# No-broadcast theorem

In physics, 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. Here, the word "broadcast" is used in the sense of conveying the state to two or more recipients. For multiple recipients to each receive the state, there must be, in some sense, a way of duplicating the state. The no-broadcast theorem generalizes the no-cloning theorem for mixed states.

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 it is impossible to create a state in a Hilbert space such that the partial trace and . Although here we work with mixed states, a broadcasting machine would have to work on any pure state ensemble of

## See also

- No-communication theorem
- No-hiding theorem
^{[1]} - 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)