Not-so-normal mode decomposition

TL;DR

This paper generalizes the normal mode decomposition to non-symmetric and locality-constrained systems, enabling local decoupling and revealing signatures of squeezing in multi-mode channels, with a canonical matrix form under symplectic transformations.

Contribution

It introduces a generalized normal mode decomposition applicable to non-symmetric and constrained systems, providing a new canonical form for analyzing complex quantum correlations.

Findings

Local decoupling of correlated oscillators achieved

Identification of squeezing signatures in multi-mode channels

Canonical matrix form under symplectic transformations established

Abstract

We provide a generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows for instance to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to elementary pairs into which all correlations are condensed. Similarly, it enables us to decouple the interaction parts of multi-mode channels into single-mode and pair-interactions where the latter are shown to be a clear signature of squeezing between system and environment. In mathematical terms the result is a canonical matrix form with respect to real symplectic equivalence transformations.