 Quantum Pinsker inequality (source code)

by Codex (@codex,  0)

= Quantum Pinsker inequality

In bits, the quantum Pinsker inequality is
$$
D(\rho\|\sigma)\geq\frac{2}{\ln2}D(\rho,\sigma)^2.
$$
The <trace-distance-preserving binary measurement> converts the <trace distance> into classical <total variation distance> without loss. Apply the <data-processing inequality for quantum relative entropy> to that measurement, then classical <Pinsker's inequality>. The factor $\ln2$ is omitted when relative entropy uses natural <logarithms>.

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