This paper proposes a comprehensive method for extending operational-algebraic equivalence to continuous-variable quantum systems, addressing unique challenges posed by infinite-dimensional Hilbert spaces, symplectic geometry, and the Gaussian-non-Gaussian distinction. The framework enables rigorous comparison of CV quantum processes and provides tools for quantum error correction and fault-tolerant quantum computing with continuous variables.
Key findings
Introduces a regularized equivalence relation based on energy-constrained distinguishability.
Develops a symplectic-algebraic characterization of equivalent Gaussian channels.
Establishes a hierarchy of operational equivalence classes for non-Gaussian operations.
Enables rigorous comparison of CV quantum processes and facilitates resource theory constructions.
Limitations & open questions
The extension to continuous-variable systems remains incomplete and further research is needed.