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Quantum relative entropy between pre- and post-measurement states

Firstly notice that the divergences are $$ D(\rho\|\rho_{\mathrm{rank-one}}) = - S(\rho) + S(\rho_{\mathrm{rank-one}}) $$ and $$ D(\rho\|\rho_{\mathrm{coarse}}) = - S(\rho) + S(\rho_{\mathrm{coarse}}) ...
Rammus's user avatar
  • 5,863
1 vote

Which quantum entropies are meaningful with respect to continuous distributions of states?

I've found a partial answer for the case of conditional min-entropy, due to Ref. [1] (Appendix IV.B): Consider a fixed ensemble $\{(\rho_B(x), p(x))\}_{x \in \Sigma}$, where $p(x)$ is a probability ...
forky40's user avatar
  • 7,123
1 vote

Does the quantum relative entropy have a direct operational interpretation?

I would argue yes, in the context of recoverability. Given a quantum channel $\mathcal{N}: L(A) \to L(B)$ and a state $\sigma$ on $A$, we say that a quantum channel $\mathcal R: L(B) \to L(A)$ is a $(...
Rammus's user avatar
  • 5,863

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