A First Introduction to Quantum Physics by Pieter Kok

Author:Pieter Kok
Language: eng
Format: epub, pdf
ISBN: 9783319922072
Publisher: Springer International Publishing

(7.18)

The trace of is then given by

(7.19)

This is called the purity of the state . By contrast, the pure state for the photon coming out of the interferometer without BS1 can be written as the density matrix

(7.20)

Moreover, since there is no classical uncertainty about the absence of BS1 the quantum state is pure and . The trace of the diagonal elements of is therefore

(7.21)

Pure states have a purity of 1.

There are also maximally mixed states. These are quantum states with maximum classical uncertainty, where we know nothing about the path of the photon. We can construct such a state by sending photons at detectors and based on the random outcome of a fair coin. The density matrix for this state is

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