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

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 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/ √ 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.

Measurement of two-photon position–momentum Einstein–Podolsky–Rosen correlations through single-photon intensity measurements

“…Nevertheless, for conceptual clarity, we numerically calculate the inherent error as a function of the intrinsic degree of coherence P of the state in order to directly illustrate how E scales with the mixedness of the state. P is also known as a measure of the purity of the state [51][52][53]. It ranges from 0 to 1, with P = 0 implying a completely mixed state and P = 1 implying a pure state.…”

Direct measurement of atomic entanglement via cavity photon statistics

“…However, for certain classes of two-qubit states, there are proposals for quantifying entanglement without reconstructing the entire density matrix [7,8,9,10,11,12,13,14,15]. Moreover, for pure two-qubit states, it has been shown that the reduced density matrix of one of the subsystems contains information about entanglement [16], implying that the two-qubit entanglement can be measured by making measurements on only one of the subsystems without requiring joint measurements [17,18,19,20,21]. Implementing this concept, several groups have measured entanglement of such two-qubit states experimentally by making measurement on only one of the subsystems [18,19,20].…”

Direct Measurement of Atomic Entanglement via Cavity Photon Statistics

“…[7][8][9][10][11][12][13][14][15] Moreover, for pure two-qubit states, it has been shown that the reduced density matrix of one of the subsystems contains information about entanglement, [16] implying that the two-qubit DOI: 10.1002/andp.202100395 entanglement can be measured by making measurements on only one of the subsystems without requiring joint measurements. [17][18][19][20][21] Implementing this concept, several groups have measured entanglement of such two-qubit states experimentally by making measurement on only one of the subsystems. [18][19][20] This concept has also been used in the context of verifying entanglement in continuous-variable systems.…”