Testing quantum dynamics using signaling

We consider a physical system in which the description of states and measurements follow the usual quantum mechanical rules. We also assume that the dynamics is linear, but may not be fully quantum (i.e., unitary). We show that in such a physical system, certain complementary evolutions, namely, cloning and deleting operations that give a better fidelity than quantum mechanically allowed ones, in one (inaccessible) region, lead to signaling to a far-apart (accessible) region. To show such signaling, one requires certain two-party quantum correlated states shared between the two regions. Subsequent measurements are performed only in the accessible part to detect such phenomenon.

Figure 1

A pictorial representation of the states $\mid \psi ⟩\mid \psi ⟩$, $\mid \varphi ⟩\mid \varphi ⟩$, $\mid \Psi ⟩$, $\mid \Phi ⟩$, $\mid {\Psi }^{\prime }⟩$, and $\mid {\Phi }^{\prime }⟩$.

Figure 2

Schematic description of the arrangement in the case of cloning. The down conversion crystal is denoted as a box, and delay mirror, mirrors, and half-silvered mirror are denoted, respectively, by DM, M, and HSM. See text for details.