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

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

2007-07-23

arxiv.org/abs/0707.3284v2

Phys. Rev. A 76, 042334 (2007)

Physics

Quantum Physics

7 pages, 1 figure. Discussion expanded, to appear in PRA

Scientific paper

10.1103/PhysRevA.76.042334

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 [arXiv:0706.1561]. In analogy with the finite-dimensional case, we demonstrate that the $1 \times M$ 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 a novel entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes.

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