satisfies K ≥ R. By explicitly modeling Eve’s optimal collective attack as a purification of the channel (using an ancillary TMSV and a unitary dilation), the authors derive a general lower bound \