Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Quantum optics and quantum information
- Part II Quantum information in photons and atoms
- Part III Quantum information in many-body systems
- 8 Quantum communication with continuous variables
- 9 Quantum computation with continuous variables
- 10 Atomic ensembles in quantum information processing
- 11 Solid-state quantum information carriers
- 12 Decoherence of solid-state qubits
- 13 Quantum metrology
- Appendix A Baker–Campbell–Haussdorff relations
- Appendix B The Knill–Laflamme–Milburn protocol
- Appendix C Cross–Kerr nonlinearities for single photons
- References
- Index
13 - Quantum metrology
from Part III - Quantum information in many-body systems
Published online by Cambridge University Press: 05 July 2014
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Quantum optics and quantum information
- Part II Quantum information in photons and atoms
- Part III Quantum information in many-body systems
- 8 Quantum communication with continuous variables
- 9 Quantum computation with continuous variables
- 10 Atomic ensembles in quantum information processing
- 11 Solid-state quantum information carriers
- 12 Decoherence of solid-state qubits
- 13 Quantum metrology
- Appendix A Baker–Campbell–Haussdorff relations
- Appendix B The Knill–Laflamme–Milburn protocol
- Appendix C Cross–Kerr nonlinearities for single photons
- References
- Index
Summary
In this chapter we consider the physical limits to information extraction. This is an important aspect of optical quantum information processing in that many high-precision experiments (such as gravitational wave detection) are implemented in optical systems, i.e., interferometers. It is not surprising that just as in computation and communication, the use of quintessentially quantum mechanical properties allows us to improve the sensitivity in interferometry. We start this chapter with a derivation of the Fisher information and the Cramér-Rao bound, which tell us how much information we can extract about a parameter in a set of measurements. In Section 13.2 we introduce the statistical distance between two probability distributions. This can in turn be used to determine how many times the system needs to be queried before we can determine which probability distribution governs the system. In addition, we make a connection between the statistical distance and the angle between states in Hilbert space. In Sections 13.3 and 13.4 we derive bounds on how fast quantum states evolve to orthogonal states, and how entangled states can be used to improve parameter estimation. Finally, in Section 13.5 we present a number of approaches for implementing quantum metrology in optical systems, most importantly in optical interferometers.
Parameter estimation and Fisher information
In the theory of computation, discrete variables have the benefit that a practically perfect readout is often possible.
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- Information
- Introduction to Optical Quantum Information Processing , pp. 421 - 453Publisher: Cambridge University PressPrint publication year: 2010