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 (14)

• Quantum information with continuous variables
• Quasi-Normal Modes of Stars and Black Holes
• Experimental demonstration of quantum memory for light
• Sonic analog of gravitational black holes in Bose-Einstein condensates
• The Real Symplectic Groups in Quantum Mechanics and Optics
• Quantum Capacities of Bosonic Channels
• One-mode Bosonic Gaussian channels: a full weak-degradability classification
• Mode-Wise Entanglement of Gaussian States
• Creating stable molecular condensate using a generalized Raman adiabatic passage scheme
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Teleportation and spin squeezing utilizing multimode entanglement of light with atoms
• Gaussian localizable entanglement
• Generic Entanglement and Standard Form for N-mode Pure Gaussian States
• Key distillation from Gaussian states by Gaussian operations

Cited by in corpus (22)

• Operator-sum Representation for Bosonic Gaussian Channels
• Multi-mode bosonic Gaussian channels
• Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure
• Quantum Energy Lines and the optimal output ergotropy problem
• Minimal energy cost of entanglement extraction
• Is nonclassicality-breaking the same thing as entanglement-breaking?
• Entanglement structure of quantum fields through local probes
• Subtraction better than addition: Entanglement in multimode squeezed vacuum post-interface with photons
• Power Spectrum Identification for Quantum Linear Systems
• Identification of single-input-single-output quantum linear systems
• On the transitional behavior of quantum Gaussian memory channels
• On the constrained classical capacity of infinite-dimensional covariant quantum channels
• Gaussian local unitary equivalence of $n$-mode Gaussian states and Gaussian transformations by local operations with classical communication
• Standard super-activation for Gaussian channels requires squeezing
• Optimal encoding of oscillators into more oscillators
• The structure of general quantum Gaussian observable
• Incoherent Gaussian equivalence of $m-$mode Gaussian states
• Frozen condition of quantum coherence
• Partial-transpose-guided entanglement classes and minimum noise filtering in many-body Gaussian quantum systems
• Symplectic analogs of polar decomposition and their applications to bosonic Gaussian channels
• A new approach to characterize qubit channels
• Some aspects of the interplay between bipartite correlations and quantum channels