One tool to solve every quantum cloning problem numerically

Quantum cloning—copying quantum states as faithfully as physics allows—has known theoretical limits, but turning those limits into actual physical operations has required case-by-case algebra. This framework recasts every cloning problem as a semidefinite program, automatically spitting out the Kraus operators (the concrete instructions for a quantum device) from the solution. As a practical payoff, it quantifies how well an eavesdropper can clone qubits in a noisy BB84 channel, bridging the gap between information-theoretic bounds and real-world security analysis.