Effective Quantum Time Travel

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, to realize encrypted measurements of future states for which the decryption key becomes available only after the state is created, and to probabilistically realize a multistage quantum state processing within the time needed to complete only one stage. The probabilistic nature of the process resolves any paradox.