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

Journal Article · Mon Oct 15 04:00:00 EDT 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.76.042334· OSTI ID:21020703

Adesso, Gerardo ^[1]; CNR-INFM Coherentia, Naples ^[2]; Giampaolo, Salvatore M ^[3]; Illuminati, Fabrizio ^[3]; CNR-INFM Coherentia, Naples ^[2]

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1. Dipartimento di Fisica 'E. R. Caianiello', Universita degli Studi di Salerno, Via S. Allende, I-84081 Baronissi (Saudi Arabia), Salerno (Italy)
2. Italy
3. Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Saudi Arabia), Salerno (Italy)

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 1xM 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.

• OSTI ID: 21020703
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 76; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ENTROPY
EUCLIDEAN SPACE
GAUSSIAN PROCESSES
QUANTUM COMPUTERS
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
QUBITS