Physics – Quantum Physics
Scientific paper
2011-09-02
Physics
Quantum Physics
12 pages, 6 figures
Scientific paper
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.
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