Fig. 1
From: Characterising the correlations of prepare-and-measure quantum networks
Scenario and assumptions. The behaviour of a two-receiver prepare-and-measure (P&M) quantum network is generally described by p = [p(ab|xy, z)], which expresses the probability of z transiting to outcomes a, b given measurement inputs x, y. In the quantum setting, the set of conditional probabilities are given by \(p(ab|xy,z) = \langle \phi _z|E_x^aE_y^b|\phi _z\rangle\), with the constraint that 〈ϕz|ϕz′〉 = λzz′ is fixed. Our consideration hence assumes three conditions: (1) the set of code states are pure states, (2) the Gram matrix of these states is known, and (3) the receivers are independent of each other (they do not share any quantum resources, although classical randomness is allowed)
