Not-so-normal mode decomposition

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.

4 pages, 2 figures, published version

References in corpus (6)

• Experimental demonstration of quantum memory for light
• Quantum Capacities of Bosonic Channels
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• Mode-Wise Entanglement of Gaussian States
• Gaussian localizable entanglement
• Generic Entanglement and Standard Form for N-mode Pure Gaussian States

Cited by in corpus (3)

• Multi-mode bosonic Gaussian channels
• Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure
• A new approach to characterize qubit channels