1109.0349 (Ryo Namiki)

Einstein-Podolsky-Rosen-like correlation on a coherent-state basis and
inseparability of two-mode Gaussian states    [PDF]

Ryo Namiki

The strange property of the Einstein-Podolsky-Rosen (EPR) correlation between
two remote physical systems is a primitive object on the study of quantum
entanglement. In order to understand the entanglement in canonical
continuous-variable systems, a pair of the EPR-like uncertainties is an
essential tool in both theoretical and experimental approaches. Here, we use a
normalized pair of the EPR-like uncertainties to discuss the role of the
canonical uncertainty relation in the inseparability problem. As another
physically reasonable tool, we introduce a state overlap to a classically
correlated mixture on a coherent-state basis and consider its role in the
inseparability problem. The separable condition associated with the overlap
determines the strength of the EPR-like correlation on the coherent-state basis
in order that the state is entangled. In a standard form of two-mode Gaussian
states, the separable conditions with the EPR-like uncertainties and the
separable condition with the overlap to the classically correlated mixture are
linked by a simple embrace relation. This establishes potential utility of the
coherent-state-based approach for the inseparability problem. We also consider
an experimental measurement scheme for estimation of the state overlap by a
heterodyne measurement and a photon detection with a feedforward operation. The
parallelism between the separable condition with the state overlap and the
quantum-domain condition with the Gaussian distributed coherent states is
discussed associated with the standard continuous-variable quantum
teleportation process. Thereby, we succeed in reconciling the condition on the
channel fidelity to the condition on the resource entanglement for the
teleportation including a non-unit-gain effect.

View original: http://arxiv.org/abs/1109.0349