A First Introduction to Quantum Computing and Information by Bernard Zygelman

Author:Bernard Zygelman
Language: eng
Format: epub, pdf
ISBN: 9783319916293
Publisher: Springer International Publishing

(5.3)

The fact that the expectation values (5.2) and (5.3) differ demonstrates that the two scenarios are not equivalent. In Hilbert space, any state, whether computational basis or superposition , is called a coherent or pure state. In fact, a coherent state is just a synonym for a Hilbert space state. So is there such a thing as an in-coherent state? In scenario (B) each scientist possesses a qubit in coherent state , but case (A) describes an ensemble of measurement values obtained from a statistical mixture of two different coherent states. The postulates itemized in the previous chapters taught us how to compile, via the Born rule, statistics for systems described by a coherent, or pure, state. But we seem to lack a vocabulary that allows a convenient framework for statistical mixtures of coherent states. The von-Neumann density matrix or density operator, provides that framework.

To incorporate both pure and mixed ensembles, von Neumann introduced the concept of a density operator. The operator

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