No-Deleting and No-Broadcasting Theorems
Quantum information cannot be deleted against a copy, nor broadcast to independent parties; these complement the no-cloning theorem.
The counterparts to no-cloning
The no-cloning theorem forbids copying an unknown quantum state. Two related results complete the picture: the no-deleting theorem and the no-broadcasting theorem. Together they show that quantum information cannot be freely created, destroyed, or distributed the way classical information can.
No-deleting
The no-deleting theorem is the time-reversed partner of no-cloning. Given two identical copies of an unknown state, there is no unitary operation that deletes one copy while leaving a blank standard state, without moving the information elsewhere. You cannot erase quantum information into nothing; at best you can move it. This reflects the reversibility of unitary evolution.
No-broadcasting
No-broadcasting generalises no-cloning to mixed states. Even when full copying is impossible, one might hope to produce a joint state whose two marginals each match the original. The theorem says this is possible only for a commuting family of states — essentially classical ones. Genuinely quantum (non-commuting) states cannot be broadcast to two parties.
Why they follow
- Linearity of quantum mechanics forbids a universal copier (no-cloning)
- Reversibility forbids a universal eraser against a copy (no-deleting)
- Distinguishability constraints forbid broadcasting non-commuting states
Consequences
These no-go theorems are not mere curiosities. They mean quantum information behaves like a conserved, non-duplicable substance that can be moved but not freely multiplied or erased. This shapes error correction, which must protect information without copying it, and it underpins the security guarantees of quantum communication, where an adversary can neither copy nor cleanly broadcast intercepted qubits.