Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Quantum optics and quantum information
- 1 The quantum theory of light
- 2 Quantum information processing
- 3 Figures of merit
- Part II Quantum information in photons and atoms
- Part III Quantum information in many-body systems
- Appendix A Baker–Campbell–Haussdorff relations
- Appendix B The Knill–Laflamme–Milburn protocol
- Appendix C Cross–Kerr nonlinearities for single photons
- References
- Index
3 - Figures of merit
from Part I - Quantum optics and quantum information
Published online by Cambridge University Press: 05 July 2014
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Quantum optics and quantum information
- 1 The quantum theory of light
- 2 Quantum information processing
- 3 Figures of merit
- Part II Quantum information in photons and atoms
- Part III Quantum information in many-body systems
- Appendix A Baker–Campbell–Haussdorff relations
- Appendix B The Knill–Laflamme–Milburn protocol
- Appendix C Cross–Kerr nonlinearities for single photons
- References
- Index
Summary
Before we begin our detailed discussion of optical quantum information processing, we need to introduce certain figures of merit that quantify how well our information processor is performing. For a quantum computer, the time and resources it takes to complete a task are good measures, but we are faced with the problem that we do not know what the final design for a quantum computer will be. We therefore need additional figures of merit that are applicable in a wide range of situations. We first introduce the concept of the ‘density operator’, which will be used to describe quantum states about which we have incomplete knowledge. We then define the ‘fidelity’, which is used for assessing how close we are to a particular desired quantum state, and we discuss different measures of entanglement. The later part of the chapter will focus on figures of merit that are particularly relevant for assessing optical states, namely the first-order correlation functions, and the visibility of interference phenomena.
Density operators and superoperators
Classical physics often confronts us with situations where we can say only a limited amount about the state of a system: we can measure certain ‘bulk’ variables such as the temperature and pressure, but we do not know all of the details of the microscopic make-up of the state. For example, we typically have very little knowledge of the positions and velocities of all the atoms that constitute the system.
- Type
- Chapter
- Information
- Introduction to Optical Quantum Information Processing , pp. 90 - 110Publisher: Cambridge University PressPrint publication year: 2010