Gauge Theory and Geometric Phase in Quantum Systems

David H. Oaknin

Arno Böhm, Ali Mostafazadeh, Hiroyasu Koizumi +2 more

David Viennot, José Lages

A new approach is proposed, extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states). This new approach is based on an analogy between open quantum systems and dissipative quantum systems which uses a C *-module structure. The gauge theory associated with these new geometric phases does not employ the usual principal bundle structure but a higher structure, a categorical principal bundle (the so-called principal 2-bundle or non-Abelian bundle gerbe) which is sometimes a non-Abelian twisted bundle. The need to site the gauge theory in this higher structure is a geometrical manifestation of the decoherence induced by the environment on the quantum system.

Karl-Peter Marzlin, Stephen D. Bartlett, Barry C. Sanders

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.

At Wien

A Bruno, Antonio Capolupo, S Kak +2 more

We discuss the presence of a geometrical phase in the evolution of a qubit state and its gauge structure. The time evolution operator is found to be the free energy operator, rather than the Hamiltonian operator.