Intrinsic measure of coherence for high-dimensional systems


Abstract: The widely-adopted resource-theoretical framework proposed by Baumgratz et al., Phys. Rev. Lett. 113, 140401, (2014) for quantifying coherence in high-dimensional quantum systems is manifestly basis-dependent and has unphysical implications. Recently, Yao et al., Sci. Rep. 6, 32010, (2016) have conjectured a basis-independent measure PN for N-dimensional quantum states, defined in analogy with the degree of polarization P2 for 2-dimensional polarization states of light, as the Frobenius distance of the state from the maximally-incoherent state. In this paper, we demonstrate that in addition to the above geometric interpretation, the measure PN also shares all the other known interpretations of P2 as well, namely: (i) it is the norm of the Bloch-vector representing the state, (ii) it is the visibility of projective measurements on the state, (iii) it is the maximum pairwise-coherence of the state over all orthonormal bases, and (iv) it is determined by the purity of the state. Our results establish the suitability of P N as an intrinsic measure of coherence for high-dimensional states of light fields in the orbital-angular-momentum (OAM) and photon number (Fock) basis.

arXiv preprint arXiv:1712.03475

Girish Kulkarni