SU(1,1) symmetry of multimode squeezed states

Abstract

We show that a class of multimode optical transformations that employ linear optics plus two-mode squeezing can be expressed as SU(1,1) operators. These operations are relevant to state-of-the-art continuous variable quantum information experiments including quantum state sharing, quantum teleportation, and multipartite entangled states. Using this SU(1,1) description of these transformations, we obtain a new basis for such transformations that lies in a useful representation of this group and lies outside the often-used restriction to Gaussian states. We analyze this basis, show its application to a class of transformations, and discuss its extension to more general quantum optical networks.

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• Quasienergy operators and generalized squeezed states for systems of trapped ions
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• Entanglement Entropy in the $\sigma$-Model with the de Sitter Target Space
• Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals
• Quantum properties of the three-mode squeezed operator: triply concurrent parametric amplifiers
• Higher-order properties and Bell-inequality violation for the three-mode enhanced squeezed state