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Concept
No-communication theorem
Summary
In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurement of a subsystem of the total state, to communicate information to another observer. The theorem is important because, in quantum mechanics, quantum entanglement is an effect by which certain widely separated events can be correlated in ways that, at first glance, suggest the possibility of communication faster-than-light. The no-communication theorem gives conditions under which such 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 violations of local realism obtained in tests of Bell's theorem. In these experiments, the no-communication theorem shows that failure of local realism does not lead to what could be referred to as "spooky communication at a distance" (in analogy with Einstein's labeling of quantum entanglement as requiring "spooky action at a distance" on the assumption of QM's completeness).
The no-communication theorem states that, within the context of quantum mechanics, it is not possible to transmit classical bits of information by means of carefully prepared mixed or pure states, whether entangled or not. The theorem is only a sufficient condition that states that if the Kraus matrices commute then there can be no communication through the quantum entangled states and this is applicable to all communication. From a relativity and quantum field perspective also faster than light or "instantaneous" communication is disallowed.
Being only a sufficient condition there can be extra cases where communication is not allowed and there can be also cases where is still possible to communicate through the quantum channel encoding more than the classical information.
In regards to communication a quantum channel can always be used to transfer classical information by means of shared quantum states.
Official source
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