Quantum Compressed Sensing (QCS) is an efficient framework that exploits signal sparsity to reconstruct quantum states and quantum-inspired communication signals using fewer measurements than conventional approaches. It combines compressed sensing theory with quantum information processing to reduce sampling complexity and computational cost in high- dimensional systems. Advanced estimation techniques such as OMP-based methods, deep learning-assisted recovery, and quantum-inspired neural models improve reconstruction accuracy under noisy conditions. These approaches utilize sparsity in quantum states, wireless channels, and system parameters while lowering the burden of quantum measurements. QCS is particularly useful in emerging applications like next-generation wireless networks, quantum sensing, and optical communication where measurement resources are limited. Compared to classical compressed sensing, QCS methods offer better scalability and stronger resilience to estimation errors. They also enable modeling of quantum features such as superposition and correlated system behavior. Performance evaluation is typically carried out using metrics like BER versus SNR, MMSE, and recovery accuracy. Overall, QCS supports efficient signal acquisition and reliable estimation in large-scale quantum-aware systems.