Quantum Entanglement: An Analysis via the Orthogonality Relation

Shengjun Wu

Alexander A. Klyachko, A.S. Shumovsky

The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are defined in terms of the orthogonal basis of Lie algebra, corresponding to the dynamic symmetry group. We discuss the relativity of entanglement with respect to the choice of basic observables and a way of stabilization of robust entanglement in physical systems.

K. Hess

Zhi Zeng

We theoretically propose a simple and efficient scheme for the complete analysis of high-dimensional Bell states in N dimensions. The mutually orthogonal high-dimensional entangled states can be unambiguously distinguished by obtaining the parity and relative phase information of entanglement independently. Based on this approach, we present the physical realization of photonic four-dimensional Bell state measurement with the current technology. The proposed scheme will be useful for quantum information processing tasks that utilize high-dimensional entanglement.

Manuel Aschwanden

Qinglong Lin, Fatih Yaman, Govind Prasad Agrawal

We present a general quantum theory capable of describing photon statistics under the combined effects of four-wave mixing and Raman scattering inside optical fibers. Our theory is vectorial in nature and includes all polarization effects. Our analysis shows that spontaneous Raman scattering degrades the pair correlation in all cases but the extent of degradation depends on the pumping configuration employed. In a single-pump configuration, photon pairs can be created with polarization either parallel or orthogonal to the pump. Our results show that the orthogonal configuration can improve the extent of quantum correlation considerably over a broad bandwidth. In the case of a dual-pump configuration, we show that imbalance of two pump powers can be used to improve the quality of photon pairs. We show that orthogonally polarized pumps can generate photon pairs automatically in a polarization-entangled state. In particular, orthogonal pumping with circular polarizations produces such an entangled state with relatively high quality. We also quantify the quality of polarization entanglement as well as energy-time entanglement constructed using correlated photon pairs.