Atemporal diagrams for quantum circuits

Robert B. Griffiths, Shengjun Wu, Li Yu, and Scott M. Cohen
Phys. Rev. A 73, 052309 – Published 11 May 2006

Abstract

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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  • Received 24 August 2005

DOI:https://doi.org/10.1103/PhysRevA.73.052309

©2006 American Physical Society

Authors & Affiliations

Robert B. Griffiths, Shengjun Wu*, and Li Yu

  • Physics Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213, USA

Scott M. Cohen

  • Physics Department, Duquesne University, Pittsburgh, Pennsylvania 15282, USA

  • *Present address: Hefei National Laboratory for Physical Science at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.

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Issue

Vol. 73, Iss. 5 — May 2006

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