Experimentally, a simple implementation of a quantum channel is fiber optic (or free-space for that matter) transmission of single photons. Single photons can be transmitted up to 100 km in standard fiber optics before losses dominate. The photon's time-of-arrival (time-bin entanglement) or polarization are used as a basis to encode quantum information for purposes such as quantum cryptography. The channel is capable of transmitting not only basis states (e.g. |0>, |1>) but also superpositions of them (e.g. |0>+|1>). The coherence of the state is maintained during transmission through the channel. Contrast this with the transmission of electrical pulses through wires (a classical channel), where only classical information (e.g. 0s and 1s) can be sent. Channel capacity The cb-norm of a channel Before giving the definition of channel capacity, the preliminary notion of the norm of complete boundedness, or cb-norm of a channel needs to be discussed. When considering the capacity of a channel , we need to compare it with an "ideal channel" . For instance, when the input and output algebras are identical, we can choose to be the identity map. Such a comparison requires a metric between channels. Since a channel can be viewed as a linear operator, it is tempting to use the natural operator norm. In other words, the closeness of to the ideal channel can be defined by However, the operator norm may increase when we tensor with the identity map on some ancilla. To make the operator norm even a more undesirable candidate, the quantity may increase without bound as The solution is to introduce, for any linear map between C*-algebras, the cb-norm Definition of channel capacity The mathematical model of a channel used here is same as the classical one. Let be a channel in the Heisenberg picture and be a chosen ideal channel. To make the comparison possible, one needs to encode and decode Φ via appropriate devices, i.e. we consider the composition where E is an encoder and D is a decoder. In this context, E and D are unital CP maps with appropriate domains. The quantity of interest is the best case scenario: with the infimum being taken over all possible encoders and decoders. To transmit words of length n, the ideal channel is to be applied n times, so we consider the tensor power The operation describes n inputs undergoing the operation independently and is the quantum mechanical counterpart