In this paper, a novel pinching antenna-aided spatial multiplexing (PASM) architecture is conceived, which intrinsically amalgamates the benefits of flexible radiating element placement with radio-frequency (RF) chain transmission. Specifically, we leverage the deterministic phase variation along dielectric waveguides as a zero-power phase-control mechanism, where each waveguide fed by a single RF chain drives multiple pinching antennas (PAs) acquiring position-dependent phase shifts. Then, the PASM propagation environment is characterized by a realistic channel model encompassing Rician small-scale fading, correlated shadowing, and large-scale path loss. Based on this, a low-complexity vector approximate message passing (VAMP) detector is conceived, which exploits a waveguide-structured prior for jointly processing the signals associated with all PAs. Moreover, we derive an analytical upper bound on the bit error rate (BER) for the maximum likelihood (ML) detector to quantify the achievable performance limits. Finally, our simulation results demonstrate that the proposed PASM architecture achieves substantial signal-to-noise ratio (SNR) gain over the conventional phase-shifter-aided spatial multiplexing (PSSM), while the VAMP detector strikes an attractive trade-off between the system performance and computational complexity.