Book contents
- Frontmatter
- Contents
- Introduction
- Part I Quantum information
- 1 Quantum bits and quantum gates
- 2 An atom in a laser field
- 3 Spins in magnetic fields
- 4 Photon techniques
- 5 Two qubits and beyond
- 6 Measurement and entanglement
- Part II Quantum computation
- Part III Quantum communication
- Appendix: Quantum mechanics
- References
- Index
6 - Measurement and entanglement
from Part I - Quantum information
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Introduction
- Part I Quantum information
- 1 Quantum bits and quantum gates
- 2 An atom in a laser field
- 3 Spins in magnetic fields
- 4 Photon techniques
- 5 Two qubits and beyond
- 6 Measurement and entanglement
- Part II Quantum computation
- Part III Quantum communication
- Appendix: Quantum mechanics
- References
- Index
Summary
We now have all the basic tools we need to describe systems of one and two qubits. In this final chapter of Part I we look at some of the consequences of the peculiar properties of qubits when they are used to encode information. Many of these results can be traced to the properties of quantum measurement.
Measuring a single qubit
A key result in quantum information theory is that it is impossible to accurately characterize a single qubit. In other words, there is no experiment, or sequence of experiments, which allows us to find out the state of a single quantum bit.
The reason for this problem is twofold. Firstly, we have to make some sort of decision about the basis we will use for the measurement. For example, when measuring a single qubit the most popular choice is to make a measurement in the computational basis. This is equivalent to asking the qubit whether it is in state |0⧽ or state |1⧽. If the qubit is indeed in one of the basis states the measurement process is simple, and we will get the obvious answer of 0 if it is in |0⧽ and 1 if it is in |1⧽. If, however, the qubit is in a superposition, such as α|0⧽+β|1⧽, then the situation is more difficult. Characterizing the state now means determining the values of the two complex numbers α and β, but the measurement can only return the answer 0 or 1, and for a superposition state one of these two answers will be returned at random, with probabilities |α|2 and |β|2, respectively.
- Type
- Chapter
- Information
- Quantum Information, Computation and Communication , pp. 55 - 64Publisher: Cambridge University PressPrint publication year: 2012