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Quantum Automata Cannot Detect Biased Coins, Even in the Limit

Authors Guy Kindler, Ryan O'Donnell

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  • quantum automata

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Abstract

Aaronson and Drucker (2011) asked whether there exists a quantum finite automaton that can distinguish fair coin tosses from biased ones by spending significantly more time in accepting states, on average, given an infinite sequence of tosses. We answer this question negatively.

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Guy Kindler and Ryan O'Donnell. Quantum Automata Cannot Detect Biased Coins, Even in the Limit. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 15:1-15:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ICALP.2017.15

Author Details

Guy Kindler
Ryan O'Donnell

References

  1. Scott Aaronson. The NEW ten most annoying questions in quantum computing, May 2014. URL: http://www.scottaaronson.com/blog/?p=1792.
  2. Scott Aaronson and Andrew Drucker. Advice coins for classical and quantum computation. In Proceedings of the 38th Annual International Colloquium on Automata, Languages and Programming, pages 61-72, 2011. Google Scholar
  3. Bernhard Baumgartner and Heide Narnhofer. The structures of state space concerning quantum dynamical semigroups. Reviews in Mathematical Physics, 24(2):1250001, 2012. Google Scholar
  4. Raffaella Carbone and Yan Pautrat. Irreducible decompositions and stationary states of quantum channels. Technical Report 1507.08404, arXiv, 2015. Google Scholar
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  7. Michael Wolf. Quantum channels &operations: guided tour, 2012. URL: http://www-m5.ma.tum.de/foswiki/pub/M5/Allgemeines/MichaelWolf/QChannelLecture.pdf.
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