Hydrogen-rich compounds have been extensively studied both theoretically and experimentally in the quest for novel high-temperature superconductors. Reports on sulfur hydride attaining metallicity under pressure and exhibiting superconductivity at temperatures as high as 200 K have spurred an intense search for room-temperature superconductors in hydride materials. Recently, compressed phosphine was reported to metallize at pressures above 45 GPa, reaching a superconducting transition temperature (T_C) of 100 K at 200 GPa. However, neither the exact composition nor the crystal structure of the superconducting phase have been conclusively determined. In this work, the phase diagram of PH_n (n = 1,2,3,4,5,6) was extensively explored by means of ab initio crystal structure predictions using the minima hopping method (MHM). The results do not support the existence of thermodynamically stable PH_n compounds, which exhibit a tendency for elemental decomposition at high pressure even when vibrational contributions to the free energies are taken into account. Although the lowest energy phases of PH_1,2,3 display T_C\'s comparable to experiments, it remains uncertain if the measured values of T_C can be fully attributed to a phase-pure compound of PH_n.