Fig. 4.

Circuit diagram representation of the Gedankenexperiment. The actions of the agents during the protocol correspond to isometries (boxes) that act on particular subsystems (wires). For example, the measurement of S by agent F in the second protocol step, which starts at time n:10, induces an isometry $U_{S\to L}^{\mathrm{10}\to \mathrm{20}}$ from S to F’s lab L, analogous to the one defined by (2). The subsystems labelled by $\overline{F}$, F, $\overline{W}$, and W contain the agents themselves. Similarly, $\overline{D}$, $D$, $\overline{E}$, and $E$ are “environment” subsystems, which include the agents’ measurement devices. The states of these subsystems depend on the measurement outcome, which is indicated by their label. For example, $∣+\frac{1}{2}⟩$_F is the state of F when the agent has observed $z=+\frac{1}{2}$