Charles H. Bennett, IBM TJ Watson Research Center
Abstract
We study discuss various models of closed timelike curves (CTCs), and their utility (assuming they exist) for distinguishing nonorthogonal quantum states or speeding up hard computations. CTCs are notorious for giving rise to the "grandfather paradox"---initial conditions admitting no consistent future. One widely used model of CTCs, Deutsch's 1991 mixed-state-fixed-point model, abolishes the grandfather paradox, and was formerly thought to have dramatic consequences for quantum computation and cryptanalysis. However, we show that when the tasks of computation and state discrimination are properly formulated, such CTCs provide no help in state discrimination and have not been shown to help speed up hard computations. An alternate "post-selected" CTC model, exploits the grandfather paradox instead of avoiding it, using it as a putative physical mechanism for enforcing the otherwise abstract mathematical idea of post-selection. We discuss whether the existence of such CTCs would have major consequences for computation, cryptography and ordinary notions of causality. Joint work with Debbie Leung, Graeme Smith, and John Smolin.