Experimental investigation of the nonlocal advantage of quantum coherence

Nonlocal advantage of quantum coherence (NAQC) based on coherence complementarity relations is generally viewed as a stronger nonclassical correlation than Bell nonlocality. An arbitrary two-qubit state with NAQC must be an entangled state, which demonstrates that the criterion of NAQC can also be regarded as an entanglement witness. In this paper, we experimentally investigate the NAQC for Bell-diagonal states with high fidelity in an optics-based platform. We perform local measurements on a subsystem in three mutually unbiased bases and reconstruct the density matrices of the measured states by a quantum state tomography process. By analyzing characteristics of the $l_1$ norm, relative entropy, and skew information of coherence with parameters of quantum states, NAQC for the quantum states is accurately captured, and it shows that our experimental results are well compatible with the theoretical predictions. Our results have shown that NAQC could be a new kind of entanglement witness and a useful physical resource for quantum information processing.

Figure 1

Experimental setup. (a) The source module, which is used to generate mixed polarization-entangled photon pairs, mainly includes a high-power tunable diode laser, three half-wave plates (HWPs), a polarization beam splitter (PBS), a beam splitter (BS), two mirrors, and two type-I $\beta$-barium borate (BBO) crystals. (b) The UMZ module, whose purpose is to achieve the proportionate mixing of quantum states, includes an attenuator (ATT), a HWP, two mirrors, and two BSs. (c) The measurement module, which is used to realize local measurement on photon A, consists of two wave plates ($P_1$ and $P_2$) and a PBS. (d) The tomography module, whose function is to reconstruct quantum states, includes two quarter-wave plates (QWPs), two HWPs, two PBSs, two 3-nm interference filter (IFs), two single-photon detector (SPDs), and a dual-channel logic coincidence meter.

Figure 2

Tomographic results for the four maximally entangled states. (a) $\mathrm{Re}\left({\rho }_1\right)$, (b) $\mathrm{Re}\left({\rho }_2\right)$, (c) $\mathrm{Re}\left({\rho }_3\right)$, and (d) $\mathrm{Re}\left({\rho }_4\right)$ in the upper plots represent real parts of ${\rho }_1,{\rho }_2,{\rho }_3$, and ${\rho }_4$, respectively. (${\mathrm{a}}^{\prime }$) $\mathrm{Im}\left({\rho }_1\right)$, (${\mathrm{b}}^{\prime }$) $\mathrm{Im}\left({\rho }_2\right)$, (${\mathrm{c}}^{\prime }$) $\mathrm{Im}\left({\rho }_3\right)$, and (${\mathrm{d}}^{\prime }$) $\mathrm{Im}\left({\rho }_4\right)$ in the lower plots represent imaginary parts of these states.

Figure 3

Experimental results and the corresponding theoretical predictions. The horizontal axis represents the parameter $q$ of the initial BDS. The vertical axis on the right represents concurrence, and the vertical axis on the left represents the $l_1$ norm of coherence ($L_{1}C$) and the maximum violation of CHSH inequality. The black squares, blue rhombus, and red circles denote the experimental results of $C\left({\rho }_{AB}\right),B_{max}\left({\rho }_{AB}\right)$, and $N_{l_1}\left({\rho }_{AB}\right)$, respectively. The solid lines in different colors are the corresponding theoretical predictions, respectively.

Figure 4

Experimental results and the corresponding theoretical predictions. The vertical axis on the left represents the relative entropy of coherence (ReC). The red circles denote the experimental results of $N_{re}\left({\rho }_{AB}\right)$.

Figure 5

Experimental results and the corresponding theoretical predictions. The vertical axis on the left represents the skew information of coherence (SkC), and the red circles denote the experimental results of $N_{sk}\left({\rho }_{AB}\right)$.