Coherence for vectorial waves and majorization

Abstract

We show that majorization provides a powerful approach to the coherence conveyed by partially polarized transversal electromagnetic waves. Here we present the formalism, provide some examples and compare with standard measures of polarization and coherence of vectorial waves.

Resource-theoretic approach to vectorial coherence

“…The complexity of the subject has motivated the introduction of several different measures of vectorial-field coherence that can actually be mutually contradicting [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. So, it emerges that a meta-theory is needed if we want to apprehend the elusive concept of coherence in this rather rich context.…”

“…The results in Refs. [16,27] indicate that the measures µ g (Γ) and µ F,max (Γ) given by Eqs. ( 2) and ( 3), respectively, are proper coherence monotones after their behavior under random unitary transformations and majorization.…”