Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations

Gerardo Adesso, Salvatore M. Giampaolo, and Fabrizio Illuminati
Phys. Rev. A 76, 042334 – Published 26 October 2007

Abstract

We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits [S. M. Giampaolo and F. Illuminati, Phys. Rev. A 76, 042301 (2007)]. In analogy with the finite-dimensional case, we demonstrate that the 1×M bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a, uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes.

  • Figure
  • Received 22 July 2007

DOI:https://doi.org/10.1103/PhysRevA.76.042334

©2007 American Physical Society

Authors & Affiliations

Gerardo Adesso1,2,3, Salvatore M. Giampaolo4,2, and Fabrizio Illuminati4,2,5,*

  • 1Dipartimento di Fisica “E. R. Caianiello,” Università degli Studi di Salerno, Via S. Allende, I-84081 Baronissi (SA), Salerno, Italy
  • 2CNR-INFM Coherentia, Napoli, Italy; CNISM, Unità di Salerno, Salerno, Italy; and INFN, Sezione di Napoli-Gruppo Collegato di Salerno, Salerno, Italy
  • 3Grup d’Informació Quàntica, Universitat Autónoma de Barcelona, E-08193 Bellaterra, Barcelona, Spain
  • 4Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Salerno, Italy
  • 5ISI Foundation for Scientific Interchange, Viale Settimio Severo 65, I-10133 Turin, Italy

  • *Corresponding author. illuminati@sa.infn.it

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Issue

Vol. 76, Iss. 4 — October 2007

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