(5) Light propagation on rotating reference frame: light propagates with constant speed of c relative to any inertial reference frame is one of the postulates in special relativity. Does light propagate symmetrically in a non-inertial rotating system along and against the rotation? According to Einstein's theory of special relativity, the speed of light is independent of the motion of its source. The theory, however, is only valid for inertial reference frames. Is the speed of light a constant when its source is attached to a non-inertial reference system? This question has been recognized as fundamentally important since the early days of the relativity theory, especially in connection with the experimental observation of Sagnac: apparently light propagates anisotropically along and against the rotation of the Sagnac interferometer. Considering the rotation of the Earth, we may have to ask a similar question: Is the East-West and the West-East one-way speed of light isotropic? Although, historically, this question has resulted in a confusing problem debated in the physics community, the problem received special attention in recent years due to the modern applications in which ultra-high accuracy timing and positioning are involved on the rotating Earth. We are currently studying the one-way propagation of light on a rotating platform along and against the rotation.

(6) Characterizing entanglement has turned out to be a very difficult. A collaboration with Prof. Arthur Pittenger or the UMBC Department of Mathematics and Statistics has led to a series of papers to study this problem. In particular, a general form of entanglement witness based on the geometry of the space of density matrices was derived Convexity and the separability problem of quantum mechanical density matrices Geometry of entanglement witnesses and local detection of entanglement . A number of methods have been devised to reconstruct density matrices. Recently, we have examined the use of mutually unbiased bases (MUB) to study the Wigner functions for finite dimensional systems. Two orthonormal bases are said to be mutually unbiased if the scalar product between any pair of vectors, one from each basis, equals one over the dimension of the space. In Hilbert spaces with dimensions that are powers of prime number a complete set of MUB can be found. That is a set such an arbitrary density matrix can be expressed as a convex combination of sums of projections onto these basis vectors Mutually unbiased bases, generalized spin matrices and separability , Wigner Functions and Separability for Finite Systems .