Time Travel: Deutsch vs. Teleportation

The quantum teleportation protocol can be used to probabilistically simulate a quantum circuit with backward-in-time connections. This allows us to analyze some conceptual problems of time travel in the context of physically realizable situations free of paradoxes. As an example one can perform encrypted measurements of future states for which the decryption key becomes available in the future. Likewise, the gauge-like freedom of locally changing the direction of time flow in quantum circuits can lead to conceptual and computational simplifications. I contrast this situation with Deutsch’s treatment of quantum mechanics in the presence of closed time-like curves pointing out some of its deficiencies and problems.