No-broadcast theorem

The no-broadcast theorem is a result in quantum information theory. In the case of pure quantum states, it is a corollary of the no-cloning theorem: since quantum states cannot be copied in general, they cannot be broadcast. For mixed states, it generalizes no-cloning.

The no-cloning theorem says that it is impossible to create two copies of a state given a single copy of the state.

The no-broadcast theorem says that, given a single copy of a state, it is impossible to create a state such that one part of it is the same as the original state and the other part is also the same as the original state. I.e., given an initial state ρ₁ it is impossible to create a state ρ_AB such that Tr_Aρ_AB = ρ₁ and Tr_Bρ_AB = ρ₁. Although here we work with mixed states, a broadcasting machine would have to work on any pure state ensemble of ρ₁.

See also

• No-communication theorem
• Quantum teleportation
• Quantum entanglement
• Quantum information
• Uncertainty principle
• Transactional interpretation

References

• Noncommuting Mixed States Cannot Be Broadcast, H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa and B. Schumacher, Phys. Rev. Lett. 76, 15, 2818--2821 (1996). (prl.aps.org, ArXiv)