receives, B prepares his (quantum) system in a specific state. In the Schrödinger picture, the first part of the channel 1 simply consists of A making a measurement, i.e. it is the observable map: If, in the event of the i-th measurement outcome, B prepares his system in state Ri, the second part of the channel 2 takes the above classical state to the density matrix The total operation is the composition Channels of this form are called measure-and-prepare or in Holevo form. In the Heisenberg picture, the dual map is defined by A measure-and-prepare channel can not be the identity map. This is precisely the statement of the no teleportation theorem, which says classical teleportation (not to be confused with entanglement-assisted teleportation) is impossible. In other words, a quantum state can not be measured reliably. In the channel-state duality, a channel is measure-and-prepare if and only if the corresponding state is separable. Actually, all the states that result from the partial action of a measure-and-prepare channel are separable, and for this reason measure-and-prepare channels are also known as entanglement-breaking channels. Pure channel Consider the case of a purely quantum channel in the Heisenberg picture. With the assumption that everything is finite-dimensional, is a unital CP map between spaces of matrices By Choi's theorem on completely positive maps, must take the form where N ≤ nm. The matrices Ki are called Kraus operators of (after the German physicist Karl Kraus, who introduced them). The minimum number of Kraus operators is called the Kraus rank of . A channel with Kraus rank 1 is called pure. The time evolution is one example of a pure channel. This terminology again comes from the channel-state duality. A channel is pure if and only if its dual state is a pure state. Teleportation In quantum teleportation, a sender wishes to transmit an arbitrary quantum state of a particle to a possibly distant receiver. Consequently, the teleportation process is a quantum channel. The apparatus for the process itself requires a quantum channel for the transmission of one particle of an entangled-state to the receiver. Teleportation occurs by a joint measurement of the sent particle and the remaining entangled particle. This measurement results in classical information which must be sent to the receiver to complete the teleportation. Importantly, the classical information can be sent after the quantum channel has ceased to exist. In the experimental setting