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

• URL: http://arxiv.org/abs/2003.03372v1
• Date: Fri, 6 Mar 2020 04:45:47 GMT
• Title: Intrinsic degree of coherence of two-qubit states and measures of two-particle quantum correlations
• Authors: Nilakantha Meher, Abu Saleh Musa Patoary, Girish Kulkarni, Anand K. Jha
• Abstract summary: A basis-invariant measure of coherence known as the intrinsic degree of coherence has been established for classical and single-particle quantum states. We show that the intrinsic degree of coherence of a two-qubit state puts an upper bound on the violations of Bell inequalities. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, a basis-invariant measure of coherence known as the intrinsic degree of coherence has been established for classical and single-particle quantum states [JOSA B {\bf 36}, 2765 (2019)]. Using the same mathematical construction, in this article, we 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, first of all, we 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 intrinsic degree of coherence less than $1/\sqrt{3}$ 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 parametric down-conversion of a pump photon, we propose an experimental scheme for measuring the intrinsic degree of coherence of two-qubit states. We also present our theoretical study showing how the intrinsic degree of coherence of a pump photon dictates the maximum intrinsic degree of coherence of the generated two-qubit state.

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