Three-twist knot

In quantum mechanics, and especially quantum information processing, the entropy exchange of a quantum operation $\varphi$ acting on the density matrix ${\rho }_Q$ of a system $Q$ is defined as

$S(\rho ,\varphi )\equiv S[Q^{\prime },R^{\prime }]=S({{\rho }_{Q^{\prime }R}}^{\prime })$

where $S({{\rho }_{Q^{\prime }R}}^{\prime })$ is the von Neumann entropy of the system $Q$ and a fictitious purifying auxiliary system $R$ after they are operated on by $\varphi$. Here,

${\rho }_{QR}=|QR⟩⟨QR|$ ,

${\mathrm{T}\mathrm{r}}_R[{\rho }_{QR}]={\rho }_Q$ ,

and

${{\rho }_{Q^{\prime }R}}^{\prime }=\varphi [{\rho }_{QR}]$ .

References

• Nielsen, Michael A. and Isaac L. Chuang (2000). Quantum Computation and Quantum Information, Cambridge University Press, ISBN 0-521-63503-9

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