Non Abelian structures and the geometric phase of entangled qudits

Journal Article · Mon Dec 15 00:00:00 EST 2014 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2014.08.021· OSTI ID:22403465

Oxman, L.E., E-mail: [e-mail]; Khoury, A.Z., E-mail: [e-mail]

In this work, we address some important topological and algebraic aspects of two-qudit states evolving under local unitary operations. The projective invariant subspaces and evolutions are connected with the common elements characterizing the su(d) Lie algebra and their representations. In particular, the roots and weights turn out to be natural quantities to parametrize cyclic evolutions and fractional phases. This framework is then used to recast the coset contribution to the geometric phase in a form that generalizes the usual monopole-like formula for a single qubit.

• OSTI ID: 22403465
• Journal Information: Annals of Physics (New York), Vol. 351; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GEOMETRY
LIE GROUPS
MATHEMATICAL EVOLUTION
MATHEMATICAL SPACE
QUANTUM ENTANGLEMENT
QUANTUM STATES
QUBITS
TOPOLOGY