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Information gain when measuring an unknown qubit
KTH, School of Engineering Sciences (SCI), Applied Physics.ORCID iD: 0000-0002-2082-9583
2018 (English)In: European journal of physics, ISSN 0143-0807, E-ISSN 1361-6404, Vol. 39, no 1, 015403Article in journal (Refereed) Published
Abstract [en]

In quantum information the fundamental information-containing system is the qubit. A measurement of a single qubit can at most yield one classical bit. However, a dichotomous measurement of an unknown qubit will yield much less information about the qubit state. We use Bayesian inference to compute how much information one progressively gets by making sucessive, individual measurements on an ensemble of identically prepared qubits. Perhaps surprisingly, even if the measurements are arranged so that each measurement yields one classical bit, that is, the two possible measurement outcomes are a priori equiprobable, it takes almost a handful of measurements before one has gained one bit of information about the gradually concentrated qubit probability density. We also show that by following a strategy that reaps the maximum information per measurement, we are led to a mutually unbiased basis as our measurement bases. This is a pleasing, although not entirely surprising, result.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2018. Vol. 39, no 1, 015403
Keyword [en]
quantum information, quantum measurement, qubit, mutually unbiased basis, Shannon entropy, Bayesian inference
National Category
Atom and Molecular Physics and Optics
Identifiers
URN: urn:nbn:se:kth:diva-220820DOI: 10.1088/1361-6404/aa94e4ISI: 000418387100002Scopus ID: 2-s2.0-85040311937OAI: oai:DiVA.org:kth-220820DiVA: diva2:1173060
Funder
Linnaeus research environment CADICSSwedish Research Council, 621-2014-5410
Note

QC 20180111

Available from: 2018-01-11 Created: 2018-01-11 Last updated: 2018-01-22Bibliographically approved

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Björk, Gunnar

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