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

Formulation

The term quantum information refers to information stored in the state of a quantum system. Two quantum states ρ₁ and ρ₂ are identical if the measurement results of any physical observable have the same expectation value for ρ₁ and ρ₂. Thus measurement

Measurement in quantum mechanics

The framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus....

 can be viewed as an information channel

Quantum channel

In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit...

 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

Density matrix

In quantum mechanics, a density matrix is a self-adjoint positive-semidefinite matrix of trace one, that describes the statistical state of a quantum system...

. Suppose one has a quantum system in some mixed state ρ. Prepare an ensemble, of the same system, as follows:

1. Perform a measurement on ρ.
2. According to the measurement outcome, prepare a system in some pre-specified state.

The no-teleportation theorem states that the result will be different from ρ, 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 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.

See also

Among other "no-go" theorems in quantum information are:

• No-communication theorem
  No-communication theorem
  In 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...
  
  . Entangled states cannot be used to transmit classical information superluminally (faster than the speed of light).
• No-cloning theorem. Quantum states cannot be copied.
• No-broadcast theorem
  No-broadcast theorem
  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...
  
  . A generalization of no cloning theorem (in the case of pure states).

With the aid of shared entanglement

Quantum entanglement

Quantum 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 states can be teleported, see

• Quantum teleportation
  Quantum teleportation
  Quantum 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...