No-broadcasting theorem

The generalized quantum no-broadcasting theorem, originally proven by Barnum, Caves, Fuchs, Jozsa and Schumacher for mixed states of finite-dimensional quantum systems,[1] says that given a pair of quantum states which do not commute, there is no method capable of taking a single copy of either state and succeeding, no matter which state was supplied and without incorporating knowledge of which state has been supplied, in producing 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. That is, given an initial unknown state ${\displaystyle \rho _{i},}$ drawn from the set ${\displaystyle \{\rho _{i}\}_{i\in \{1,2\}}}$ such that ${\displaystyle [\rho _{1},\rho _{2}]\neq 0}$, there is no process (using physical means independent of those used to select the state) guaranteed to create a state ${\displaystyle \rho _{AB}}$ in a Hilbert space ${\displaystyle H_{A}\otimes H_{B}}$ whose partial traces are ${\displaystyle \operatorname {Tr} _{A}\rho _{AB}=\rho _{i}}$ and ${\displaystyle \operatorname {Tr} _{B}\rho _{AB}=\rho _{i}}$. Such a process was termed broadcasting in that paper.

The second theorem states that local broadcasting is only possible when the state is a classical probability distribution.[3] This means that a state can only be broadcast locally if it does not have any quantum correlations.[4] Luo reconciled this theorem with the generalized no-broadcast theorem by making the conjecture that when a state is a classical-quantum state, correlations (rather than the state itself) in a bipartite state can be locally broadcast.[3] By mathematically proving that his conjecture and the two theorems all relate to and imply one another, Luo proved that all three statements are logically equivalent.[3]

• No-communication theorem
• No-hiding theorem[5]
• Quantum teleportation
• Quantum entanglement
• Quantum information
• Uncertainty principle