arXiv subjects

S. Salimi

Publications and source records attributed to S. Salimi.

At least 55 records · Page 3Linked to original sources

arXiv2012

Correlation dynamics of three spin under a classical dephasing environment

By starting from the stochastic Hamiltonian of the three correlated spins and modeling their frequency fluctuations as caused by dephasing noisy environments described by Ornstein-Uhlenbeck processes, we study the dynamics of quantum correlations, including entanglement and quantum discord. We prepared initially our open system with Greenberger-Horne-Zeilinger or W state and present the exact solutions for evolution dynamics of entanglement and quantum discord between three spins under both Markovian and non-Markovian regime of this classical noise. By comparison the dynamics of entanglement with that of quantum discord we find that entanglement can be more robust than quantum discord against this noise. It is shown that by considering non-Markovian extensions the survival time of correlations prolong.

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arXiv2012

Mixing-time and large-decoherence in continuous-time quantum walks on one-dimension regular networks

In this paper, we study mixing and large decoherence in continuous-time quantum walks on one dimensional regular networks, which are constructed by connecting each node to its $2l$ nearest neighbors($l$ on either side). In our investigation, the nodes of network are represented by a set of identical tunnel-coupled quantum dots in which decoherence is induced by continuous monitoring of each quantum dot with nearby point contact detector. To formulate the decoherent CTQWs, we use Gurvitz model and then calculate probability distribution and the bounds of instantaneous and average mixing times. We show that the mixing times are linearly proportional to the decoherence rate. Moreover, adding links to cycle network, in appearance of large decoherence, decreases the mixing times.

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arXiv2012

Concurrence for a two-qubits mixed state consisting of three pure states in the framework of SU(2) coherent states

A simplified expression of concurrence for two-qubit mixed state having no more than three non-vanishing eigenvalues is obtained. Basing on SU(2) coherent states, the amount of entanglement of two-qubit pure states is studied and conditions for entanglement are calculated by formulating the measure in terms of some new parameters (amplitudes of coherent states). This formalism is generalized to the case of two-qubit mixed states using the simplified expression of concurrence.

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arXiv2012

Quantum discord evolution of three-qubit states under noisy channels

We investigated the dissipative dynamics of quantum discord for correlated qubits under Markovian environments. The basic idea in the present scheme is that quantum discord is more general, and possibly more robust and fundamental, than entanglement. We provide three initially correlated qubits in pure Greenberger-Horne-Zeilinger (GHZ) or W state and analyse the time evolution of the quantum discord under various dissipative channels such as: Pauli channels $σ_{x}$, $σ_{y}$, and $σ_{z}$, as well as depolarising channels. Surprisingly, we find that under the action of Pauli channel $σ_{x}$, the quantum discord of GHZ state is not affected by decoherence. For the remaining dissipative channels, the W state is more robust than the GHZ state against decoherence. Moreover, we compare the dynamics of entanglement with that of the quantum discord under the conditions in which disentanglement occurs and show that quantum discord is more robust than entanglement except for phase flip coupling of the three qubits system to the environment.

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arXiv2012

Asymptotic entanglement in 1D quantum walks with a time-dependent coined

Discrete-time quantum walk evolve by a unitary operator which involves two operators a conditional shift in position space and a coin operator. This operator entangles the coin and position degrees of freedom of the walker. In this paper, we investigate the asymptotic behavior of the coin position entanglement (CPE) for an inhomogeneous quantum walk which determined by two orthogonal matrices in one-dimensional lattice. Free parameters of coin operator together provide many conditions under which a measurement perform on the coin state yield the value of entanglement on the resulting position quantum state. We study the problem analytically for all values that two free parameters of coin operator can take and the conditions under which entanglement becomes maximal are sought.

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arXiv2011

Symmetry and Quantum Transport on Networks

We study the classical and quantum transport processes on some finite networks and model them by continuous-time random walks (CTRW) and continuous-time quantum walks (CTQW), respectively. We calculate the classical and quantum transition probabilities between two nodes of the network. We numerically show that there is a high probability to find the walker at the initial node for CTQWs on the underlying networks due to the interference phenomenon, even for long times. To get global information (independent of the starting node) about the transport efficiency, we average the return probability over all nodes of the network. We apply the decay rate and the asymptotic value of the average of the return probability to evaluate the transport efficiency. Our numerical results prove that the existence of the symmetry in the underlying networks makes quantum transport less efficient than the classical one. In addition, we find that the increasing of the symmetry of these networks decreases the efficiency of quantum transport on them.

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arXiv2010

Prefect Transfer of Quantum States on Spin Chain with Dzyaloshinskii- Moriya interaction in inhomogeneous Magnetic field

In this work, we use the Hamiltonian of a modified Dzyaloshinskii-Moriya model and investigate the perfect transfer of the quantum state on the spin networks. In this paper, we calculate fidelity in which fidelity depends on magnetic field and another parameters. Then, by using the numerical analysis we show that the fidelity of the transferred state is determined by magnetic field $B$, exchange coupling $J$ and the Dzyaloshinskii- Moriya interaction $D$. We also found that the perfect transfer of the quantum state is possible with condition $B \gg Γ^2ω^{N/2}$ where $Γ=((J+iD)/2)$ and $ω=Γ^*/ Γ$.

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arXiv2010

Perfect state transfer via quantum probability theory

The transfer of quantum states has played an important role in quantum information processing. In fact, transfer of quantum states from point $A$ to $B$ with unit fidelity is very important for us and we focus on this case. In recent years, in represented works, they designed Hamiltonian in a way that a mirror symmetry creates with with respect to network center. In this paper, we stratify the spin network with respect to an arbitrary vertex of the spin network o then we design coupling coefficient in a way to create a mirror symmetry in Hamiltonian with respect to center. By using this Hamiltonian and represented approach, initial state that have been encoded on the first vertex in suitable time and with unit fidelity from it's antipodes vertex can be received. In his work, there is no need to external control.

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arXiv2010

D-concurrence bounds for pair coherent states

The pair coherent state is a state of a two-mode radiation field which is known as a state with non-Gaussian wave function. In this paper, the upper and lower bounds for D-concurrence (a new entanglement measure) have been studied over this state and calculated.

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arXiv2010

Pseudo-Hermitian continuous-time quantum walks

In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it pseudo-Hermitian continuous-time quantum walk. We introduce a method to obtain the probability distribution of walk on any vertex and then study a specific system. We observe that the probability distribution on certain vertices increases compared to that of the Hermitian case. This formalism makes the transport process faster and can be useful for search algorithms.

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arXiv2009

The effect of decoherence on mixing time in continuous-time quantum walks on one-dimension regular networks

In this paper, we study decoherence in continuous-time quantum walks (CTQWs) on one-dimension regular networks. For this purpose, we assume that every node is represented by a quantum dot continuously monitored by an individual point contact(Gurvitz's model). This measuring process induces decoherence. We focus on small rates of decoherence and then obtain the mixing time bound of the CTQWs on one-dimension regular network which its distance parameter is $l\geq 2$. Our results show that the mixing time is inversely proportional to rate of decoherence which is in agreement with the mentioned results for cycles in \cite{FST,VKR}. Also, the same result is provided in \cite{SSRR} for long-range interacting cycles. Moreover, we find that this quantity is independent of distance parameter $l(l\geq 2)$ and that the small values of decoherence make short the mixing time on these networks.

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arXiv2009

The effect of large-decoherence on mixing-time in Continuous-time quantum walks on long-range interacting cycles

In this paper, we consider decoherence in continuous-time quantum walks on long-range interacting cycles (LRICs), which are the extensions of the cycle graphs. For this purpose, we use Gurvitz's model and assume that every node is monitored by the corresponding point contact induced the decoherence process. Then, we focus on large rates of decoherence and calculate the probability distribution analytically and obtain the lower and upper bounds of the mixing time. Our results prove that the mixing time is proportional to the rate of decoherence and the inverse of the distance parameter ($\emph{m}$) squared. This shows that the mixing time decreases with increasing the range of interaction. Also, what we obtain for $\emph{m}=0$ is in agreement with Fedichkin, Solenov and Tamon's results \cite{FST} for cycle, and see that the mixing time of CTQWs on cycle improves with adding interacting edges.

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arXiv2009

Mixing and Decoherence in Continuous-time quantum walks on long-range interacting cycles

We study the effect of small decoherence in continuous-time quantum walks on long-range interacting cycles, which are constructed by connecting all the two nodes of distance m on the cycle graph. In our investigation, each node is continuously monitored by an individual point contact, which induces the decoherence process. We obtain the analytical probability distribution and the mixing time upper bound. Our results show that, for small rates of decoherence, themixing time upper bound is independent of distance parameter m and is proportional to inverse of decoherence rate.

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arXiv2009

Continuous-time quantum walks on semi-regular spidernet graphs via quantum probability theory

We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical transport processes on graphs, and calculate the spacetime transition probabilities between two vertices of the lattice. Then we analytically show that there are two power law decays $\sim t^{-3}$ and $\sim t^{-1.5}$ at the beginning of the transport for transition probability in the continuous-time quantum and classical random walk respectively. This results illustrate the decay of quantum mechanical transport processes is quicker than that of the classical one. Due to the result, the characteristic time $t_c$, which is the time when the first maximum of the probabilities occur on an infinite graph, for the quantum walk is shorter than that of the classical walk. Therefore, we can interpret that the quantum transport speed on spidernet is faster than that of the classical one. In the end, we investigate the results by numerical analysis for two examples.

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arXiv2009

Investigation of quantum roulette

In this paper, by using permutation matrices as a representation of symmetric group $S_N$ and Fourier matrix, we investigate quantum roulette with an arbitrary $N$-state. This strategy, which we introduce, is general method that allows us to solve quantum game for an arbitrary $N$-state. We consider the interaction between the system and its environment and study the effect of the depolarizing channel on this strategy. Finally, as an example we employ this strategy for quantum roulette with N=3.

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arXiv2009

Continuous-time quantum walks on star graphs

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for $N$-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on $K_2$ graphs (Complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

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arXiv2009

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

In this paper we define direct product of graphs and give a recipe for obtained probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph obtain by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determine probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product cayley graphs (complete cycle, complete $K_n$, charter and $n$-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as $t\longrightarrow \infty$ but for quantum state is not always satisfy.

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arXiv2008

Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory

The method of the quantum probability theory only requires simple structural data of graph and allows us to avoid a heavy combinational argument often necessary to obtain full description of spectrum of the adjacency matrix. In the present paper, by using the idea of calculation of the probability amplitudes for continuous-time quantum walk in terms of the quantum probability theory, we investigate quantum central limit theorem for continuous-time quantum walks on odd graphs.

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