Quantum measurements with prescribed symmetry

Quantum measurements with prescribed symmetry We introduce a method to determine whether a given generalized quantum measurement is isolated or if it belongs to a family of measurements having the same prescribed symmetry. The technique proposed reduces to solving a linear system of equations in some relevant cases. As a consequence, we provide a simple derivation of the maximal family of symmetric informationally complete positive operator-valued measure SIC-POVM in dimension 3. Furthermore, we show that the following remarkable geometrical structures are isolated, so that free parameters cannot be introduced: (a) maximal sets of mutually unbiased bases in prime power dimensions from 4 to 16, (b) SIC-POVM in dimensions from 4 to 16, and (c) contextual Kochen-Specker sets in dimension 3, 4, and 6, composed of 13, 18, and 21 vectors, respectively. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Quantum measurements with prescribed symmetry

Preview Only

Quantum measurements with prescribed symmetry

Abstract

We introduce a method to determine whether a given generalized quantum measurement is isolated or if it belongs to a family of measurements having the same prescribed symmetry. The technique proposed reduces to solving a linear system of equations in some relevant cases. As a consequence, we provide a simple derivation of the maximal family of symmetric informationally complete positive operator-valued measure SIC-POVM in dimension 3. Furthermore, we show that the following remarkable geometrical structures are isolated, so that free parameters cannot be introduced: (a) maximal sets of mutually unbiased bases in prime power dimensions from 4 to 16, (b) SIC-POVM in dimensions from 4 to 16, and (c) contextual Kochen-Specker sets in dimension 3, 4, and 6, composed of 13, 18, and 21 vectors, respectively.
Loading next page...
 
/lp/aps_physical/quantum-measurements-with-prescribed-symmetry-CMvcnIhgnu
Publisher
American Physical Society (APS)
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.022105
Publisher site
See Article on Publisher Site

Abstract

We introduce a method to determine whether a given generalized quantum measurement is isolated or if it belongs to a family of measurements having the same prescribed symmetry. The technique proposed reduces to solving a linear system of equations in some relevant cases. As a consequence, we provide a simple derivation of the maximal family of symmetric informationally complete positive operator-valued measure SIC-POVM in dimension 3. Furthermore, we show that the following remarkable geometrical structures are isolated, so that free parameters cannot be introduced: (a) maximal sets of mutually unbiased bases in prime power dimensions from 4 to 16, (b) SIC-POVM in dimensions from 4 to 16, and (c) contextual Kochen-Specker sets in dimension 3, 4, and 6, composed of 13, 18, and 21 vectors, respectively.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Aug 3, 2017

There are no references for this article.

Sorry, we don’t have permission to share this article on DeepDyve,
but here are related articles that you can start reading right now:

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off