Optimal discrimination of quantum states

Weir, Graeme (2018) Optimal discrimination of quantum states. PhD thesis, University of Glasgow.

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Printed Thesis Information: https://eleanor.lib.gla.ac.uk/record=b3314965

Abstract

Quantum state discrimination is a fundamental task in the field of quantum communication and quantum information theory. Unless the states to be discriminated are mutually orthogonal, there will be some error in any attempt to determine which state was sent. Several strategies to optimally discriminate between quantum states exist, each maximising some figure of merit. In this thesis we mainly investigate the minimum-error strategy, in which the probability of correctly guessing the signal state is maximised. We introduce a method for constructing the optimal Positive-Operator Valued Measure (POVM) for this figure of merit, which is applicable for arbitrary states and arbitrary prior probabilities. We then use this method to solve minimum-error state discrimination for the so-called trine states with arbitrary prior probabilities - the first such general solution for a set of quantum states since the two-state case was solved when the problem of state discrimination was first introduced. We also investigate the difference between local and global measurements for a bipartite ensemble of states, and find that in certain circumstances the local measurement is superior. We conclude by finding a bipartite analogue to the Helstrom conditions, which indicate when a POVM satisfies the minimum-error criteria.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: quantum information, quantum state discrimination, quantum measurement.
Subjects: Q Science > QC Physics
Colleges/Schools: College of Science and Engineering > School of Physics and Astronomy
Supervisor's Name: Croke, Dr. Sarah and Barnett, Prof. Stephen
Date of Award: 2018
Depositing User: Graeme Weir
Unique ID: glathesis:2018-30616
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 05 Jun 2018 14:14
Last Modified: 11 Jul 2018 07:46
URI: http://theses.gla.ac.uk/id/eprint/30616

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