Unambiguous discrimination among oracle operators

Anthony Chefles*, Akira Kitagawa, Masahiro Takeoka, Masahide Sasaki, Jason Twamley

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    31 Citations (Scopus)

    Abstract

    We address the problem of unambiguous discrimination among oracle operators. The general theory of unambiguous discrimination among unitary operators is extended with this application in mind. We prove that entanglement with an ancilla cannot assist any discrimination strategy for commuting unitary operators. We also obtain a simple, practical test for the unambiguous distinguishability of an arbitrary set of unitary operators on a given system. Using this result, we prove that the unambiguous distinguishability criterion is the same for both standard and minimal oracle operators. We then show that, except in certain trivial cases, unambiguous discrimination among all standard oracle operators corresponding to integer functions with fixed domain and range is impossible. However, we find that it is possible to unambiguously discriminate among the Grover oracle operators corresponding to an arbitrarily large unsorted database. The unambiguous distinguishability of standard oracle operators corresponding to totally indistinguishable functions, which possess a strong form of classical indistinguishability, is analysed. We prove that these operators are not unambiguously distinguishable for any finite set of totally indistinguishable functions on a Boolean domain and with arbitrary fixed range. Sets of such functions on a larger domain can have unambiguously distinguishable standard oracle operators, and we provide a complete analysis of the simplest case, that of four functions. We also examine the possibility of unambiguous oracle operator discrimination with multiple parallel calls and investigate an intriguing unitary superoperator transformation between standard and entanglement-assisted minimal oracle operators.

    Original languageEnglish
    Article number016
    Pages (from-to)10183-10213
    Number of pages31
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume40
    Issue number33
    DOIs
    Publication statusPublished - 17 Aug 2007

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