No Arabic abstract
We introduce and formalize the concept of information flux in a many-body register as the influence that the dynamics of a specific element receive from any other element of the register. By quantifying the information flux in a protocol, we can design the most appropriate initial state of the system and, noticeably, the distribution of coupling strengths among the parts of the register itself. The intuitive nature of this tool and its flexibility, which allow for easily manageable numerical approaches when analytic expressions are not straightforward, are greatly useful in interacting many-body systems such as quantum spin chains. We illustrate the use of this concept in quantum cloning and quantum state transfer and we also sketch its extension to non-unitary dynamics.
The importance of transporting quantum information and entanglement with high fidelity cannot be overemphasized. We present a scheme based on adiabatic passage that allows for transportation of a qubit, operator measurements and entanglement, using a 1-D array of quantum sites with a single sender (Alice) and multiple receivers (Bobs). Alice need not know which Bob is the receiver, and if several Bobs try to receive the signal, they obtain a superposition state which can be used to realize two-qubit operator measurements for the generation of maximally entangled states.
We utilize the relation between soliton solutions of the mKdV and the combined mKdV-KdV equation and the Dirac equation to construct electrostatic fields which yield exact zero energy states of graphene.
An algebraic framework for quantization in presence of arbitrary number of point-like defects on the line is developed. We consider a scalar field which interacts with the defects and freely propagates away of them. As an application we compute the Casimir force both at zero and finite temperature. We derive also the charge density in the Gibbs state of a complex scalar field with defects. The example of two delta-defects is treated in detail.
We develop a systematic and efficient approach for numerically solving the non-Markovian quantum state diffusion equations for open quantum systems coupled to an environment up to arbitrary orders of noises or coupling strengths. As an important application, we consider a real-time simulation of a spin-boson model in a strong coupling regime that is difficult to deal with using conventional methods. We show that the non-Markovian stochastic Schr{o}dinger equation can be efficiently implemented as a real--time simulation for this model, so as to give an accurate description of spin-boson dynamics beyond the rotating-wave approximation.
Dynamics of entanglement is investigated on the basis of exactly solvable models of multiple-quantum (MQ) NMR spin dynamics. It is shown that the time evolution of MQ coherences of systems of coupled nuclear spins in solids is directly connected with dynamics of the quantum entanglement. We studied analytically dynamics of entangled states for two- and three-spin systems coupled by the dipole-dipole interaction. In this case dynamics of the quantum entanglement is uniquely determined by the time evolution of MQ coherences of the second order. The real part of the density matrix describing MQ dynamics in solids is responsible for MQ coherences of the zeroth order while its imaginary part is responsible for the second order. Thus, one can conclude that dynamics of the entanglement is connected with transitions from the real part of the density matrix to the imaginary one and vice versa. A pure state which generalizes the GHZ and W states is found. Different measures of the entanglement of this state are analyzed for three-partite systems.