No teleportation theorem

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In quantum information theory, the no teleportation theorem states that quantum information cannot be measured with complete accuracy.

[edit] Formulation

The term quantum information refers to information stored in the state of a quantum system. Two quantum states ρ₁ and ρ₂ are different if the measurement results of any physical observable have the same expectation value for ρ₁ and ρ₂. Thus measurement can be viewed as an information 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 a density matrix. Suppose now one has an ensemble, denoted by Σ, of a quantum system in some mixed state ρ. Prepare an ensemble, of the same system, as follows:

Perform measurement on each member of Σ.
According to the measurement outcome, prepare a system in some pre-specified state.

The no-teleportation theorem states that the resulting ensemble will be different from ρ, irrespective of how the preparation procedure is related to measurement outcome. A quantum state cannot be determined via measurement. In other words, if a quantum channel is measurement 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.