Information-theoretic lower bounds for mixed-state cloning

Develop information-theoretic methods that prove the optimal Ω(krd/ε) lower bound for cloning k additional copies of arbitrary rank-at-most-r mixed quantum states.

Background

The paper proves the optimal cloning lower bound using representation theory and projector states. The authors compare this argument with information-theoretic lower bounds previously obtained for state learning and with earlier information-theoretic limitations on cloning.

The unresolved question is whether those information-theoretic techniques can reproduce the full Ω(krd/ε) lower bound for mixed-state cloning, rather than merely the representation-theoretic proof supplied here.