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Closed timelike curves via post-selection: theory and experimental demonstration

"Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can in principle interact with its former self in the past. ... we report the results of an experiment demonstrating our theory's resolution of the well-known `grandfather paradox.' ... This paper proposes an empirical self-consistency condition for closed timelike curves: we demand that a generalized measurement made before a quantum system enters a closed timelike curve yield the same statistics– including correlations with other measurements – as would result if the same measurement were made after the system exits from the curve. That is, the closed time-like curve behaves like an ideal, noiseless quantum channel that displaces systems in time without affecting the correlations with external systems. ... they (CTCs) are based on (Aharonov's) post-selection ... In other words, no matter how hard the time-traveler tries, she finds her grandfather a tough guy to kill. Because P-CTCs are based on post-selected teleportation, their predictions can be experimentally demonstrated. ... The teleportation circuit forms a polarization interferometer whose visibility was measured to be 93 ± 3% ... The probe qubits are never found in the states 01 or 10: time travel succeeds only when the quantum gun misfires, leaving the polarization unchanged and the probe qubits in 00 or 11. Our suicidal photons obey the Novikov principle and never succeed in travelling back in time and killing their former selves. The required non- linearity is due to post-selection here: no CTCs nor any

evidence of the nonlinear signature of a P-CTC has ever been observed in nature up to now. ... Unlike Deutsch’s CTCs, our P-CTCs always send pure states to pure states: they do not create entropy. As a result, P-CTCs provide a distinct resolution to Deutsch’s unproved theorem paradox, in which the time traveller reveals the proof of a theorem to a mathematician, who

includes it in the same book from which the traveller has learned it (rather, will learn it). How did the proof come into existence? ...

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