  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 lightwave 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.
