Two Qubits in the Dirac Representation

Details Two Qubits in the Dirac Representation Two Qubits in the Dirac Representation

Publishing date

2000-06-29

URL

arxiv.org/abs/quant-ph/0006129v1

Science

Physics

Field

Quantum Physics

Additional info

11 pages

Type

Scientific paper

Digital Object Identifier

10.1103/PhysRevA.64.024303

Abstract

A general two qubit system expressed in terms of the complete set of unit and fifteen traceless, Hermitian Dirac matrices, is shown to exhibit novel features of this system. The well-known physical interpretations associated with the relativistic Dirac equation involving the symmetry operations of time-reversal T, charge conjugation C, parity P, and their products are reinterpreted here by examining their action on the basic Bell states. The transformation properties of the Bell basis states under these symmetry operations also reveal that C is the only operator that does not mix the Bell states whereas all others do. In a similar fashion, expressing the various logic gates introduced in the subject of quantum computers in terms of the Dirac matrices shows for example, that the NOT gate is related to the product of time-reversal and parity operators.

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