Inquantum information theory, theno-teleportation theorem states that an arbitrary quantum state cannot be converted into a sequence ofclassical bits (or even an infinite number of such bits); nor can such bits be used to reconstruct the original state, thus "teleporting" it by merely moving classical bits around. Put another way, it states that the unit ofquantum information, thequbit, cannot be exactly, precisely converted into classical information bits. This should not be confused withquantum teleportation, which does allow a quantum state to be destroyed in one location, and an exact replica to be created at a different location.
In crude terms, the no-teleportation theorem stems from theHeisenberg uncertainty principle and theEPR paradox: although a qubit can be imagined to be a specific direction on theBloch sphere, that direction cannot bemeasured precisely, for the general case; if it could, the results of that measurement would be describable with words, i.e. classical information.
The no-teleportation theorem is implied by theno-cloning theorem: if it were possible to convert a qubit into classical bits, then a qubit would be easy to copy (since classical bits are trivially copyable).
The termquantum information refers to information stored in thestate of a quantum system. Twoquantum statesρ1 andρ2 are identical if the measurement results of any physical observable have the same expectation value forρ1 andρ2. Thusmeasurement can be viewed as aninformation channel with quantum input and classical output, that is, performing measurement on a quantum system transforms quantum information into classical information. On the other hand, preparing a quantum state takes classical information to quantum information.
In general, a quantum state is described by adensity matrix. Suppose one has a quantum system in some mixed stateρ. Prepare an ensemble, of the same system, as follows:
The no-teleportation theorem states that the result will be different fromρ, irrespective of how the preparation procedure is related to measurement outcome. A quantum state cannot be determined via a single measurement. In other words, if a quantum channel measurement is followed by preparation, it cannot be the identity channel. Once converted to classical information, quantum information cannot be recovered.
In contrast, perfect transmission is possible if one wishes to convert classical information to quantum information then back to classical information. For classical bits, this can be done by encoding them in orthogonal quantum states, which can always be distinguished.
Among otherno-go theorems in quantum information are:
With the aid ofshared entanglement, quantum states can be teleported, see
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