Probing quantum state space: does one have to learn everything to learn something?
Jussi Schultz; Alessandro Toigo; Claudio Carmeli; Teiko Heinosaari
Probing quantum state space: does one have to learn everything to learn something?
Jussi Schultz
Alessandro Toigo
Claudio Carmeli
Teiko Heinosaari
Royal Society Publishing
Julkaisun pysyvä osoite on:
https://urn.fi/URN:NBN:fi-fe2021042717631
https://urn.fi/URN:NBN:fi-fe2021042717631
Tiivistelmä
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.
Kokoelmat
- Rinnakkaistallenteet [19207]