Unordered Tuples in Quantum Computation

Robert Furber; Bas Westerbaan

doi:10.4204/EPTCS.195.15

Unordered Tuples in Quantum Computation

Robert Furber, Bas Westerbaan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

It is well known that the C*-algebra of an ordered pair of qubits is M_2 (x) M_2. What about unordered pairs? We show in detail that M_3 (+) C is the C*-algebra of an unordered pair of qubits. Then we use Schur-Weyl duality to characterize the C*-algebra of an unordered n-tuple of d-level quantum systems. Using some further elementary representation theory and number theory, we characterize the quantum cycles. We finish with a characterization of the von Neumann algebra for unordered words.

Original language	English
Title of host publication	2th International Workshop on Quantum Physics and Logic, U.K., July 15-17, 2015
Editors	Chris Heunen, Peter Selinger, Jamie Vicary
Publisher	Open Publishing Association
Pages	196-207
Number of pages	12
DOIs	https://doi.org/10.4204/EPTCS.195.15
Publication status	Published - 4 Nov 2015
Event	12th International Workshop on Quantum Physics and Logic - Oxford, United Kingdom Duration: 13 Jul 2015 → 17 Jul 2015 http://www.cs.ox.ac.uk/qpl2015/

Publication series

Name	Electronic Proceedings in Theoretical Computer Science
Publisher	Open Publishing Association
Volume	195
ISSN (Electronic)	2075-2180

Workshop

Workshop	12th International Workshop on Quantum Physics and Logic
Abbreviated title	QPL 2015
Country/Territory	United Kingdom
City	Oxford
Period	13/07/15 → 17/07/15
Internet address	http://www.cs.ox.ac.uk/qpl2015/

Access to Document

10.4204/EPTCS.195.15Licence: All Rights Reserved

http://eptcs.web.cse.unsw.edu.au/paper.cgi?QPL2015.15Licence: All Rights Reserved

Cite this

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title = "Unordered Tuples in Quantum Computation",

abstract = "It is well known that the C*-algebra of an ordered pair of qubits is M_2 (x) M_2. What about unordered pairs? We show in detail that M_3 (+) C is the C*-algebra of an unordered pair of qubits. Then we use Schur-Weyl duality to characterize the C*-algebra of an unordered n-tuple of d-level quantum systems. Using some further elementary representation theory and number theory, we characterize the quantum cycles. We finish with a characterization of the von Neumann algebra for unordered words.",

author = "Robert Furber and Bas Westerbaan",

year = "2015",

month = nov,

day = "4",

doi = "10.4204/EPTCS.195.15",

language = "English",

series = "Electronic Proceedings in Theoretical Computer Science",

publisher = "Open Publishing Association",

pages = "196--207",

editor = "Chris Heunen and Peter Selinger and Jamie Vicary",

booktitle = "2th International Workshop on Quantum Physics and Logic, U.K., July 15-17, 2015",

address = "Australia",

note = "12th International Workshop on Quantum Physics and Logic, QPL 2015 ; Conference date: 13-07-2015 Through 17-07-2015",

url = "http://www.cs.ox.ac.uk/qpl2015/",

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Furber, R & Westerbaan, B 2015, Unordered Tuples in Quantum Computation. in C Heunen, P Selinger & J Vicary (eds), 2th International Workshop on Quantum Physics and Logic, U.K., July 15-17, 2015. Electronic Proceedings in Theoretical Computer Science, vol. 195, Open Publishing Association, pp. 196-207, 12th International Workshop on Quantum Physics and Logic, Oxford, United Kingdom, 13/07/15. https://doi.org/10.4204/EPTCS.195.15

Unordered Tuples in Quantum Computation. / Furber, Robert; Westerbaan, Bas.
2th International Workshop on Quantum Physics and Logic, U.K., July 15-17, 2015. ed. / Chris Heunen; Peter Selinger; Jamie Vicary. Open Publishing Association, 2015. p. 196-207 (Electronic Proceedings in Theoretical Computer Science; Vol. 195).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Furber, Robert

AU - Westerbaan, Bas

PY - 2015/11/4

Y1 - 2015/11/4

N2 - It is well known that the C*-algebra of an ordered pair of qubits is M_2 (x) M_2. What about unordered pairs? We show in detail that M_3 (+) C is the C*-algebra of an unordered pair of qubits. Then we use Schur-Weyl duality to characterize the C*-algebra of an unordered n-tuple of d-level quantum systems. Using some further elementary representation theory and number theory, we characterize the quantum cycles. We finish with a characterization of the von Neumann algebra for unordered words.

AB - It is well known that the C*-algebra of an ordered pair of qubits is M_2 (x) M_2. What about unordered pairs? We show in detail that M_3 (+) C is the C*-algebra of an unordered pair of qubits. Then we use Schur-Weyl duality to characterize the C*-algebra of an unordered n-tuple of d-level quantum systems. Using some further elementary representation theory and number theory, we characterize the quantum cycles. We finish with a characterization of the von Neumann algebra for unordered words.

U2 - 10.4204/EPTCS.195.15

DO - 10.4204/EPTCS.195.15

M3 - Conference contribution

T3 - Electronic Proceedings in Theoretical Computer Science

SP - 196

EP - 207

BT - 2th International Workshop on Quantum Physics and Logic, U.K., July 15-17, 2015

A2 - Heunen, Chris

A2 - Selinger, Peter

A2 - Vicary, Jamie

PB - Open Publishing Association

T2 - 12th International Workshop on Quantum Physics and Logic

Y2 - 13 July 2015 through 17 July 2015

ER -

Unordered Tuples in Quantum Computation

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