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Intrinsic degree of coherence of classical and quantum states

In the context of the two-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 paper, by extending the concepts of visibility, degree of coherence, and weightage of the 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→∞ limit to quantify the intrinsic degree of coherence P∞ of infinite-dimensional states in the orbital angular momentum, photon number, and position-momentum degrees of freedom.