Quantum and classical information transmission acts and reducibilities

We survey the physical resources needed to transmit intact quantum states reliably between two separated parties, and the extent to which these resources can be substituted for one another. To avoid violations of physical law, the intact transmission of a general quantum state requires both a quantum resource, which cannot be cloned, and a directed resource, which cannot propagate superluminally. The sharing of entanglement requires only the former, while purely classical communication requires only the latter. In teleportation the two requirements are met by two separate systems, while in the direct, unimpeded transmission of qubit, they are met by the same system. Quantum data compression optimizes the use of quantum channels, allowing redundant quantum data, such as random sequence of two non-orthogonal states, to be compressed to a bulk approximating its von Neumann entropy, then recovered at the receiving end with negligible distortion. Entanglement purification enables impure entangled states, such as Einstein-Podolsky-Rosen pairs shared through a noisy channel, to be purified and used for reliable teleportation, thereby allowing a noisy quantum channel to stimulate a noiseless one. These results can be expressed as equivalences and reductions among various combinations of the following primitives: transmitting an intact 2-state quantum system or qubit: sharing a maximally entangled EPR pair of 2-state particles or obit: sending a 1-bit secret message, sending a 1-bit public message, sharing a secret random bit, and transmitting a qubit corrupted by noise or eavesdropping.