Geometric phase induced changes in the correlation properties of the entangled states

Erik Sjöqvist

M. S. Williamson, Vlatko Vedral

When an entangled state evolves under local unitaries, the entanglement in the state remains fixed. Here we show that the dynamical phase acquired by an entangled state in such a scenario can always be understood as the sum of the dynamical phases of its subsystems. In contrast, the equivalent statement for the geometric phase is not generally true unless the state is separable. For an entangled state an additional term is present, the mutual geometric phase, that measures the change the additional correlations present in the entangled state make to the geometry of the state space. For $N$ qubit states we find that this change can be explained solely by classical correlations for states with a Schmidt decomposition and solely by quantum correlations for $W$ states.

S. Mohammadi Almas, G. Najarbashi, Ali Tavana

Samira Nazifkar, Hakimeh Jaghouri

Recent studies show that two completely distinct fields as quantum information and string theory realization can be related and share some of the same properties. So, the knowledge on quantum information of some special quantum systems provides new insights on the sting theory. We analytically study geometric discord and measurement induced nonlocality for a Horodeckis' 33 bound entangled state to find quantum correlation. We find that there is a simultaneous sudden change point in the geometric discord and the measurement-induced nonlocality in the region of the bound entangled states, which is considerable. Moreover, we investigate the lower bound of geometric discord and the upper bound of measurement-induced nonlocality for this system. This study leads to some new and interesting novel results as well.

Abdel‐Baset A. Mohamed, H. A. Hessian

A system consists of two charged qubits are initially prepared in a maximum entangled Bell state and having no mutual interaction, where each qubit interacts independently with a superconducting transmission line resonator. An analytical solution of the time evolution of the final state of the system with the effect of a phase decoherence is found. In previous works, quantum correlations are only investigated in X-state for the models which are as our model. In this work, the analytical formulas of the geometric quantum discord (GQD) and measurement-induced non-locality (MIN) are introduced for a general state of two-qubit (non-X-state). Quantum correlations are studied via GQD and MIN with quantum entanglement (QE). It is found that a sudden disappearance only occurs for QE, while MIN and GQD still exist. Due to the increase in the amplitude of the coherent states, the intervals of the sudden disappearance of QE increase and MIN and GQD decrease. It is interesting to note that initial correlations can be lost and they reach their stationary correlations with the increase in the intrinsic decoherence. The stationary correlation of MIN can be destroyed, it reach zero value, when both the decoherence effect and detuning are present simultaneously. By starting with different types of Bell-like states, the stationary correlations as well as the time intervals of sudden disappearance have notable changes. It is possible to control the quantum correlations with certain parameter sets.

Dorje C. Brody, Lane P. Hughston, Matthew F. Parry