Mutually Unbiased Bases for Continuous Variables

Stefan Weigert; Michael Wilkinson

doi:10.1103/PhysRevA.78.020303

Mutually Unbiased Bases for Continuous Variables

Stefan Weigert, Michael Wilkinson

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For N=2, the golden ratio occurs in the definition of these mutually unbiased bases suggesting the relevance of number theory not only in the finite-dimensional setting.

Original language	English
Article number	020303
Number of pages	4
Journal	Physical Review A
Volume	78
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevA.78.020303
Publication status	Published - 29 Aug 2008

Keywords

STATE DETERMINATION
COHERENT STATES
HILBERT-SPACE
QUANTUM

Access to Document

10.1103/PhysRevA.78.020303

http://pra.aps.org/abstract/PRA/v78/i2/e020303

Cite this

@article{9cc28c39204141c282e82e8585bcb6e3,

title = "Mutually Unbiased Bases for Continuous Variables",

abstract = "The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For N=2, the golden ratio occurs in the definition of these mutually unbiased bases suggesting the relevance of number theory not only in the finite-dimensional setting.",

keywords = "STATE DETERMINATION, COHERENT STATES, HILBERT-SPACE, QUANTUM",

author = "Stefan Weigert and Michael Wilkinson",

year = "2008",

month = aug,

day = "29",

doi = "10.1103/PhysRevA.78.020303",

language = "English",

volume = "78",

journal = "Physical Review A",

issn = "1050-2947",

publisher = "American Physical Society",

number = "2",

}

TY - JOUR

T1 - Mutually Unbiased Bases for Continuous Variables

AU - Weigert, Stefan

AU - Wilkinson, Michael

PY - 2008/8/29

Y1 - 2008/8/29

N2 - The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For N=2, the golden ratio occurs in the definition of these mutually unbiased bases suggesting the relevance of number theory not only in the finite-dimensional setting.

AB - The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For N=2, the golden ratio occurs in the definition of these mutually unbiased bases suggesting the relevance of number theory not only in the finite-dimensional setting.

KW - STATE DETERMINATION

KW - COHERENT STATES

KW - HILBERT-SPACE

KW - QUANTUM

UR - http://www.scopus.com/inward/record.url?scp=51049091848&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.78.020303

DO - 10.1103/PhysRevA.78.020303

M3 - Article

SN - 1050-2947

VL - 78

JO - Physical Review A

JF - Physical Review A

IS - 2

M1 - 020303

ER -

Mutually Unbiased Bases for Continuous Variables

Abstract

Keywords

Access to Document

Other files and links

Cite this