A1 Refereed original research article in a scientific journal
Quantum state discrimination via repeated measurements and the rule of three
Authors: Bullock Tom, Heinosaari Teiko
Publisher: Birkhauser
Publication year: 2021
Journal: Quantum Studies: Mathematics and Foundations
Journal name in source: Quantum Studies: Mathematics and Foundations
Volume: 8
First page : 137
Last page: 155
ISSN: 2196-5609
eISSN: 2196-5617
DOI: https://doi.org/10.1007/s40509-020-00233-7
Web address : https://link.springer.com/article/10.1007/s40509-020-00233-7
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/50415852
The task of state discrimination for a set of mutually orthogonal pure states is trivial if one has access to the corresponding sharp (projection-valued) measurement, but what if we are restricted to an unsharp measurement? Given that any realistic measurement device will be subject to some noise, such a problem is worth considering. In this paper, we consider minimum error state discrimination for mutually orthogonal states with a noisy measurement. We show that by considering repetitions of commutative Lüders measurements on the same system we are able to increase the probability of successfully distinguishing states. In the case of binary Lüders measurements, we provide a full characterisation of the success probabilities for any number of repetitions. This leads us to identify a ‘rule of three’, where no change in probability is obtained from a second measurement but there is noticeable improvement after a third. We also provide partial results for N-valued commutative measurements where the rule of three remains, but the general pattern present in binary measurements is no longer satisfied.
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