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

Recently, a basis-invariant measure of coherence known as the intrinsic degree of coherence has been established for classical and single-particle quantum states [ J. Opt. Soc. Am. B 36 , 2765 ( 2019 ) JOBPDE 0740-3224 10.1364/JOSAB.36.002765 ]. In this article, we use the same mathematical construction to define the intrinsic degree of coherence of two-qubit states and demonstrate its usefulness in quantifying two-particle quantum correlations and entanglement. In this context, we first show that the intrinsic degree of coherence of a two-qubit state puts an upper bound on the violations of Bell inequalities that can be achieved with the state and that a two-qubit state with an intrinsic degree of coherence less than 1 / 3 cannot violate Bell inequalities. We then show that the quantum discord of a two-qubit state, which quantifies the amount of quantum correlations available in the two-qubit state for certain tasks, is bounded from above by the intrinsic degree of coherence of the state. Next, in the context of two-particle entanglement, we show that the range of values that the concurrence of a two-qubit state can take is decided by the intrinsic degree of coherence of the two-qubit state together with that of the individual qubits. Finally, for the polarization two-qubit states generated by the parametric down-conversion of a pump photon, we propose an experimental scheme to measure the intrinsic degree of coherence of two-qubit states. We also present our theoretical study that shows how the intrinsic degree of coherence of a pump photon dictates the maximum intrinsic degree of coherence of the generated two-qubit state.