Quantum Interactions with Closed Timelike Curves and Superluminal Signaling

Abstract

There is now a significant body of results on quantum interactions with closed timelike curves (CTCs) in the quantum information literature, for both the Deutsch model of CTC interactions (D-CTCs) and the projective model (P-CTCs). As a consequence, there is a prima facie argument exploiting entanglement that CTC interactions would enable superluminal and, indeed, effectively instantaneous signaling. In cases of spacelike separation between the sender of a signal and the receiver, whether a receiver measures the local part of an entangled state or a disentangled state to access the signal can depend on the reference frame. We propose a consistency condition that gives priority to either an entangled perspective or a disentangled perspective in spacelike separated scenarios. For D-CTC interactions, the consistency condition gives priority to frames of reference in which the state is disentangled, while for P-CTC interactions the condition selects the entangled state. Using the consistency condition, we show that there is a procedure that allows Alice to signal to Bob in the past via relayed superluminal communications between spacelike separated Alice and Clio, and spacelike separated Clio and Bob. This opens the door to time travel paradoxes in the classical domain. Ralph (arXiv:1107.4675) first pointed this out for P-CTCs, but we show that Ralph's procedure for a 'radio to the past' is flawed. Since both D-CTCs and P-CTCs allow classical information to be sent around a spacetime loop, it follows from a result by Aaronson and Watrous (Proc.Roy.Soc.A, 465:631-647 (2009)) for CTC-enhanced classical computation that a quantum computer with access to P-CTCs would have the power of PSPACE, equivalent to a D-CTC-enhanced quantum computer.

8 pages, 3 figures. Revised version of paper presented at conference 'Quantum Mechanics Seen Through Closed Timelike Curves,' Fondation des Treilles, France, June 24--28, 2013. Version 4 corrects some typos, adds reference to paper by C.H. Bennett et al. Selected by editors of Physical Review as Editor's Choice

References in corpus (6)

• Closed timelike curves via post-selection: theory and experimental demonstration
• The quantum mechanics of time travel through post-selected teleportation
• Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems?
• Quantum state cloning using Deutschian closed timelike curves
• Closed Timelike Curves Make Quantum and Classical Computing Equivalent
• The preparation problem in nonlinear extensions of quantum theory

Cited by in corpus (7)

• Nonclassical advantage in metrology established via quantum simulations of hypothetical closed timelike curves
• Deutschian closed timelike curves can create entanglement
• Quantum physics, fields and closed timelike curves: The D-CTC condition in quantum field theory
• Time-travelling billiard-ball clocks: a quantum model
• The D-CTC condition is generically fulfilled in classical (non-quantum) statistical systems
• Quantum Signaling to the Past Using P-CTCS
• Looping back to the past through free fall in a controlled warp drive spacetime