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Phys. Rev. A 67, 022316 (2003) [9 pages]

Entanglement gauge and the non-Abelian geometric phase with two photonic qubits

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Karl-Peter Marzlin1,2, Stephen D. Bartlett1, and Barry C. Sanders1
1Department of Physics and Centre for Advanced Computing—Algorithms and Cryptography, Macquarie University, Sydney, New South Wales 2109, Australia
2Fachbereich Physik der Universität Konstanz, Postfach 5560 M674, D-78457 Konstanz, Germany

Received 17 September 2002; published 28 February 2003

We introduce the entanglement gauge describing the combined effects of local operations and nonlocal unitary transformations on bipartite quantum systems. The entanglement gauge exploits the invariance of nonlocal properties for bipartite systems under local (gauge) transformations. This new formalism yields observable effects arising from the gauge geometry of the bipartite system. In particular, we propose a non-Abelian gauge theory realized via two separated spatial modes of the quantized electromagnetic field manipulated by linear optics. In this linear optical realization, a bipartite state of two separated spatial modes can acquire a non-Abelian geometric phase.

© 2003 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.67.022316
DOI:
10.1103/PhysRevA.67.022316
PACS:
03.67.-a, 42.50.Dv, 03.65.Vf, 02.20.-a