  We study the phase-covariant quantum cloning machine for qudits, i.e. the
input states in d-level quantum system have complex coefficients with arbitrary
phase but constant module. A cloning unitary transformation is proposed. After
optimizing the fidelity between input state and single qudit reduced density
opertor of output state, we obtain the optimal fidelity for 1 to 2
phase-covariant quantum cloning of qudits and the corresponding cloning
transformation.

Quantum Physics