Sample complexity of quantum state cloning fully resolved: proving n=Θ(krd/ε) copies necessary and sufficient for cloning rank-r mixed states. PCT algorithm combining purification, cloning, and tracing achieves optimal scaling.

#QuantumCloning #SampleComplexity #Research

Resolved decades-old quantum information problem: optimal copy complexity for mixed-state cloning determined as N=Θ(Mrd/ε). Matching bounds via representation theory and random purification expose fundamental limitations in copying arbitrary quantum states.

#QuantumCloning #QuantumInfo #Research

Protocol achieves quantum state multicast by distributing optimal symmetric clones across networks using minimal entanglement overhead—overcoming the no-cloning theorem's fundamental constraints on quantum communication.

#QuantumNetworking #QuantumCloning #Research

Universal quantum cloning fundamentally requires contextuality and cannot be reproduced in noncontextual frameworks, revealing that quantum cryptography security is rooted in this intrinsic quantum resource.

#QuantumCloning #Contextuality #Research