Attainability of quantum state discrimination bounds with collective measurements on finite copies

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Conlon, Lorcan O. and Koh, Jin Ming and Shajilal, Biveen and Sidhu, Jasminder and Lam, Ping Koy and Assad, Syed M. (2024) Attainability of quantum state discrimination bounds with collective measurements on finite copies. Other. arXiv, Ithaca, NY. (https://doi.org/10.48550/arXiv.2408.06678)

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Abstract

One of the fundamental tenets of quantum mechanics is that non-orthogonal states cannot be distinguished perfectly. When distinguishing multiple copies of a mixed quantum state, a collective measurement, which generates entanglement between the different copies of the unknown state, can achieve a lower error probability than non-entangling measurements. The error probability that can be attained using a collective measurement on a finite number of copies of the unknown state is given by the Helstrom bound. In the limit where we can perform a collective measurement on asymptotically many copies of the quantum state, the quantum Chernoff bound gives the attainable error probability. It is natural to ask at what rate does the error tend to this asymptotic limit, and whether the asymptotic limit can be attained for any finite number of copies. In this paper we address these questions. We find analytic expressions for the Helstrom bound for arbitrarily many copies of the unknown state in several simple qubit examples. Using these analytic expressions, we investigate how the attainable error rate changes as we allow collective measurements on finite numbers of copies of the quantum state. We also investigate the necessary conditions to saturate the M-copy Helstrom bound. It is known that a collective measurement on all M-copies of the unknown state is always sufficient to saturate the M-copy Helstrom bound. However, general conditions for when such a measurement is necessary to saturate the Helstrom bound remain unknown. We investigate specific measurement strategies which involve entangling operations on fewer than all M-copies of the unknown state. For many regimes we find that a collective measurement on all M-copies of the unknown state is necessary to saturate the M-copy Helstrom bound.

ORCID iDs

Conlon, Lorcan O., Koh, Jin Ming, Shajilal, Biveen, Sidhu, Jasminder ORCID logoORCID: https://orcid.org/0000-0002-6167-8224, Lam, Ping Koy and Assad, Syed M.;
  • Item type:Monograph(Other)
    ID code:91864
    Dates:
    Date
    Event
    13 August 2024
    Published
    Notes:Comments very welcome
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:22 Jan 2025 15:59
    Last modified:29 Jan 2025 04:51
    URI:https://strathprints.strath.ac.uk/id/eprint/91864
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