The no-cloning theorem says you can’t make an exact copy of an arbitrary unknown quantum state. It’s a fundamental rule of how quantum systems work. In quantum mechanics, all physical processes are governed by unitary operations, which are linear and preserve the inner product (or angle) between any two quantum states. Suppose a machine could copy any quantum state. It would have to take a state |ψ⟩ and an empty register |0⟩ and turn them into |ψ⟩ ⊗ |ψ⟩. That would mean if you gave it two different inputs |a⟩ and |b⟩, it would produce |a⟩ ⊗ |a⟩ and |b⟩ ⊗ |b⟩. But linear evolution requires that the inner product between inputs must match the inner product between outputs. Before cloning, the inner product is ⟨a|b⟩. After cloning, it becomes ⟨a|b⟩². These are only equal if ⟨a|b⟩ is 0 or 1 - that is, if the states are orthogonal or identical. So such a cloning machine can’t work for arbitrary states. This result has major implications. You can clone classical information (like 0s and 1s), since those correspond to orthogonal quantum states. But in the quantum world, information encoded in superpositions or entangled states can’t be copied. This is what makes quantum key distribution secure - an eavesdropper can’t copy qubits to measure them later without disturbing the transmission. In short, the no-cloning theorem follows directly from the basic math of quantum mechanics. It’s a core reason why quantum information behaves so differently from classical information. [[Non-orthogonal states]]