No-deleting theorem

The no-deleting theorem states that no state-independent unitary operation can erase one of two identical unknown quantum states while preserving the other.

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Quantum unitarity: The condition that quantum evolution preserves inner products and total probability. Preserved inner products make a unitary transformation unable to erase distinctions between unknown inputs.
No-cloning theorem: The theorem that an unknown quantum state cannot be copied perfectly by a state-independent physical operation. It is the complementary restriction: unknown states cannot be copied or deleted perfectly.
No-hiding theorem: A theorem stating that information missing from a quantum system after a unitary process resides in its environment. It explains where information goes when a system appears to lose a state.
Quantum error correction: Methods for protecting quantum information by encoding it across multiple physical degrees of freedom. Error correction manipulates encoded states without relying on perfect deletion of unknown quantum information.
Inner product: A mathematical operation that measures overlap between vectors, including quantum state vectors. The theorem follows by comparing input and output state overlaps.
Quantum information: Information encoded in quantum systems, including properties unavailable in classical information theory. The theorem is a constraint on manipulating quantum information.
Quantum erasure: A process that removes a quantum system’s state while transferring its information to another system or environment. Information transfer can erase a local copy without violating the no-deleting theorem.
Quantum cryptography: Cryptographic methods that use quantum systems to establish or protect information. Restrictions on copying and deletion help underpin security arguments about quantum data.
Quantum state: A mathematical description encoding the probabilities of outcomes for measurements on a quantum system. The theorem concerns transformations of unknown quantum states.
Quantum superposition: A quantum state formed as a linear combination of other possible states. Linearity forces a proposed deletion operation to work consistently across superpositions.