Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction

Area of Science:

• Quantum Cryptography
• Theoretical Computer Science

Background:

• Establishing security for continuous-variable quantum key distribution (CV-QKD) against general attacks in finite-size regimes is a significant challenge.
• Existing methods like uncertainty principle techniques and standard de Finetti reductions are insufficient for realistic CV-QKD protocols using coherent states.

Purpose of the Study:

• To develop a novel theoretical framework for proving the security of CV-QKD protocols against general attacks under realistic finite-size conditions.
• To rigorously validate the assumption that Gaussian collective attacks are the most potent threat to CV-QKD.

Main Methods:

• Introduction of a new Gaussian de Finetti reduction exploiting U(n) symmetry, distinct from traditional S_n-based methods.
• Utilizing generalized SU(2,2) coherent states and an energy test to globally truncate the Hilbert space.
• Demonstrating equivalence between security against general attacks and security against Gaussian collective attacks.

Main Results:

• The proposed Gaussian de Finetti reduction successfully establishes security for CV-QKD in realistic finite-size scenarios.
• The method overcomes limitations of previous approaches that required unrealistically large block lengths.
• Security against general attacks is shown to be reducible to security against Gaussian collective attacks.

Conclusions:

• The developed Gaussian de Finetti reduction provides a robust method for assessing CV-QKD security.
• This work rigorously confirms the optimality of Gaussian collective attacks against CV-QKD protocols.
• The findings pave the way for more practical and secure quantum communication systems.