Enhanced violation of the Collins-Gisin-Linden-Massar-Popescu inequality with optimized time-bin-entangled ququarts

High-dimensional quantum entanglement is drawing attention because it enables us to perform quantum information tasks that are robust against noises. To test the nonlocality of entangled qudits, the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality has been proposed and demonstrated using qudits based on orbital angular momentum, time-energy uncertainty, and frequency bins. Here, we report the generation and observation of time-bin entangled ququarts. We implemented a measurement for the CGLMP inequality test using cascaded delay Mach-Zehnder interferometers fabricated by using planar light-wave circuit technology, with which we achieved a precise and stable measurement for time-bin-entangled ququarts. In addition, we generated an optimized entangled state by modulating the pump pulse intensities, with which we can observe the theoretical maximum violation for the CGLMP inequality test. As a result, we successfully observed a Bell-type parameter $S_4=2.774\pm 0.025$ violating the CGLMP inequality for the maximally entangled state and an enhanced Bell-type parameter $S_4=2.913\pm 0.023$ for the optimized entangled state.

Figure 1

Concept of the optimized time-bin-entangled ququarts generation. (a) Intensities of the input light. (b) Intensities of the pump pulses generated through SHG. (c) Photon count histogram of the photon pairs generated via SPDC.

Figure 2

Concept of measurement using cascaded delay MZIs for four dimensions.

Figure 3

Experimental setup. CW laser: Continuous wave laser. IM 1, IM 2: Lithium niobate intensity modulators. EDFA: Erbium-doped fiber amplifier. FBG: Fiber Bragg grating filter. VA: Variable attenuator. PPLN: Periodically poled lithium niobate waveguide. BPF: Band-pass filter. WDM: Wavelength demultiplexing filter. PC: Polarization controller. Pol: Polarizer. 1-bit delay MZI, 2-bit delay MZI: Delay Mach-Zehnder interferometers fabricated using PLC. SNSPD: Superconducting nanowire single photon detector. TIA: Time interval analyzer.

Figure 4

Coincidence counts for the maximally entangled state as a function of phase shifts for Alice's interferometers.

Figure 5

Coincidence counts for the maximally entangled state as a function of phase shifts for Alice and Bob's interferometers.

Figure 6

Normalized histogram of single counts for the optimized entangled state at channel A measured after the WDM in Fig. 3.

Figure 7

Normalized coincidence counts for the maximally entangled state and the optimized entangled state as a function of phase shifts for Alice's interferometers when Bob set his phase at 0.