2007/07/31 by Gerardo Adesso, S. M. Giampaolo, Salvatore M. Giampaolo +1
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Discrete mathematics #Gaussian #Mathematics #Multipartite entanglement #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Squashed entanglement #Symplectic geometry #Unitary state #quant-ph
paper · pdf · doi:10.1103/physreva.76.042334
published as Phys. Rev. A 76, 042334 (2007) · 7 pages, 1 figure. Discussion expanded, to appear in PRA
arxiv created 2007/10/03 · openalex publication_date 2007/10/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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\ifmmode×\else\texttimes\fiM 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.