This paper considers the problem of detecting a high dimensional signal based on compressed measurements with physical layer secrecy guarantees. First, we propose a collaborative compressive detection (CCD) framework to compensate for the performance loss due to compression with a single sensor. We characterize the tradeoff between dimensionality reduction achieved by a universal compressive sensing (CS)-based measurement scheme and the achievable performance of CCD analytically. Next, we consider a scenario where the network operates in the presence of an eavesdropper who wants to discover the state of the nature being monitored by the system. To keep the data secret from the eavesdropper, we propose to use cooperating trustworthy nodes that assist the fusion center (FC) by injecting artificial noise to deceive the eavesdropper. We also design the system by determining the optimal values of parameters which maximize the CS-based collaborative detection performance at the FC while ensuring perfect secrecy at the eavesdropper. Experiments are conducted on synthetic data sets for spectrum sensing in cognitive radio networks to verify theoretical findings.