Searcharxiv⌕ Search

arXiv subjects

G. Najarbashi

Publications and source records attributed to G. Najarbashi.

14 recordsLinked to original sources
arXiv2016

Quantum phase transition in the Dzyaloshinskii-Moriya interaction with inhomogeneous magnetic field: Geometric approach

In this paper, we generalize the results of S. Oh (Physics Letters A. 644-647 \textbf{373 }) to Dzyaloshinski-Moriya model under nonuniform external magnetic field to investigate the relation between entanglement, geometric phase (or Berry phase) and quantum phase transition. We use quaternionic representation to relate the geometric phase to the quantum phase transition. For small values of DM parameter, the Berry phase is more appropriate than the concurrence measure, while for large values, the concurrence is a good indicator to show the phase transition. On the other hand, by increasing the DM interaction the phase transition occurs for large values of anisotropy parameter. In addition, for small values of magnetic field the concurrence measure is appropriate indicator for quantum phase transition, but for large values of magnetic field the Berry phase shows a sharp changes in the phase transition points. The results show that the Berry phase and concurrence form a complementary system from phase transition point of view.

quant-ph↗
arXiv2016

Comparison of Qubit and Qutrit like Entangled Squeezed and Coherent States of Light

Squeezed state of light is one of the important subjects in quantum optics which is generated by optical nonlinear interactions. In this paper, we especially focus on qubit like entangled squeezed states (ESS's) generated by beam splitters, phase-shifter and cross Kerr nonlinearity. Moreover the Wigner function of two-mode qubit and qutrit like ESS are investigated. We will show that the distances of peaks of Wigner functions for two-mode ESS are entanglement sensitive and can be a witness for entanglement. Like the qubit cases, monogamy inequality is fulfilled for qutrit like ESS. These trends are compared with those obtained for qubit and qutrit like entangled coherent states (ECS).

quant-ph↗
arXiv2016

One-Mode Wigner Quasi-probability Distribution Function for Entangled Coherent States Generated by Beam Splitter and Cavity QED

In this paper, we use the displacement operator together with parity operation to construct the superposition of two coherent states. By transmitting this superposition from 50-50 beam splitter the two-mode qubit like ECS is generated. Moreover, we introduce a controllable method for producing qutrit like ECS using atom-field interaction in cavity QED and beam splitter. We will show that the distances of peaks of Wigner functions for reduced density matrices of two-mode ECS's are entanglement sensitive and can be a witness for entanglement. To confirm the results we use concurrence measure to compare bipartite entanglement of ECS's with the behavior of peaks of Wigner functions. Moreover, we investigate decoherence effects on Wigner function, arising from transmitting ECS's through noisy channels.

quant-ph↗
arXiv2015

Two and Three-Qubits Geometry, Quaternionic and Octonionic Conformal Maps, and Intertwining Stereographic Projection

In this paper the geometry of two and three-qubit states under local unitary groups is discussed. We first review the one qubit geometry and its relation with Riemannian sphere under the action of group $SU(2)$. We show that the quaternionic stereographic projection intertwines between local unitary group $SU(2)\otimes SU(2)$ and quaternionic Möbius transformation. The invariant term appearing in this operation is related to concurrence measure. Yet, there exists the same intertwining stereographic projection for much more global group $Sp(2)$, generalizing the familiar Bloch sphere in 2-level systems. Subsequently, we introduce octonionic stereographic projection and octonionic conformal map (or octonionic Möbius maps) for three-qubit states and find evidence that they may have invariant terms under local unitary operations which shows that both maps are entanglement sensitive.

quant-ph↗
arXiv2015

Noise Effects on Entangled Coherent State Generated via Atom-Field Interaction and Beam Splitter

In this paper, we introduce a controllable method for producing two and three-mode entangled coherent states (ECS's) using atom-field interaction in cavity QED and beam splitter. The generated states play central roles in linear optics, quantum computation and teleportation. We especially focus on qubit, qutrit and qufit like ECS's and investigate their entanglement by concurrence measure. Moreover, we illustrate decoherence properties of ECS's due to noisy channels, using negativity measure. At the end the effect of noise on monogamy inequality is discussed.

quant-ph↗
arXiv2015

Entanglement of Multi-qudit States Constructed by Linearly Independent Coherent States: Balanced Case

Multi-mode entangled coherent states are important resources for linear optics quantum computation and teleportation. Here we introduce the generalized balanced N-mode coherent states which recast in the multi-qudit case. The necessary and sufficient condition for bi-separability of such balanced N-mode coherent states is found. We particularly focus on pure and mixed multi-qubit and multi-qutrit like states and examine the degree of bipartite as well as tripartite entanglement using the concurrence measure. Unlike the N-qubit case, it is shown that there are qutrit states violating monogamy inequality. Using parity, displacement operator and beam splitters, we will propose a scheme for generating balanced N-mode entangled coherent states for even number of terms in superposition.

quant-ph↗
arXiv2012

Entanglement of Multipartite Fermionic Coherent States for Pseudo Hermitian Hamiltonians

In this paper the entanglement of multi-qubit fermionic pseudo Hermitian coherent states (FPHCS) described by anticommutative Grassmann numbers is studied. The pseudo-Hermitian versions of the well known maximally entangled pure states such as Bell and GHZ, W and biseparable states are introduced through integrating over the tensor products of FPHCSs with suitable choice of Grassmannian weight functions. Meanwhile as an illustration, the method is applied to tensor product of 2 and 3 qubit pseudo Hermitian systems. Then the measures of concurrence and average entropy are applied to quantify the entanglement of the pseudo two and three qubit states respectively.

quant-ph↗
arXiv2011

Maximal Entanglement of Two-qubit States Constructed by Linearly Independent Coherent States

In this paper, we find the necessary and sufficient condition for the maximal entanglement of the state, $ |ψ>=μ|α>|β>+λ|α>|δ>+ ρ|γ>|β>+ν|γ>|δ>,$ constructed by linearly independent coherent states with \emph{real parameters} when $<α|γ>=<β|δ>$. This is a further generalization of the classified nonorthogonal states discussed in Ref. Physics Letters A {\bf{291}}, 73-76 (2001).

quant-ph↗
arXiv2010

Generalized Grassmannian Coherent States For Pseudo-Hermitian $n$ Level Systems

The purpose of this paper is to generalize fermionic coherent states for two-level systems described by pseudo-Hermitian Hamiltonian \cite{Trifonov}, to n-level systems. Central to this task is the expression of the coherent states in terms of generalized Grassmann variables. These kind of Grassmann coherent states satisfy bi-overcompleteness condition instead of over-completeness one, as it is reasonably expected because of the biorthonormality of the system. Choosing an appropriate Grassmann weight function resolution of identity is examined. Moreover Grassmannian coherent and squeezed states of deformed group $SU_{q}(2)$ for three level pseudo-Hermitian system are presented.

quant-ph↗
arXiv2010

Entanglement in multi-qubit pure fermionic coherent states

In this paper we investigate the entanglement of multi-qubit fermionic coherent states described by anticommutative Grassmann numbers. Choosing an appropriate weight function, we show that it is possible to construct some entangled pure states, consisting of {\bf{GHZ}}, {\bf{W}}, Bell and biseparable states, by tensor product of fermion coherent states. Moreover a comparison with maximal entangled bosonic coherent states is presented and it is shown that in some cases they have fermionic counterpart which are maximal entangled after integration with suitable weight functions.

quant-ph↗
arXiv2007

Multi-qubit stabilizer and cluster entanglement witnesses

One of the problems concerning entanglement witnesses (EWs) is the construction of them by a given set of operators. Here several multi-qubit EWs called stabilizer EWs are constructed by using the stabilizer operators of some given multi-qubit states such as GHZ, cluster and exceptional states. The general approach to manipulate the multi-qubit stabilizer EWs by exact(approximate) linear programming (LP) method is described and it is shown that the Clifford group play a crucial role in finding the hyper-planes encircling the feasible region. The optimality, decomposability and non-decomposability of constructed stabilizer EWs are discussed.

quant-ph↗
arXiv2007

Floating Entanglement Witness Measure and Genetic Algorithm

In this paper based on the notion of entanglement witness, a new measure of entanglement called floating entanglement witness measure is introduced which satisfies some of the usual properties of a good entanglement measure. By exploiting genetic algorithm, we introduce a classical algorithm that computes floating entanglement witness measure. This algorithm also provides a method for finding entanglement witness for a given entangled state.

quant-ph↗
arXiv2006

Manipulating Multi-qudit Entanglement Witnesses by Using Linear Programming

A new class of entanglement witnesses (EWs) called reduction type entanglement witnesses is introduced, which can detect some multi-qudit entangeled states including PPT ones with Hilbert space of dimension $d_{_{1}}\otimes d_{_{2}}\otimes...\otimes d_{_{n}}$. The novelty of this work comes from the fact that the feasible regions turn out to be convex polygons, hence the manipulation of these EWs reduces to linear programming which can be solved \emph{exactly} by using simplex method. The decomposability and non-decomposability of these EWs are studied and it is shown that it has a close connection with eigenvalues and optimality of EWs. Also using the Jamiołkowski isomorphism, the corresponding possible positive maps, including the generalized reduction maps of Ref. \cite{Hall1}, are obtained.

quant-ph↗