Figure 1

Model of a qubit interacting with a CTC formed by a wormhole. (a) As seen by an observer far away from the wormhole. The qubit suffers an elastic collision with a second qubit described by the unitary $U$. The qubit can be scattered into the future mouth of the wormhole (F). It emerges from the past mouth of the wormhole (P), in the past, and becomes the second qubit in the elastic collision, thus forming a CTC. It can then be scattered into an output mode that is subsequently detected. (b) As “seen” by the qubit. Either propagating forward along the path of the qubit from the initial state or back along the path of the qubit from the detector leads to infinite strings of identical interactions with copies of the qubit. Multiple interactions with the unitary represent cases where the qubit is repeatedly scattered through the wormhole. This equivalent circuit can be solved in the limit of many interactions to give a unique solution to the CTC interaction.Reuse & Permissions

Figure 2

Generic description of state production where, for a single shot, the global output state, $|\varphi \rangle$, is always pure provided sufficient ancillary environmental modes are included. The initial state of the qubit is $|0\rangle$ and that of the environmental modes is $|E\rangle$. The state of the qubit is obtained by tracing over the environmental modes. The process that produces the output is modeled as a unitary $U_s$. The macroscopic arrangement of the apparatus producing the process is modeled by the classical parameters determining the unitary.Reuse & Permissions

Figure 3

Model of a bipartite qubit state where one of the subsystems is interacting with a CTC formed by a wormhole. After the interactions both arms are measured. As for Fig. 1, (a) shows the view from outside while (b) represents the qubits view. Considering the case where the qubits do not interact with the wormhole at all (i.e., when $U=\text{SWAP}$) uniquely identifies the modes shown striking detectors as the only ones observed in the equivalent circuit (b).Reuse & Permissions

Figure 4

Depiction of the equivalent circuit as a quantum channel consisting of (a) many identical processes $\epsilon$; (b) with the addition of decohering elements; and (c) where we consider blocks of $n$ processes that are sufficient in number to lead to convergence to the fixed point but for which decoherence can be neglected. Nevertheless, for $N$ processes ($N\gg n$) decoherence is significant.Reuse & Permissions