What can we learn from time-traveling quantum computers?

Over the last several decades, a new strategy for attempting to understand quantum mechanics has emerged: analyzing the theory in terms of what quantum mechanical systems can do. This information-theoretic approach to the interpretation of quantum mechanics characterizes the difference between the quantum world and the classical world by delineating what kinds of classically impossible computations and communication protocols can be achieved by exploiting quantum effects.

This approach has opened up a potential avenue for synthesizing quantum mechanics with a particular aspect of general relativity: the possible existence of closed timelike curves (CTCs). A CTC is a path through spacetime along which a system can travel, which will lead it to its own past. David Deutsch (1991) developed the first quantum computational model with negative time-delayed information paths, which is intended to give a quantum mechanical analysis of the behavior of CTCs.

However, Deutsch's model is controversial because it entails certain effects that ordinary quantum mechanics rules out as impossible. Exactly how to adjudicate this conflict has been debated in the recent literature. In my paper, I will detail a protocol that generates one of these disputed effects. The example Iâ€™ll focus on shows how a CTC-assisted quantum computational circuit can be used for the instantaneous transmission of information between two spatially separated observers, which is impossible according to ordinary quantum mechanics

I will consider an argument by Cavalcanti et al. (2012) which purports to show that the protocol must fail. I will argue that this position is not well justified. The argument the authors explicitly give for their view is based upon a misinterpretation of the special theory of relativity, and the most plausible justifications they would offer instead are weak enough that we should consider the possibility of the instantaneous transmission of information to be an open question.

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