  In the context of the 2-dimensional (2D) polarization states of light, the
degree of polarization P2 is equal to the maximum value of the degree of
coherence over all possible bases. Therefore, P2 can be referred to as the
intrinsic degree of coherence of a 2D state. In addition to (i) the maximum
degree of coherence interpretation, P2 also has the following interpretations:
(ii) it is the Frobenius distance between the state and the maximally
incoherent identity state, (iii) it is the norm of the Bloch-vector
representing the state, (iv) it is the distance to the center-of-mass in a
configuration of point masses with magnitudes equal to the eigenvalues of the
state, (v) it is the visibility in a polarization interference experiment, and
(vi) it is the weightage of the pure part of the state. Among these six
interpretations of P2, the Bloch vector norm, Frobenius distance, and center of
mass interpretations have previously been generalized to derive an analogous
basis-independent measure PN for N-dimensional (ND) states. In this article, by
extending the concepts of visibility, degree of coherence, and weightage of
pure part to ND spaces, we show that these three remaining interpretations of
P2 also generalize to the same quantity PN , establishing PN as the intrinsic
degree of coherence of ND states. We then extend PN to the N -> Infinity limit
to quantify the intrinsic degree of coherence P_Infinity of
infinite-dimensional states in the orbital angular momentum (OAM), photon
number, and position-momentum degrees of freedom.
