Quantum mechanics near closed timelike curves

Z. Gedik

Einstein's field equations of gravitation are known to admit closed timelike curve (CTC) solutions. Deutsch approached the problem from the quantum information point of view and proposed a self-consistency condition. In this work, the Deutsch equation is formulated as an eigenvalue problem. The disappearance of entanglement between two qubits in an Einstein-Podolsky-Rosen (EPR) state near a CTC is demonstrated. The method is utilized to analyze the discontinuous evolution of two chronology respecting (CR) qubits near a CTC.

Zoltán Papp

Hrvoje Nikolić

We explore some implications of the hypothesis that quantum mechanics (QM) is universal, i.e., that QM does not merely describe information accessible to observers, but that it also describes the observers themselves. From that point of view, "free will" (FW) - the ability of experimentalists to make free choices of initial conditions - is merely an illusion. As a consequence, by entangling a part of brain (responsible for the illusion of FW) with a distant particle, one may create nonlocal correlations that can be interpreted as superluminal signals. In addition, if FW is an illusion, then QM on a closed timelike curve can be made consistent even without the Deutch nonlinear consistency constraint.

Jacques Pienaar, Timothy C. Ralph, Casey R. Myers

Toy models for quantum evolution in the presence of closed timelike curves have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require nontrivial interactions between the future and past that lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the closed timelike curve, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenberg's uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time dilation suggests that OTCs provide a novel alternative to existing proposals for the behavior of quantum systems under gravity.

K. B. Wharton