arXiv subjects

Ghader Najarbashi

Publications and source records attributed to Ghader Najarbashi.

5 recordsLinked to original sources

arXiv2024

Quantum Phase Transitions in the Spin 1 Bilinear-Biquadratic Heisenberg Model Based on Classical and Quantum Correlations

We investigate thermal and nonthermal quantum correlations in the one dimensional spin 1 bilinear-biquadratic Heisenberg model. Using tools from quantum information theory such as generalized concurrence, negativity, and various measures of quantum, classical, and total correlations in bipartite states we demonstrate that these measures effectively identify quantum phase transitions (QPTs) at critical points. Our negativity analysis reveals nearly identical results at zero or very low temperatures. Importantly, we find that partial concurrence, defined with the reduced density matrix, detects more quantum critical points than total concurrence. Additionally, we argue that spin chains with an odd number of spins are more effective than those with an even number in identifying QPTs.

quant-ph↗

arXiv2024

Geometric phase for mixed squeezed-coherent states

In this paper, we investigate the geometric phase (GP) acquired by two-mode mixed squeezed-coherent states (SCSs) during unitary cyclic evolution, focusing on the influence of squeezing parameters and classical weight. We analyze the GP for three distinct mixed states characterized by different configurations of the SCSs. Our results reveal that increasing the squeezing parameters of individual modes compresses the GP contours in different patterns: linearly, hyperbolically, and elliptically, depending on the mixed-state configuration. This behavior highlights the precision enhancement in squeezed states through uncertainty adjustment, aligning with theoretical predictions.

quant-ph↗

arXiv2023

Geometric phase for two-mode entangled squeezed-coherent states

In this paper, we study the geometric phase (GP) of two-mode entangled squeezed-coherent states (ESCSs), undergoing a unitary cyclic evolution. It is revealed that by increasing the squeezing parameter of the first or the second mode of a balanced ESCS, the GP compresses in an elliptical manner along the axis of the coherence parameter of the corresponding mode. While in the case of unbalanced ESCS, the GP compresses in a hyperbolic manner by increasing the squeezing parameters of either mode. By generalizing to higher constituting-state dimensions, it is found that the GPs of both balanced and unbalanced ESCSs, increase for a specific value of the coherence parameter. Based on these findings, using the interferometry approach, we suggest a theoretical scheme for the physical generation of the balanced ESCS.

quant-ph↗

arXiv2016

Relation Between Stereographic Projection and Concurrence Measure in Bipartite Pure States

One-qubit pure states, living on the surface of Bloch sphere, can be mapped onto the usual complex plane by using stereographic projection. In this paper, after reviewing the entanglement of two-qubit pure state, it is shown that the \emph{quaternionic} stereographic projection is related to concurrence measure. This is due to the fact that every two-qubit state, in ordinary complex field, corresponds to the one-qubit state in quaternionic skew field, called quaterbit. Like the one-qubit states in complex field, the stereographic projection maps every quaterbit onto a quaternion number whose complex and quaternionic parts are related to Schmidt and concurrence terms respectively. Rather, the same relation is established for three-qubit state under \emph{octonionic} stereographic projection which means that if the state is bi-separable then, quaternionic and octonionic terms vanish. Finally, we generalize recent consequences to $2 \otimes N$ and $4\otimes N$ dimensional Hilbert spaces ($N\geq 2$) and show that, after stereographic projection, the quaternionic and octonionic terms are entanglement sensitive. These trends are easily confirmed by direct computation for general multi-particle W- and GHZ-states.

quant-ph↗

arXiv2011

Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems

In this paper, we investigate the entanglement of multi-partite Grassmannian coherent states (GCSs) described by Grassmann numbers for $n>2$ degree of nilpotency. Choosing an appropriate weight function, we show that it is possible to construct some well-known entangled pure states, consisting of {\bf GHZ}, {\bf W}, Bell, cluster type and bi-separable states, which are obtained by integrating over tensor product of GCSs. It is shown that for three level systems, the Grassmann creation and annihilation operators $b$ and $b^†$ together with $b_{z}$ form a closed deformed algebra, i.e., $SU_{q}(2)$ with $q=e^{\frac{2πi}{3}}$, which is useful to construct entangled qutrit-states. The same argument holds for three level squeezed states. Moreover combining the Grassmann and bosonic coherent states we construct maximal entangled super coherent states.

math-ph↗