The problem of bipartite entanglement in partially coherent paraxial vector light fields is addressed. A generalized uncertainty principle suited for the polarization-spatial degrees of freedom is introduced. Partial transpose is implemented through the obtained generalized uncertainty principle. Partial transpose is shown to be necessary and sufficient in detecting entanglement for a class of partially coherent vector light fields which have a spatial part to be Gaussian. An experimental realization of the studied entangled states using classical optical interferometry is outlined.
A class of uncertainty relations for partially coherent light is derived; the uncertainty relations in this class express the fact that the product of the effective widths of the space-domain intensity and the spatial-frequency-domain intensity of the light has a lower bound and that this lower bound is inversely proportional to the overall degree of coherence. The different members of this class of uncertainty relations correspond to different choices of the quantity that measures the overall degree of coherence. One particular uncertainty relation has the property of being compatible with the ordinary uncertainty principle; the corresponding overall degree of coherence might therefore be considered the best possible choice of all the quantities that measure the overall degree of coherence of the light.
A class of uncertainty relations for partially coherent light is derived; the uncertainty relations in this class express the fact that the product of the effective widths of the space-domain intensity and the spatial-frequency-domain intensity of the light has a lower bound and that this lower bound is inversely proportional to the overall degree of coherence. The different members of this class of uncertainty relations correspond to different choices of the quantity that measures the overall degree of coherence. One particular uncertainty relation has the property of being compatible with the ordinary uncertainty principle; the corresponding overall degree of coherence might therefore be considered the best possible choice of all the quantities that measure the overall degree of coherence of the light.