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arXiv:quant-ph/0610174 · Physical Review Letters

Impossibility of the Counterfactual Computation for All Possible Outcomes

Lev Vaidman A

Published Apr 18, 2007• 58 citations
arXivHTMLPDF

Abstract

A recent proposal for counterfactual computation [O. Hosten et al. Nature (London) 439, 949 (2006) is analyzed. It is argued that the method does not provide counterfactual computation for all possible outcomes. The explanation involves a novel paradoxical feature of pre- and postselected quantum particles: The particle can reach a certain location without being on the path that leads to this location.

DOI
10.1103/physrevlett.98.160403

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A recent proposal for counterfactual computation [O. Hosten et al. Nature (London) 439, 949 (2006) is analyzed. It is argued that the method does not provide counterfactual computation for all possible outcomes. The explanation involves a novel paradoxical feature of pre- and postselected quantum particles: The particle can reach a certain location without being on the path that leads to this location.
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Mitchison and Jozsa recently suggested that the "chained-Zeno" counterfactual computation protocol recently proposed by Hosten et al. is counterfactual for only one output of the computer. This claim was based on the existing abstract algebraic definition of counterfactual computation, and indeed according to this definition, their argument is correct. However, a more general definition (physically adequate) for counterfactual computation is implicitly assumed by Hosten et. al. Here we explain in detail why the protocol is counterfactual and how the "history tracking" method of the existing description inadequately represents the physics underlying the protocol. Consequently, we propose a modified definition of counterfactual computation. Finally, we comment on one of the most interesting aspects of the error-correcting protocol.