In Cavalcanti and Skrzypczyk (2017), section IIA, pag. 3, while introducing the idea of quantum steering, the authors introduce the idea of Local Hidden State model as following (emphasis mine):

A LHS model refers to the situation where a source sends a classical message $\lambda$ to one of the parties, say Alice, and a corresponding quantum state $\rho_\lambda$ to the other party, Bob. Given that Alice decides to apply measurement $x$, the variable $\lambda$ instructs Alice’s measurement device to output the result a with probability $p(a|x, \lambda)$. Additionally it is also considered that the classical message $\lambda$ can be chosen according to a distribution $\mu(\lambda)$. Bob does not have access to the classical variable $\lambda$, so the final assemblage he observes is composed by the elements $$\sigma_{a|x}=\int d\lambda \mu(\lambda)p(a|x,\lambda)\rho_\lambda.$$

I'm struggling to grasp the general picture here. Isn't this equivalent to saying that Alice and Bob share a state of the form $$\sum_\lambda |\lambda\rangle\!\langle\lambda|\otimes \rho_\lambda,$$ for some choice of a computational basis $|\lambda\rangle$ for Alice? In particular, it's the wording that "the source sends a classical message to Alice" that confuses me. What is a "classical message" here? Do we just mean that Alice is not allowed to perform measurements or operations that probe the coherence between different states $|\lambda\rangle$, for some choice of computational basis that was chosen beforehand?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.