Compression of signals is the operation to remove the redundancy of the original message and shorten the total code length. The redundancy and the compression limit usually depend on the properties of the signals. For quantum signals, it was recently predicted by quantum information theory that there exists a compression scheme that exceeds the limit predicted by the conventional (classical) information theory. In general, quantum carriers include the redundancy due to the overlap of wavefunctions between the carriers. The idea to remove such additional redundancy is to control quantum correlations between these carriers appropriately. In this experiment, we have performed the compression and decompression operations of three qubit signals encoded in a single photon's orthogonal polarization and it's four optical paths. The linear optics compressor entangles these qubits and compressed the three qubit signals into two qubit signals, and then the signals are decompressed again by the linear optics decompressor. We have observed the higher decompression fidelity for our scheme compared to the scheme that have not employed any entangling operations. Fundamental coding theorems in quantum information theory are quantum source coding theorem and quantum channel coding theorem. Now, we have succeeded to experimentally demonstrate these theorems. The present result demonstrated the former and our previous result (demonstration of the super-additive quantum coding gain) demonstrated the latter.