@article{bibcite_15271,
  author = {Kamil Korzekwa and Stanis{\l}aw Czach{\'o}rski and Zbigniew Pucha{\l}a and Karol {\.Z}yczkowski},
  title = {Coherifying quantum channels},
  abstract = {<p>Is it always possible to explain random stochastic transitions between states of a finite-dimensional system as arising from the deterministic quantum evolution of the system? If not, then what is the minimal amount of randomness required by quantum theory to explain a given stochastic process? Here, we address this problem by studying possible coherifications of a quantum channel $\Phi$, i.e., we look for channels $\Phi^{\mathcal{C}}$ that induce the same classical transitions $T$, but are "more coherent". To quantify the coherence of a channel $\Phi$ we measure the coherence of the corresponding Jamio{\l}kowski state $J_{\Phi}$. We show that the classical transition matrix $T$ can be coherified to reversible unitary dynamics if and only if $T$ is unistochastic. Otherwise the Jamio{\l}kowski state $J_\Phi^{\mathcal{C}}$ of the optimally coherified channel is mixed, and the dynamics must necessarily be irreversible. To asses the extent to which an optimal process $\Phi^{\mathcal{C}}$ is indeterministic we find explicit bounds on the entropy and purity of $J_\Phi^{\mathcal{C}}$, and relate the latter to the unitarity of $\Phi^{\mathcal{C}}$. We also find optimal coherifications for several classes of channels, including all one-qubit channels. Finally, we provide a non-optimal coherification procedure that works for an arbitrary channel $\Phi$ and reduces its rank (the minimal number of required Kraus operators) from $d^2$ to $d$.</p>
},
  year = {2018},
  journal = {New Journal of Physics},
  volume = {20},
  pages = {043028},
  month = {04/2018},
  url = {https://doi.org/10.1088/1367-2630/aaaff3},
  doi = {10.1088/1367-2630/aaaff3},
  language = {eng},
}