Atemporal diagrams for quantum circuits

Details Atemporal diagrams for quantum circuits Atemporal diagrams for quantum circuits

2005-07-21

arxiv.org/abs/quant-ph/0507215v2

Physical Review A 73, 052309 (2006)

Physics

Quantum Physics

Minor changes in references. Latex 32 pages, 13 figures in text using PSTricks

Scientific paper

10.1103/PhysRevA.73.052309

A system of diagrams is introduced that allows the representation of various elements of a quantum circuit, including measurements, in a form which makes no reference to time (hence ``atemporal''). It can be used to relate quantum dynamical properties to those of entangled states (map-state duality), and suggests useful analogies, such as the inverse of an entangled ket. Diagrams clarify the role of channel kets, transition operators, dynamical operators (matrices), and Kraus rank for noisy quantum channels. Positive (semidefinite) operators are represented by diagrams with a symmetry that aids in understanding their connection with completely positive maps. The diagrams are used to analyze standard teleportation and dense coding, and for a careful study of unambiguous (conclusive) teleportation. A simple diagrammatic argument shows that a Kraus rank of 3 is impossible for a one-qubit channel modeled using a one-qubit environment in a mixed state.

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