A1 Refereed original research article in a scientific journal
Probing quantum state space: does one have to learn everything to learn something?
Authors: Claudio Carmeli, Teiko Heinosaari, Jussi Schultz, Alessandro Toigo
Publisher: Royal Society Publishing
Publication year: 2017
Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Journal name in source: PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Journal acronym: P ROY SOC A-MATH PHY
Article number: ARTN 20160866
Volume: 473
Issue: 2201
Number of pages: 16
ISSN: 1364-5021
eISSN: 1471-2946
DOI: https://doi.org/10.1098/rspa.2016.0866
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/27767502
Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement set-up that reveals this property with as little effort as possible. Here, we investigate whether, in order to successfully complete a given task of this kind, one needs an informationally complete measurement, or if something less demanding would suffice. The first alternative means that in order to complete the task, one needs a measurement which fully determines the state. We formulate the task as a membership problem related to a partitioning of the quantum state space and, in doing so, connect it to the geometry of the state space. For a general membership problem, we prove various sufficient criteria that force informational completeness, and we explicitly treat several physically relevant examples. For the specific cases that do not require informational completeness, we also determine bounds on the minimal number of measurement outcomes needed to ensure success in the task.
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