arXiv subjects

M. A. Jafarizadeh

Publications and source records attributed to M. A. Jafarizadeh.

At least 19 recordsLinked to original sources

arXiv2020

Nonlinear entanglement witnesses for four qubits in mutually unbiased bases

Entanglement witness is a Hermitian operator that is useful for detecting the genuine multipartite entanglement of mixed states. Nonlinear entanglement witnesses have the advantage of a wider detection range in the entangled region. We construct genuine entanglement witnesses for four qubits density matrices in the mutually unbiased basis. First, we find the convex feasible region with positive partial transpose states. Then, to reveal the entangled regions, we present some appropriate linear entanglement witnesses and, we find the envelope of this family of linear witnesses as a nonlinear witness. Finally, we study thermal entanglement and we show for some Hamiltonians the witnesses can detect the entanglement at all temperatures.

quant-ph↗

arXiv2019

Algebraic cluster models calculations for shape phase transitions of boson-fermion systems

The Algebraic Cluster Model(ACM) is an interacting boson model that gives the relative motion of the cluster configurations in which all vibrational and rotational degrees of freedom are present from the outset. We schemed a solvable extended transitional Hamiltonian based on affine $ {SU(1,1)} $ Lie algebra within the framework for two-, three- and four- body algebraic cluster models that explains both regions $ O(4)\leftrightarrow U(3) $, $ O(7)\leftrightarrow U(6) $ and $ O(10)\leftrightarrow U(9) $, respectively . We offer that this method can be used to study of $kα+ x$ nucleon structures with k = 2, 3,4 and x = 1, 2, . . . , in specific x = 1,2 such as structures $^{9}Be$,$^{9}B$,$^{10}B$ ; $^{13}C$, $^{13}N$, $^{14}N$; $^{17}O$, $^{17}F$. Numerical extraction to the energy levels, the expectation value of boson number operator and behavior of the overlap of the ground-state wave function within the control parameters of this evaluated Hamiltonian are presented. The effect of the coupling of the odd particle to an even-even boson core is discussed along the shape transition and, in particular, at the critical point.

nucl-th↗

arXiv2016

An explicit formula for the polynomial entanglement measures of degree 2 of even-N qubits mixed states

Characterization of the multipartite mixed state entanglement is still a challenging problem. Since due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state \r{ho} of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this Letter, we give an explicit formula for the polynomial entanglement measures of degree 2 of even-N qubits mixed states that is similar to Wooters formula in [1]. Then we discuss our findings in the framework of X density matrices and show that our formula for this type of density matrices is in the full agreement with the genuine multipartite (GM) entanglement of these states.

quant-ph↗

arXiv2015

Investigation of Nuclear Phase Transition by Solvababe supersymmetric algebraic model and its application in Ru-Rh and Zn-Cu Isotopes

Solvable supersymmetric algebraic model for descriptions of the spherical to gama unstable shape- phase transition in even and odd mass nuclei is proposed. This model is based on dual algebraic structure and Richardson - Gaudin method, where the duality relations between the unitary and quasispin algebraic structures for the boson and fermion systems are extended to mixed boson- fermion system. The structure of two type of nuclear supersymmetry schemes, based on the U(6/2) and U(6/4) supergroups, is discussed. We investigate the change in level structure induced by the phase transition by doing a quantal analysis. By using the generalized quasispin algebra, it is shown that the nuclear supersymmetry concept can be also used for transitional regions in addition to dynamical symmetry limits. Experimental evidence for the U(5)-O(6) transition in Ru-Rh and Zn- Cu supermultiplets is presented. The low-states energy spectra and B(E2)values for these nuclei have been calculated and compared with the experimental data.

nucl-th↗

arXiv2015

Solvababe supersymmetric algebraic model for descriptions of transitional even and odd mass nuclei near the critical point of the spherical to unstable shapes

Exactly solvable solution for the spherical to gamma - unstable transition in transitional nuclei based on dual algebraic structure and nuclear supersymmetry concept is proposed. The duality relations between the unitary and quasispin algebraic structures for the boson and fermion systems are extended to mixed boson-fermion system. It is shown that the relation between the even-even and odd-A neighbors implied by nuclear supersymmetry in addition to dynamical symmetry limits can be also used for transitional regions. The experimental evidences are presented for even- even [E(5)] and odd-mass [E(5/4)] nuclei near the critical point symmetry.

nucl-th↗

arXiv2015

Algebraic Solutions for $U^{BF}(5)-O^{BF}(6)$ Quantum Phase Transition in Odd Mass Number Nuclei

The spherical to deformed $γ-unstable$ shape- phase transition in odd-A nuclei is investigated by using the Dual algebraic structures and the affine $SU(1,1)$ Lie Algebra within the framework of the interacting boson - fermion model. The new algebraic solution for A-odd nuclei is introduced. In this model, Single $j = 1/2 $ and $ 3/2 $ fermions are coupled with an even-even boson core. Energy spectra, quadruple electromagnetic transitions and an expectation value of the d-boson number operator are presented. Experimental evidence for the $U^{BF} (5)-O^{BF} (6)$ transition in odd -A $Ba$ and $Rh$ isotopes is presented. The low-states energy spectra and $B(E2)$values for these nuclei have been also calculated and compared with the experimental data.

nucl-th↗

arXiv2015

Quantum discord of 2n-dimensional Bell-diagonal states

In this study, using the concept of relative entropy as a distance measure of cor- relations we investigate the important issue of evaluating quantum correlations such as entanglement, dissonance and classical correlations for 2n-dimensional Bell-diagonal states. We provide an analytical technique, which describes how we find the closest classical states(CCS) and the closest separable states(CSS) for these states. Then analytical results are obtained for quantum discord of 2n-dimensional Bell-diagonal states. As illustration, some special cases are examined. Finally, we investigate the additivity relation between the different correlations for the separable generalized bloch sphere states.

quant-ph↗

arXiv2015

Distinguishability of the symmetric states

In this paper, the distinguishability of multipartite geometrically uniform quantum states obtained from a single reference state is studied in the symmetric subspace. We specially focus our attention on the unitary transformation in a way that the produced states remain in the symmetric subspace, so rotation group with Jy as the generator of rotation is applied. The optimal probability and measurements are obtained for the pure and some special mixed separable states and the results are compared with those obtained at the previous articles for the special cases. The results are valid for lin- early dependent states. The discrimination of these states is also investigated using the separable measurement. We introduce appropriate transformation to gain the optimal separable measurements equivalent to the optimal global measurements with the same optimal probability.

quant-ph↗

arXiv2015

Entanglement entropy in the Hamming networks

We investigate the Hamming networks that their nodes are considered as quantum harmonic oscillators. The entanglement of the ground state can be used to quantify the amount of information each part of a network shares with the rest of the system via quantum fluctuations. Therefore, the Schmidt numbers and entanglement entropy between two special parts of Hamming network, can be calculated. To this aim, first we use the stratification method to rewrite the adjacency matrix of the network in the stratification basis. Then the entanglement entropy and Schmidt number for special partitions are calculated analytically by using the generalized Schur complement method. Also, we calculate the entanglement entropy between two arbitrary subsets (two equal subsets have the same number of vertices) in H(2; 3) and H(2; 4) numerically, and we give the minimum and maximum values of entanglement entropy in these two Hamming network.

quant-ph↗

arXiv2014

Investigating graph isomorphism in cospectral graphs via multiparticle quantum walk in fermionic basis and entanglement entropy

We investigate the graph isomorphism (GI) in some cospectral networks. Two graph are isomorphic when they are related to each other by a relabeling of the graph vertices. We want to investigate the GI in two scalable (n + 2)-regular graphs G4(n; n + 2) and G5(n; n + 2), analytically by using the multiparticle quantum walk. These two graphs are a pair of non-isomorphic connected cospectral regular graphs for any positive integer n. In order to investigation GI in these two graphs, we rewrite the adjacency matrices of graphs in the antisymmetric fermionic basis and show that they are different for thesepairs of graphs. So the multiparticle quantum walk is able to distinguish pairs of non- isomorph graphs. Also we construct two new graphs T4(n; n + 2) and T5(n; n + 2) and repeat the same process of G4 and G5 to study the GI problem by using multiparticle quantum walk. Then we study GI by using the entanglement entropy. To this aim, we calculate entanglement entropy between two parts of network. In our model the nodes are considered as identical quantum harmonic oscillators. The entanglement entropy between two special parts of G4(n; n+2) and G5(n; n+2) are calculated analytically. It is shown that the entanglement entropy can distinguish pairs of non-isomorphic cospectral graphs too.

quant-ph↗

arXiv2014

Entanglement entropy in the Hypercube networks

We investigate the hypercube networks that their nodes are considered as quantum harmonic oscillators. The entanglement of the ground state can be used to quantify the amount of information each part of a network shares with the rest of the system via quantum fluctuations. Therefore, the Schmidt numbers and entanglement entropy between two special parts of Hypercube network, can be calculated. To this aim, first we use the stratification method to rewrite the adjacency matrix of the network in the stratification basis which is the matrix representation of the angular momentum. Then the entanglement entropy and Schmidt number for special partitions are calculated an- alytically by using the generalized Schur complement method. Also, we calculate the entanglement entropy between two arbitrary equal subsets (two equal subsets have the same number of vertices) in H(3, 2) and H(4, 2) numerically, and we give the minimum and maximum values of entanglement entropy in these two Hypercube network. Then we can conjecture the minimum and maximum values of entanglement entropy for equal subsets in H(d, 2).

quant-ph↗

arXiv2014

Quantum stabilizer codes from Abelian and non-Abelian groups association schemes

A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes based on non-Abelian groups are constructed by bases for the regular representation from U6n, T4n, V8n and dihedral D2n groups. By using Abelian group association schemes followed by cyclic groups and non-Abelian group association schemes a list of binary stabilizer codes up to 40 qubits is given in tables 4, 5, and 10. Moreover, several binary stabilizer codes of distances 5 and 7 with good quantum parameters is presented. The preference of this method specially for Abelian group association schemes is that one can construct any binary quantum stabilizer code with any distance by using the commutative structure of association schemes

quant-ph↗

arXiv2014

Entanglement entropy and Schmidt numbers in quantum networks of coupled quantum oscillator

We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a network, are calculated. In partitioning an arbitrary graph into two parts there are some nodes in each parts which are not connected to the nodes of the other part. So these nodes of each part, can be in distinct subsets. Therefore the graph separates into four subsets. The nodes of the first and last subsets are those which are not connected to the nodes of other part. In theorem I, by using generalized Schur complement method in these four subsets, we prove that all graphs which their connections between all two alternative subsets are complete, have the same entropy. A large number of graphs satisfy this theorem. Then the entanglement entropy in the limit of large coupling and large size of system, is investigated in these graphs. One of important quantities about partitioning, is conductance of graph. The con- ductance of graph is considered in some various graphs. In these graphs we compare the conductance of graph and the entanglement entropy.

quant-ph↗

arXiv2014

Investigation graph isomorphism problem via entanglement entropy in strongly regular graphs

We investigate the quantum networks that their nodes are considered as quantum harmonic oscillators. The entanglement of the ground state can be used to quantify the amount of information one part of a network shares with the other part of the system. The networks which we studied in this paper, are called strongly regular graphs (SRG). These kinds of graphs have some special properties like they have three strata in the stratification basis. The Schur complement method is used to calculate the Schmidt number and entanglement entropy between two parts of graph. We could obtain analytically, all blocks of adjacency matrix in several important kinds of strongly regular graphs. Also the entanglement entropy in the large coupling limit is considered in these graphs and the relationship between Entanglement entropy and the ratio of size of boundary to size of the system is found. Then, area-law is studied to show that there are no entanglement entropy for the highest size of system. Then, the graph isomorphism problem is considered in SRGs by using the elements of blocks of adjacency matrices. Two SRGs with the same parameters: $(η,κ,λ,ν)$ are isomorphic if they can be made identical by relabeling their vertices. So the adjacency matrices of two isomorphic SRGs become identical by replacing of rows and columns. The nonisomirph SRGs could be distinguished by using the elements of blocks of adja- cency matrices in the stratification basis, numerically.

quant-ph↗

arXiv2013

Quantum Discord for Generalized Bloch Sphere States

In this study for particular states of bipartite quantum system in 2n?2m dimensional Hilbert space state, similar to m or n-qubit density matrices represented in Bloch sphere we call them generalized Bloch sphere states(GBSS), we give an efficient optimization procedure so that analytic evaluation of quantum discord can be performed. Using this optimization procedure, we find an exact analytical formula for the optimum positive operator valued measure (POVM) that maximize the measure of the classical correlation for these states. The presented optimization procedure also is used to show that for any concave entropy function the same POVMs are sufficient for quantum discord of mentioned states. Furthermore, We show that such optimization procedure can be used to calculate the geometric measure of quantum discord (GMQD) and then an explicit formula for GMQD is given. Finally, a complete geometric view is presented for quantum discord of GBSS. Keywords: Quantum Discord, Generalized Bloch Sphere States, Dirac matrices, Bipartite Quantum System. PACs Index: 03.67.-a, 03.65.Ta, 03.65.Ud

quant-ph↗

arXiv2013

Pairing Effect on Spectral Statistics of Even and Odd Mass Nuclei

The interplay of pairing is explored for the spectral statistics of nuclear systems with emphasis on the nearest neighbor spacing distributions by employing the kernel density and maximum likelihood estimation techniques. Different sequences prepared by all the available empirical data for low-lying energy levels of even and odd-mass nuclei in the 34 < A < 206 mass region. A deviation to more regular dynamics is apparent for even-mass nuclei in compare to odd-mass ones, and there are suggestions of effects due to unclosed proton shells on more chaotic dynamics.

nucl-th↗

arXiv2012

Description of Even-Even Xe isotopes in the transitional region of IBM

Properties of Xe isotopes isotopes are studied in the U(5)<->O(6) transitional region of Interacting Boson Model (IBM-1). The energy levels and B(E2)transition rates are calculated via the affine SU(1,1)Lie Algebra. The agreement with the most recent experimental is acceptable. The evaluated Hamiltonian control parameters suggest a spherical to (/gamma)-soft shape transition and propose the Xe(A=130)nucleus as the best candidate for the E(5)symmetry.

nucl-th↗

arXiv2012

Description of Dy (A=160)nucleus by Partial Dynamical SU(3) Symmetry

We considered the characteristic features of SU(3) partial dynamical symmetry in the interacting boson model framework to demonstrate the relevance of this technique in the nuclear spectroscopy of Dy (A=160) nucleus. The predictions of SU(3)-PDS for energy spectrum and B(E2)transition probabilities were compared with the most recent experimental data which an acceptable degree of agreement is achieved.

nucl-th↗