Geometric phase as a determinant of a qubit– environment coupling

Abstract

We investigate the qubit geometric phase and its properties in dependence on the mechanism for decoherence of a qubit weakly coupled to its environment. We consider two sources of decoherence: dephasing coupling (without exchange of energy with environment) and dissipative coupling (with exchange of energy). Reduced dynamics of the qubit is studied in terms of the rigorous Davies Markovian quantum master equation, both at zero and non-zero temperature. For pure dephasing coupling, the geometric phase varies monotonically with respect to the polar angle (in the Bloch sphere representation) parameterizing an initial state of the qubit. Moreover, it is antisymmetric about some points on the geometric phase-polar angle plane. This is in distinct contrast to the case of dissipative coupling for which the variation of the geometric phase with respect to the polar angle typically is non-monotonic, displaying local extrema and is not antisymmetric. Sensitivity of the geometric phase to details of the decoherence source can make it a tool for testing the nature of the qubit-environment interaction.

Geometric magnetism in open quantum systems

“…This so defined phase γ would in general differ from those, equally sound and useful, expressions of a Berry phase introduced for open systems in the prior literature [11][12][13][14][15][16][17][18][19][20][21].…”

“…(21), provides a straightforward way to define the Berry phase of an open quantum system. Just like the surface integral of the classical twoform (1) provides a generalization of Berry phase for chaotic classical systems [5,6], so does the surface integral of the geometric magnetism (21) provide an analogue of the Berry phase of open quantum systems, reading…”

“…Thus, the study of geometric phases in realistic open quantum systems has become of paramount importance. This problem has been typically addressed from a dynamics point of view, that is, one researches proper definitions of phases with respect to non-unitary dynamics [11][12][13][14][15][16][17][18][19][20][21] (which are the relevant ones for open systems), instead of the unitary dynamics originally considered by Berry.…”

Temperature-independent teleportation of qubits in Davies environments

“…There are two origins of temperature dependence of the Davis maps Eqs. (8)(9)(10)(11). The first is explicit, via parameter p in Eq.…”

“…They satisfy most of the desired thermodynamic and statistical-mechanical properties such as the detailed balance condition [1]. Davies approximation has recently been applied to studies of various problems in quantum information and physics of open quantum systems including entanglement dynamics [14], quantum discord [7,10], or properties of geometric phases of qubits [8].…”