Question

How do I plot the decoherence of an open system from its density matrix?

Answer 1

The most general equation that describes the decoherence of a density matrix is the Lindblad equation. It has the form

∂tρ=−[H0,ρ]+∑nγn(LnρL†n−L†nLnρ−ρL†nLn).∂tρ=−[H0,ρ]+∑nγn(LnρLn†−Ln†Lnρ−ρLn†Ln).

For the qubit case you can express the Lindblad operators LnLn in terms of Pauli matrices. So by playing around with different such operators and solving the equation, you may get a feeling of how it behaves and see what the effect is on the density matrix.

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