Can Communication Power of Separable Correlations Exceed That of Entanglement Resource?

The scenario of remote state preparation with a shared correlated quantum state and one bit of forward communication [B. Dakić et al., Nat. Phys. 8, 666 (2012)] is considered. Optimization of the transmission efficiency is extended to include general encoding and decoding strategies. The importance of the use of linear fidelity is recognized. It is shown that separable states cannot exceed the efficiency of entangled states by means of “local operations plus classical communication” actions limited to 1 bit of forward communication. It is proven however that such a surprising phenomena may naturally occur when the decoding agent has limited resources in the sense that either (i) has to use decoding which is insensitive to the change of the coordinate system in the plane in question (which is the natural choice if the receiver does not know the latter) or (ii) is forced to use bistochastic operations which may be imposed by physically inconvenient local thermodynamical conditions.

Figure 1

General scheme of RSP. For the structure of initial data, see Fig. 2. The measurement M is a quantum POVM and ${\mathrm{\Lambda }}_i$ is the decoding channel (see main text for detail of parametrization). The decoding channels ${\mathrm{\Lambda }}_i$ are supposed to belong to a fixed class $\mathrm{\Gamma }$. In this Letter we consider the most general class of all quantum channels ${\mathrm{\Gamma }}_{\text{general}}$ and restricted classes: channels invariant in the $\widehat{s}$ plane ${\mathrm{\Gamma }}_{\text{invariant}}$ (for details see text) and the bistochastic channels ${\mathrm{\Gamma }}_{\text{bistochastic}}$.

Figure 2

Initial data for Alice and Bob with (a) or without (b) shared reference frame on the $\widehat{s}$ plane.