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.

Although Charles Bennett does not seem to agree that nonlinear effectively non-unitary D- CTC’s & P-CTCs will enhance computer power beyond even that of linear unitary quantum computers - I am not convinced that Bennett et-al are correct.

There are several possible approaches to post-quantum generalization of orthodox quantum theory

1) effective “single Novikov consistent world" P-CTC using Aharonov post-selection realizable in lab in real experiments

Aug 12, 2014 - ... by Maximilian Schlosshauer in his interview volume about the foundations of quantum mechanics, ... From: Antony Valentini [view email]

Mar 11, 2002 - Submission history. From: Antony Valentini [view email] [v1] Mon, 11 Mar 2002 21 :48:32 GMT (14kb) [v2] Fri, 12 Apr 2002 15:18:07 GMT (11kb).

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3) my use of Einstein action-reaction principle lacking in orthodox quantum theory where the Schrodinger wave is source-less (i.e. all action on particles and classical fields without any direct reaction (back-reaction) from them on their Bohm pilot information fields

"Can Psychical Research Bridge the Gulf Between Matter and Mind?" Bernard Carr Proceedings of the Society for Psychical Research, Vol 59 Part 221 June 2008

4) spontaneous symmetry breaking leading to a local macro-quantum coherent order parameter (Glauber coherent state of boson elementary excitations - possibly virtual as well as real) with nonlinear non-unitary c-number dynamics fitting Stephen Weinberg’s models of NLQM.

Mar 31, 2008 - Herein we describe an extension of QFD to the Ginzburg-Landau ... nonlinear, nonunitary Schrödinger form of the Ginzburg-Landau equation

Sep 19, 2003 - Keywords: de Broglie-Bohm, Ginzburg-Landau, quantum force, quantum potential, .... Now Eq. (1) is not only nonlinear; it is also nonunitary.