I am reading Samuel L. Braunstein, Arun K. Pati, Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox. I am puzzling over the derivation in Section Perfect hiding processes. A closely related question is here.

The authors have already assumed from the outset that only the ancilla $A$ and thus its orthornomal basis $A_k$'s depend on $\psi$. Does it not already imply their conclusion "any information about $|\psi\rangle$ that is encoded globally is in fact encoded entirely within the ancilla. No information about $|\psi\rangle$ is encoded in system-ancilla correlations (nor, in fact, in system-system correlations)."? The sentence preceding it states that "We may swap $|\psi\rangle$ with any other state in the ancilla using purely ancilla-local operations". But I do not see how and why this is necessary. Moreover, what would it be like to have "system-ancilla correlations"? Would it be for $|k\rangle$ to depend on $|\psi\rangle$?

Cross-posted on physics.SE

  • $\begingroup$ each post should contain a single, laser-focused question. You can ask different questions in separate posts. Feel free to edit this post accordingly $\endgroup$
    – glS
    Commented Jan 22, 2022 at 12:43
  • $\begingroup$ @glS: Have edited accordingly. $\endgroup$
    – Hans
    Commented Jan 22, 2022 at 21:50


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