No-broadcast theorem
Encyclopedia
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
it is impossible to create a state 
such that 
and 
. Although here we work with mixed states, a broadcasting machine would have to work on any pure state ensemble of 
.
Quantum information science
Quantum information science is an area of study based on the idea that information science depends on quantum effects in physics. It includes theoretical issues in computational models as well as more experimental topics in quantum physics including what can and cannot be done with quantum...
. In the case of pure quantum states, it is a corollary
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
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
it is impossible to create a state such that 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 theoremNo-communication theoremIn quantum information theory, a no-communication theorem is a result which gives conditions under which instantaneous transfer of information between two observers is impossible. These results can be applied to understand the so-called paradoxes in quantum mechanics such as the EPR paradox or...
- Quantum teleportationQuantum teleportationQuantum teleportation, or entanglement-assisted teleportation, is a process by which a qubit can be transmitted exactly from one location to another, without the qubit being transmitted through the intervening space...
- Quantum entanglementQuantum entanglementQuantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...
- Quantum informationQuantum informationIn quantum mechanics, quantum information is physical information that is held in the "state" of a quantum system. The most popular unit of quantum information is the qubit, a two-level quantum system...
- Uncertainty principleUncertainty principleIn quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...
- Transactional interpretationTransactional interpretationThe transactional interpretation of quantum mechanics describes quantum interactions in terms of a standing wave formed by retarded and advanced waves. It was first proposed in 1986 by John G...