Quantum Channels of the Einstein-Podolsky-Rosen Kind

Abstract

An EPR-channel consists of two Hilbert spaces, H ^A and H ^B, and of a density operator sitting on the their direct product space H ^AB. The channel is triggered by a von Neumann measurement on H ^A, resulting in a state (density operator) ω ^A. Because a measurement in H ^A can be considered as a measurement in H ^AB equally well, it induces a new state in H ^AB and, hence, a new state, ω ^B, in H ^B. The map ω ^A → ω ^B depends only on the channel’s original density operator, and not on the chosen complete von Neumann measurement. This map is referred to as “channel map”.

The construction of the channel map is described together with various of its properties, including an elementary link to the modular conjugation and to some related questions.

The (noisy) quantum teleportation channel is treated as an example. Its channel map can be decomposed into two EPR channel maps.