Negative quantum channels : an introduction to quantum maps that are not completely positive /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: McCracken, James M. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham, Switzerland : Springer, [2014]
Colección:Synthesis lectures on quantum computing ; #7.
Temas:
Quantum maps.
Quantum systems.
Quantum computers.
Applications quantiques.
Systèmes quantiques.
Ordinateurs quantiques.
SCIENCE > Energy.
SCIENCE > Mechanics > General.
SCIENCE > Physics > General.
Quantum computers
Quantum maps
Quantum systems
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Introduction and definition of terms
  • Tomography
  • Non-positive reduced dynamics
  • Complete positivity
  • Physical motivation of complete positivity
  • Measures of complete positivity
  • Negative channels
  • Negative climates with diagonal composite dynamics
  • Rabi channels
  • Physical motivations for sharp operations
  • Proposed experimental demonstration of negativity
  • Implications of negative channels
  • Uses for negative channels.
  • 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.
  • 2. Tomography.
  • 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.
  • 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.
  • 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.

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