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Recently, a basis-invariant measure of coherence known as the intrinsicdegree of coherence has been established for classical and single-particlequantum states [JOSA B {\bf 36}, 2765 (2019)]. Using the same mathematicalconstruction, in this article, we define the intrinsic degree of coherence oftwo-qubit states and demonstrate its usefulness in quantifying two-particlequantum correlations and entanglement. In this context, first of all, we showthat the intrinsic degree of coherence of a two-qubit state puts an upper boundon the violations of Bell inequalities that can be achieved with the state andthat a two-qubit state with intrinsic degree of coherence less than$1/\sqrt{3}$ cannot violate Bell inequalities. We then show that the quantumdiscord of a two-qubit state, which quantifies the amount of quantumcorrelations available in the two-qubit state for certain tasks, is boundedfrom above by the intrinsic degree of coherence of the state. Next, in thecontext of two-particle entanglement, we show that the range of values that theconcurrence of a two-qubit state can take is decided by the intrinsic degree ofcoherence of the two-qubit state together with that of the individual qubits.Finally, for the polarization two-qubit states generated by parametricdown-conversion of a pump photon, we propose an experimental scheme formeasuring the intrinsic degree of coherence of two-qubit states. We alsopresent our theoretical study showing how the intrinsic degree of coherence ofa pump photon dictates the maximum intrinsic degree of coherence of thegenerated two-qubit state.

Intrinsic degree of coherence of two-qubit states and measures of two-particle quantum correlations