The relative entropy of entanglement of a given bipartite quantum state is calculated by means of a convergent iterative algorithm. When this state turns out to be nonseparable, the algorithm also provides the corresponding optimal entanglement-witness measurement.
A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms. Depending on the choice of norm, the optimizing states maximize or minimize entanglement, possibly across several bipartite cuts at the same time and possibly only among states in a specified subspace. Recognizing that convergence but not success is certain, we use the algorithm to explore topics ranging from fermionic reduced density matrices and varieties of pure quantum states to absolutely maximally entangled states and minimal output entropy of channels.
Generation of spatially inhomogeneously polarized (SIP) beams due to polarization spatial mode nonseparability is demonstrated using a polarization Sagnac interferometer. Counter propagating horizontal (H) and vertical (V) polarized Laguerre Gaussian beams of opposite topological charges(LG01)corresponding to the two binary degrees of freedom (DoF) are coherently superposed in the interferometer. Quantum inspired entanglement witness and quantification such as Bell state measurement, violation of CHSH form of Bells inequality and concurrence measurements are experimentally measured to establish nonseparability between the two DoF. As the SIP beams are equivalent to bipartite pure states, point wise Stokes polarimetry measurements are used to calculate the reduced coherency matrix corresponding to polarization DoF. Using these we calculate the linear entropy and maximized Bells measure to quantify the degree of entanglement of the SIP beams.