Perfect State Distinguishability and Computational Speedups with Postselected Closed Timelike Curves
 Todd A. Brun,
 Mark M. Wilde
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Abstract
Bennett and Schumacher’s postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch’s model. We show that even a single qubit passing through a postselected CTC (PCTC) is sufficient to do any postselected quantum measurement with certainty, and we discuss an important difference between “Deutschian” CTCs (DCTCs) and PCTCs in which the future existence of a PCTC might affect the present outcome of an experiment. Then, based on a suggestion of Bennett and Smith, we explicitly show how a party assisted by PCTCs can distinguish a set of linearly independent quantum states, and we prove that it is not possible for such a party to distinguish a set of linearly dependent states. The power of PCTCs is thus weaker than that of DCTCs because the Holevo bound still applies to circuits using them, regardless of their ability to conspire in violating the uncertainty principle. We then discuss how different notions of a quantum mixture that are indistinguishable in linear quantum mechanics lead to dramatically differing conclusions in a nonlinear quantum mechanics involving PCTCs. Finally, we give explicit circuit constructions that can efficiently factor integers, efficiently solve any decision problem in the intersection of NP and coNP, and probabilistically solve any decision problem in NP. These circuits accomplish these tasks with just one qubit traveling back in time, and they exploit the ability of postselected closed timelike curves to create grandfather paradoxes for invalid answers.
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 Title
 Perfect State Distinguishability and Computational Speedups with Postselected Closed Timelike Curves
 Journal

Foundations of Physics
Volume 42, Issue 3 , pp 341361
 Cover Date
 20120301
 DOI
 10.1007/s1070101196010
 Print ISSN
 00159018
 Online ISSN
 15729516
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Postselected closed timelike curves
 State distinguishability
 Paradoxical computation
 Industry Sectors
 Authors

 Todd A. Brun ^{(1)}
 Mark M. Wilde ^{(2)}
 Author Affiliations

 1. Communication Sciences Institute, University of Southern California, Los Angeles, CA, 90089, USA
 2. School of Computer Science, McGill University, Montreal, Quebec, H3A 2A7, Canada