Asymmetric de Finetti Theorem for Infinite-dimensional Quantum Systems

TL;DR

This paper extends the de Finetti theorem for infinite-dimensional quantum systems to asymmetric cases, enabling more versatile security analysis in quantum key distribution with continuous variables.

Contribution

It generalizes the de Finetti theorem to include asymmetric bounds and biased basis selection, broadening its applicability in quantum information.

Findings

Allows application to scenarios with asymmetric measurement statistics

Enables security analysis of QKD protocols with squeezed states

Provides theoretical foundation for asymmetric quantum state approximation

Abstract

The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires the original state to obey permutation symmetry conditioned on successful experimental verification on k of N subsystems. We generalize the de Finetti theorem to include asymmetric bounds on the variance of canonical observables and biased basis selection during the verification step. Our result thereby enables application of infinite-dimensional de Finetti theorem to situations where two conjugate measurements obey different statistics, such as the security analysis of quantum key distribution protocols based on squeezed state against coherent attack.