Conditions for the local manipulation of Gaussian states

Abstract

We present a general necessary and sufficient criterion for the possibility of a state transformation from one mixed Gaussian state to another of a bi-partite continuous-variable system with two modes. The class of operations that will be considered is the set of local Gaussian completely positive trace-preserving maps.

4 pages, 2 figures, slightly changed, references updated, conclusions unchanged

References in corpus (2)

• Separability Criterion for all bipartite Gaussian States
• Distillability Criterion for all Bipartite Gaussian States

Cited by in corpus (24)

• On the impossibility of distilling Gaussian states with Gaussian operations
• The characterization of Gaussian operations and Distillation of Gaussian States
• Gaussian transformations and distillation of entangled Gaussian states
• Entanglement Properties of the Harmonic Chain
• The entanglement cost under operations preserving the positivity of partial transpose
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Driving non-Gaussian to Gaussian states with linear optics
• The entangling power of passive optical elements
• Purity of Gaussian states: measurement schemes and time-evolution in noisy channels
• Distillation of continuous-variable entanglement with optical means
• Quantum and classical correlations in quantum Brownian motion
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs
• Entanglement concentration of continuous variable quantum states
• Experimental characterization of Gaussian quantum communication channels
• Single-passage read-out of atomic quantum memory
• Entanglement generation in continuously coupled parametric generators
• SU(1,1) symmetry of multimode squeezed states
• Enhanced continuous generation of non-Gaussianity through optomechanical modulation
• Faithful measure of Quantum non-Gaussianity via quantum relative entropy
• Quantum Decoherence of Phonons in Bose-Einstein Condensates
• Gaussian local unitary equivalence of $n$-mode Gaussian states and Gaussian transformations by local operations with classical communication
• Non-Markovian weak coupling limit of quantum Brownian motion
• Verifying single-mode nonclassicality beyond negativity in phase space
• Interconversion of pure Gaussian states using non-Gaussian operations