http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
an introduction to quantum maps that are not completely positive
Synthesis digital library of engineering and computer science
1 online resource (xv, 171 pages) : illustrations.
This book is a brief introduction to negative quantum channels, i.e., linear, trace-preserving (and consistent) quantum maps that are not completely positive. The flat and sharp operators are introduced and explained. Complete positivity is presented as a mathematical property, but it is argued that complete positivity is not a physical requirement of all quantum operations. Negativity, a measure of the lack of complete positivity, is proposed as a tool for empirically testing complete positivity assumptions.
1. Introduction and definition of terms -- 1.1 Motivation -- 1.2 Open systems -- 1.3 Density matrix -- 1.4 Mathematical structure of open systems -- 1.4.1 System state spaces -- 1.4.2 Partial trace -- 1.4.3 Assignments of subsystem states -- 1.4.4 Reduced system dynamics -- 1.5 "Vector of states" notation --
10. Physical motivations for sharp operations --
11. Negative qubit channel examples with multi-qubit baths --
12. Proposed experimental demonstration of negativity -- 12.1 Photonic root-swap operation -- 12.2 Photonic CZ operation --
13. Implications of negative channels -- 13.1 Existing experimental evidence of negative channels -- 13.2 Restrictions implied by complete positivity -- 13.3 Expanding the definition of "physically reasonable" --
14. Uses for negative channels -- 14.1 Probing the bath -- 14.1.1 Coupling alone -- 14.1.2 Correlation alone -- 14.1.3 Coupling and correlation together -- 14.1.4 Determining the completely positive parameter space -- 14.2 Speculation on utilities --
15. Conclusions -- 15.1 Complete positivity in recent years -- 15.2 Closing remarks --
3. Non-positive reduced dynamics -- 3.1 Two qubit SWAP example -- 3.2 Positivity domains interpretation --
4. Complete positivity -- 4.1 Complete positivity definition -- 4.2 Reduced system evolution as an operator sum --
5. Physical motivation of complete positivity -- 5.1 Total domain argument -- 5.2 Product state argument --
6. Measures of complete positivity -- 6.1 Local unitary composite evolution -- 6.2 Product composite states -- 6.3 Zero discord initial composite states -- 6.4 Completely positive reduced dynamics without a special form -- 6.5 Choi's matrix -- 6.6 Negativity --
7. Negative channels -- 7.1 Definitions -- 7.2 Sharp operations for negative channels --
8. Negative climates with diagonal composite dynamics -- 8.1 Specific negative channel example -- 8.2 Basis dependence --
9. Rabi channels -- 9.1 Rabi model -- 9.2 Rabi channels with no coupling -- 9.3 Rabi channels with coupling --
A. Discussions -- Discussion of the reduced system definition -- General reduced system dynamics -- General form of initial reduced system state -- Completeness relation for SQO -- Rabi model derivation -- Bibliography -- Author's biography.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
System requirements: Adobe Acrobat Reader.
Includes bibliographical references (pages 161-169).
Synthesis lectures on quantum computing ; # 7