arXiv subjects

Demetris P. K. Ghikas

Publications and source records attributed to Demetris P. K. Ghikas.

6 recordsLinked to original sources

arXiv2018

Towards an Information Geometric characterization/classification of Complex Systems. II. Critical Parameter values from the (c,d)-manifold

In our previous paper (I) we derived information geometric objects from the two parameter generalized entropy of Hanel and Thurner (2011), using the c,d parameters as labels of the corresponding manifolds. Here we follow a completely different approach by considering these parameters as coordinates of our information manifolds. This gives a manageable two-dimensional manifold amenable to easy manipulations but most importantly it offers a direct characterization of complex systems in terms of the pair of the c,d values. As a result we obtain certain characteristic values from the scalar curvature which we could conjecture that they represent complex systems with specific behavior. It is further observed that the boundary values of the c,d parameters which characterize the Hanel-Thurner classification are in some sense singular. This asks for a regularization scheme which we try to establish.

physics.data-an↗

arXiv2017

Towards an Information Geometric characterization/classification of Complex Systems. I. Use of Generalized Entropies

Using the generalized entropies which depend on two parameters we propose a set of quantitative characteristics derived from the Information Geometry based on these entropies. Our aim, at this stage, is modest, as we are first constructing some fundamental geometric objects. We first establish the existence of a two-parameter family of probability distributions. Then using this family we derive the associated metric and we state a generalized Cramer-Rao inequality. This gives a first two-parameter classification of complex systems. Finally computing the scalar curvature of the information manifold we obtain a further discrimination of the corresponding classes. Our analysis is based on the two-parameter family of generalized entropies of Hanel and Thurner (2011)

math-ph↗

arXiv2012

A new information metric and a possible higher bound for a class of measurements in the Quantum Estimation Problem

Information metrics give lower bounds for the estimation of parameters. The Cencov-Morozova-Petz Theorem classifies the monotone quantum Fisher metrics. The optimum bound for the quantum estimation problem is offered by the metric which is obtained from the symmetric logarithmic derivative. To get a better bound, it means to go outside this family of metrics, and thus inevitably, to relax some general conditions. In the paper we defined logarithmic derivatives through a phase-space correspondence. This introduces a function which quantifies the deviation from the symmetric derivative. Using this function we have proved that there exist POVMs for which the new metric gives a higher bound from that of the symmetric derivative. The analysis was performed for the one qubit case.

quant-ph↗

arXiv2011

Entangling and decohering influence of noisy perturbations. Stochastic anti-resonance in the time evolution of interacting qubits

We study the entanglement evolution of two coupled qubits in interaction with an external environment and in the presence of an external magnetic field with a stochastic component. The results show the expected degradation of entanglement due to the noise. The new effect is that the time of disentanglement depends in a non-monotonous way on the strength of the noise. We find that it is shortest for an intermediate strength value of the latter. This we call "stochastic anti-resonance". Our results could lead to a better undestanding of noisy perturbations and their role for optimal designing of quantum devices.

quant-ph↗

arXiv2007

Quantum Entanglement dependence on bifurcations and scars in non autonomous systems. The case of Quantum Kicked Top

Properties related to entanglement in quantum systems, are known to be associated with distinct properties of the corresponding classical systems, as for example stability, integrability and chaos. This means that the detailed topology, both local and global, of the classical phase space may reveal, or influence, the entangling power of the quantum system. As it has been shown in the literature, the bifurcation points, in autonomous dynamical systems, play a crucial role for the onset of entanglement. Similarly, the existence of scars among the quantum states seems to be a factor in the dynamics of entanglement. Here we study these issues for a non-autonomous system, the Quantum Kicked Top, as a collective model of a multi-qubit system. Using the bifurcation diagram of the corresponding classical limit (the Classical Kicked Top), we analyzed the pair-wise and the bi-partite entanglement of the qubits and their relation to scars, as a function of the critical parameter of the system. We found that the pair-wise entanglement and pair-wise negativity show a strong maximum precisely at the bifurcation points, while the bi-partite entanglement changes slope at these points. We have also investigated the connection between entanglement and the fixed points on the branch of the bifurcation diagram between the two first bifurcation points and we found that the entanglement measures take their extreme values precisely on these points. We conjecture that our results on this behaviour of entanglement is generic for many quantum systems with a non-linear classical analogue.

quant-ph↗

arXiv2006

A curvature dependent bound for entanglement change in classically chaotic systems

Using the Calogero-Moser model and the Nakamura equations for a multi-partite quantum system, we prove an inequality between the mean bi-partite entanglement rate of change under the variation of a critical parameter and the level-curvature. This provides an upper bound for the rate of production or distraction of entanglement induced dynamically. We then investigate the dependence of the upper bound on the degree of chaos of the system, which in turn, through the inequality, gives a measure of the stability of the entangled state. Our analytical results are supported with extensive numerical calculations.

quant-ph↗