Measuring arbitrary-order coherences: Tomography of single-mode multiphoton polarization-entangled states

A scheme is discussed for measuring Nth-order coherences of two orthogonally polarized light fields in a single spatial mode at very limited experimental cost. To implement the scheme, the only measurements needed are the Nth-order intensity moments after the light beam has passed through two quarter-wave plates, one half-wave plate, and a polarizing beam splitter for specific settings of the wave plates. It is shown that this method can be applied for arbitrarily large N. A set of explicit values is given for the settings of the wave plates, constituting an optimal measurement of the Nth-order coherences for any N. For Fock states the method introduced here corresponds to a full state tomography. Applications of the scheme to systems other than polarization optics are discussed.