  We raise a general question of quantum information theory whether the quantum
phase information can be compressed and retrieved. A general qubit contains
both amplitude and phase information, while an equatorial qubit contains only a
phase information. We study whether it is possible to compress the phase
information of n equatorial qubits into m general qubits with m being less than
n, and still those information can be retrieved perfectly. We prove that this
process is not allowed by quantum mechanics.
