Mahmoud Mahdian - Academia.edu (original) (raw)

Papers by Mahmoud Mahdian

Research paper thumbnail of Kraus representation for maps and master equation in spin star model with layered environment

arXiv (Cornell University), Apr 22, 2013

Quantum operations are usually defined as completely positive (CP), trace preserving (TP) maps on... more Quantum operations are usually defined as completely positive (CP), trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and master equation of an exactly solvable dynamic of one-qubit open system in layered environment. On the other hand, we obtain exact Nakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equation from the maps. Finally, we study a simple example to consider the relation between CP maps and initial quantum correlation and show that vanishing initial quantum correlation is not necessary for CP maps.

Research paper thumbnail of Exact dynamics of one-qubit system in layered environment

arXiv (Cornell University), Apr 22, 2013

We investigate the exact evolution of the reduced dynamics of a one qubit system as central spin ... more We investigate the exact evolution of the reduced dynamics of a one qubit system as central spin coupled to a femionic layered environment with unlimited number of layers. Also, we study the decoherence induced on central spin by analysis solution is obtained in the limit N → ∞ of an infinite number of bath spins. Finally, the Nakajima-Zwanzig (NZ) and the time-convolutionless (TCL) projection operator techniques to second order are derived.

Research paper thumbnail of Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices

Journal of Physics A: Mathematical and Theoretical, 2020

Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices suppo... more Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources by useful control schemes. In this paper, we develop an HQC algorithm using an efficient variational optimization approach to simulate open system dynamics under the Noisy-Intermediate Scale Quantum(NISQ) computer. Using the time-dependent variational principle (TDVP) method and extending it to McLachlan TDVP for density matrix which involves minimization of Frobenius norm of the error, we apply the unitary quantum circuit to obtain the time evolution of the open quantum system in the Lindblad formalism. Finally, we illustrate the use of our methods with detailed examples which are in good agreement with analytical calculations.

Research paper thumbnail of Incoherent quantum algorithm dynamics of an open system with near-term devices

Quantum Information Processing, 2020

Hybrid quantum-classical algorithms are among the most promising systems to implement quantum com... more Hybrid quantum-classical algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In this paper, at first, we investigate a quantum dynamics algorithm for the density matrix obeying the von Neumann equation using an efficient Lagrangian-based approach. And then, we consider the dynamics of the ensemble-averaged of disordered quantum systems which is described by Hamiltonian ensemble with a hybrid quantum-classical algorithm. In a recent work [Phys. Rev. Lett. 120, 030403], the authors concluded that the dynamics of an open system could be simulated by a Hamiltonian ensemble because of nature of the disorder average. We investigate our algorithm to simulating incoherent dynamics (decoherence) of open system using an efficient variational quantum circuit in the form of master equations. Despite the non-unitary evolution of open systems, our method is applicable to a wide range of problems for incoherent dynamics with the unitary quantum operation.

Research paper thumbnail of Comparison of quantum discord and relative entropy in some bipartite quantum systems

Quantum Information Processing, 2016

The study of quantum correlations in High-dimensional bipartite systems is crucial for the develo... more The study of quantum correlations in High-dimensional bipartite systems is crucial for the development of quantum computing. We propose relative entropy as a distance measure of correlations may be measured by means of the distance from the quantum state to the closest classical-classical state. In particular, We establish relations between relative entropy and quantum discord quantifiers obtained by means of orthogonal projection measurements. We show that for symmetrical X-states density matrices the quantum discord is equal to relative entropy. At the end of paper, various examples of X-states such as two-qubit and qubit-qutrit have been demonstrated.

Research paper thumbnail of Effect of Quantum correlation on Perfect K pair Quantum Network Coding

We find a protocol transmitting K quantum states crossly in the quantum networks with K pair send... more We find a protocol transmitting K quantum states crossly in the quantum networks with K pair sender-receiver and one bottleneck channels only with sharing quantum correlations between senders. In these networks senders want to multi cast perfect quantum states to receivers. Perfect send on the quantum networks is impossible just using some additional resources like quantum correlation. This protocol has been used maximum entangled states and Quantum Discord which is best indicator of the quantum nature of the correlation to sharing between senders. At first, to send perfect K states in quantum network applied some maximum entanglement states to teleport quantum states, Enistein - Podolsky - Rosen (EPR) states as simple and two qubit states and Grrenberger- Horne - Zeilinger (GHZ) states and W states as kinds of three qubit states. Then reached that there is no difference between sharing these maximum entanglement states and must send same amount of classical bits in bottleneck chann...

Research paper thumbnail of Noisy channel effect on quantum correlations of two relativistic particles

We study the quantum correlation dynamics of two relativistic particles which is transmitted thro... more We study the quantum correlation dynamics of two relativistic particles which is transmitted through one of the Pauli channels σx, σy, and σz. We compare sudden death and robustness of entanglement and geometric discord and quantum discord of two relativistic particles under noisy Pauli channels. we find out geometric discord and quantum discord may be more robust than entanglement against decoherence.

Research paper thumbnail of Perfect K-Pair Quantum Network Coding Using Superconducting Qubits

Journal of Superconductivity and Novel Magnetism, 2014

Transferring quantum states efficiently between distant nodes of an information processing circui... more Transferring quantum states efficiently between distant nodes of an information processing circuit is an essential primitive in quantum communication and information processing. Here, we present in a solid-state system base transmitting K quantum states crossly in the quantum networks with K-pair sender-receiver and one bottleneck channel with high fidelity only with sharing quantum entanglement between senders.

Research paper thumbnail of Thermal Quantum Correlations in Photosynthetic Light-Harvesting Complexes

International Journal of Theoretical Physics, 2015

Your article is protected by copyright and all rights are held exclusively by Springer Science +B... more Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media New York. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Research paper thumbnail of Exact Dynamics of a Single-Qubit System in Layered Environment

International Journal of Theoretical Physics, 2015

Research paper thumbnail of Quantifying entanglement of two relativistic particles using optimal entanglement witness

Quantum Information Processing, 2010

Research paper thumbnail of Relativistic entanglement in single-particle quantum states using non-linear entanglement witnesses

Quantum Information Processing, 2011

In this study, the spin-momentum correlation of one massive spin-1 2 and spin-1 particle states, ... more In this study, the spin-momentum correlation of one massive spin-1 2 and spin-1 particle states, which are made based on projection of a relativistic spin operator into timelike direction is investigated. It is shown that by using Non-Linear entanglement witnesses (NLEWs), the effect of Lorentz transformation would decrease both the amount and the region of entanglement.

Research paper thumbnail of Investigating a class of2⊗2⊗dbound entangled density matrices via linear and nonlinear entanglement witnesses constructed by exact convex optimization

Research paper thumbnail of Correlation Dynamics of Three-Qubit System Under a Classical Dephasing Environment

International Journal of Theoretical Physics, 2013

By starting from the stochastic Hamiltonian of the three correlated spins and modeling their freq... more 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.

Research paper thumbnail of Spin–Momentum Correlation in Relativistic Single-Particle Quantum States

International Journal of Quantum Information, 2010

This paper is concerned with the spin–momentum correlation in single-particle quantum states, whi... more This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.

Research paper thumbnail of Electric Field Effects on Quantum Correlations in Three Coupled Semiconductor Quantum Dots

International Journal of Quantum Information, 2013

We study the effect of external electric bias on the quantum correlations in the array of optical... more We study the effect of external electric bias on the quantum correlations in the array of optically excited three coupled semiconductor quantum dots. The correlations are characterized by the quantum discord and concurrence and are observed using excitonic qubits. We employ the lower bound of concurrence for thermal density matrix at different temperatures. The effect of the Förster interaction on correlations will be studied. Our theoretical model detects nonvanishing quantum discord when the electric field is on while concurrence dies, ensuring the existence of nonclassical correlations as measured by the quantum discord.

Research paper thumbnail of Detecting some three-qubit MUB diagonal entangled states via nonlinear optimal entanglement witnesses

The European Physical Journal D, 2008

Research paper thumbnail of Quantum discord evolution of three-qubit states under noisy channels

The European Physical Journal D, 2012

We investigated the dissipative dynamics of quantum discord for correlated qubits under Markovian... more 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.

Research paper thumbnail of Quantum correlations of Two-Qubit XXZ Heisenberg Chain with Dzyaloshinsky-Moriya interaction coupled to bath spin as non-Markovian environment

We consider the quantum correlations (entanglement and quantum discord) dynamics of two coupled s... more We consider the quantum correlations (entanglement and quantum discord) dynamics of two coupled spin qubits with Dzyaloshinsky-Moriya interaction influenced by a locally external magnetic field along z-direction and coupled to bath spin-1 2 particles as independent non-Markovian environment. We find that with increasing D z and decreasing J z , the value of entanglement and quantum discord increase for both antiferromagnetic and ferromagnetic materials. Not that, this growth is more for the ferromagnetic materials. In addition, we perceive that entanglement and quantum discord decrease with increased temperature and increased coupling constants between reduced system and bath. But, strong quantum correlations within the spins of bath reduce decoherence effects. We discuss about type of the constituent material of the central spins that it can speedup the quantum information processing and as a result, we perceive that one can improve and control the quantum information processing with correct selection of the properties of the reduced system (J, J z , D z).

Research paper thumbnail of Kraus representation for maps and master equation in spin star model with layered environment

arXiv (Cornell University), Apr 22, 2013

Quantum operations are usually defined as completely positive (CP), trace preserving (TP) maps on... more Quantum operations are usually defined as completely positive (CP), trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and master equation of an exactly solvable dynamic of one-qubit open system in layered environment. On the other hand, we obtain exact Nakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equation from the maps. Finally, we study a simple example to consider the relation between CP maps and initial quantum correlation and show that vanishing initial quantum correlation is not necessary for CP maps.

Research paper thumbnail of Exact dynamics of one-qubit system in layered environment

arXiv (Cornell University), Apr 22, 2013

We investigate the exact evolution of the reduced dynamics of a one qubit system as central spin ... more We investigate the exact evolution of the reduced dynamics of a one qubit system as central spin coupled to a femionic layered environment with unlimited number of layers. Also, we study the decoherence induced on central spin by analysis solution is obtained in the limit N → ∞ of an infinite number of bath spins. Finally, the Nakajima-Zwanzig (NZ) and the time-convolutionless (TCL) projection operator techniques to second order are derived.

Research paper thumbnail of Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices

Journal of Physics A: Mathematical and Theoretical, 2020

Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices suppo... more Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources by useful control schemes. In this paper, we develop an HQC algorithm using an efficient variational optimization approach to simulate open system dynamics under the Noisy-Intermediate Scale Quantum(NISQ) computer. Using the time-dependent variational principle (TDVP) method and extending it to McLachlan TDVP for density matrix which involves minimization of Frobenius norm of the error, we apply the unitary quantum circuit to obtain the time evolution of the open quantum system in the Lindblad formalism. Finally, we illustrate the use of our methods with detailed examples which are in good agreement with analytical calculations.

Research paper thumbnail of Incoherent quantum algorithm dynamics of an open system with near-term devices

Quantum Information Processing, 2020

Hybrid quantum-classical algorithms are among the most promising systems to implement quantum com... more Hybrid quantum-classical algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In this paper, at first, we investigate a quantum dynamics algorithm for the density matrix obeying the von Neumann equation using an efficient Lagrangian-based approach. And then, we consider the dynamics of the ensemble-averaged of disordered quantum systems which is described by Hamiltonian ensemble with a hybrid quantum-classical algorithm. In a recent work [Phys. Rev. Lett. 120, 030403], the authors concluded that the dynamics of an open system could be simulated by a Hamiltonian ensemble because of nature of the disorder average. We investigate our algorithm to simulating incoherent dynamics (decoherence) of open system using an efficient variational quantum circuit in the form of master equations. Despite the non-unitary evolution of open systems, our method is applicable to a wide range of problems for incoherent dynamics with the unitary quantum operation.

Research paper thumbnail of Comparison of quantum discord and relative entropy in some bipartite quantum systems

Quantum Information Processing, 2016

The study of quantum correlations in High-dimensional bipartite systems is crucial for the develo... more The study of quantum correlations in High-dimensional bipartite systems is crucial for the development of quantum computing. We propose relative entropy as a distance measure of correlations may be measured by means of the distance from the quantum state to the closest classical-classical state. In particular, We establish relations between relative entropy and quantum discord quantifiers obtained by means of orthogonal projection measurements. We show that for symmetrical X-states density matrices the quantum discord is equal to relative entropy. At the end of paper, various examples of X-states such as two-qubit and qubit-qutrit have been demonstrated.

Research paper thumbnail of Effect of Quantum correlation on Perfect K pair Quantum Network Coding

We find a protocol transmitting K quantum states crossly in the quantum networks with K pair send... more We find a protocol transmitting K quantum states crossly in the quantum networks with K pair sender-receiver and one bottleneck channels only with sharing quantum correlations between senders. In these networks senders want to multi cast perfect quantum states to receivers. Perfect send on the quantum networks is impossible just using some additional resources like quantum correlation. This protocol has been used maximum entangled states and Quantum Discord which is best indicator of the quantum nature of the correlation to sharing between senders. At first, to send perfect K states in quantum network applied some maximum entanglement states to teleport quantum states, Enistein - Podolsky - Rosen (EPR) states as simple and two qubit states and Grrenberger- Horne - Zeilinger (GHZ) states and W states as kinds of three qubit states. Then reached that there is no difference between sharing these maximum entanglement states and must send same amount of classical bits in bottleneck chann...

Research paper thumbnail of Noisy channel effect on quantum correlations of two relativistic particles

We study the quantum correlation dynamics of two relativistic particles which is transmitted thro... more We study the quantum correlation dynamics of two relativistic particles which is transmitted through one of the Pauli channels σx, σy, and σz. We compare sudden death and robustness of entanglement and geometric discord and quantum discord of two relativistic particles under noisy Pauli channels. we find out geometric discord and quantum discord may be more robust than entanglement against decoherence.

Research paper thumbnail of Perfect K-Pair Quantum Network Coding Using Superconducting Qubits

Journal of Superconductivity and Novel Magnetism, 2014

Transferring quantum states efficiently between distant nodes of an information processing circui... more Transferring quantum states efficiently between distant nodes of an information processing circuit is an essential primitive in quantum communication and information processing. Here, we present in a solid-state system base transmitting K quantum states crossly in the quantum networks with K-pair sender-receiver and one bottleneck channel with high fidelity only with sharing quantum entanglement between senders.

Research paper thumbnail of Thermal Quantum Correlations in Photosynthetic Light-Harvesting Complexes

International Journal of Theoretical Physics, 2015

Your article is protected by copyright and all rights are held exclusively by Springer Science +B... more Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media New York. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Research paper thumbnail of Exact Dynamics of a Single-Qubit System in Layered Environment

International Journal of Theoretical Physics, 2015

Research paper thumbnail of Quantifying entanglement of two relativistic particles using optimal entanglement witness

Quantum Information Processing, 2010

Research paper thumbnail of Relativistic entanglement in single-particle quantum states using non-linear entanglement witnesses

Quantum Information Processing, 2011

In this study, the spin-momentum correlation of one massive spin-1 2 and spin-1 particle states, ... more In this study, the spin-momentum correlation of one massive spin-1 2 and spin-1 particle states, which are made based on projection of a relativistic spin operator into timelike direction is investigated. It is shown that by using Non-Linear entanglement witnesses (NLEWs), the effect of Lorentz transformation would decrease both the amount and the region of entanglement.

Research paper thumbnail of Investigating a class of2⊗2⊗dbound entangled density matrices via linear and nonlinear entanglement witnesses constructed by exact convex optimization

Research paper thumbnail of Correlation Dynamics of Three-Qubit System Under a Classical Dephasing Environment

International Journal of Theoretical Physics, 2013

By starting from the stochastic Hamiltonian of the three correlated spins and modeling their freq... more 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.

Research paper thumbnail of Spin–Momentum Correlation in Relativistic Single-Particle Quantum States

International Journal of Quantum Information, 2010

This paper is concerned with the spin–momentum correlation in single-particle quantum states, whi... more This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.

Research paper thumbnail of Electric Field Effects on Quantum Correlations in Three Coupled Semiconductor Quantum Dots

International Journal of Quantum Information, 2013

We study the effect of external electric bias on the quantum correlations in the array of optical... more We study the effect of external electric bias on the quantum correlations in the array of optically excited three coupled semiconductor quantum dots. The correlations are characterized by the quantum discord and concurrence and are observed using excitonic qubits. We employ the lower bound of concurrence for thermal density matrix at different temperatures. The effect of the Förster interaction on correlations will be studied. Our theoretical model detects nonvanishing quantum discord when the electric field is on while concurrence dies, ensuring the existence of nonclassical correlations as measured by the quantum discord.

Research paper thumbnail of Detecting some three-qubit MUB diagonal entangled states via nonlinear optimal entanglement witnesses

The European Physical Journal D, 2008

Research paper thumbnail of Quantum discord evolution of three-qubit states under noisy channels

The European Physical Journal D, 2012

We investigated the dissipative dynamics of quantum discord for correlated qubits under Markovian... more 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.

Research paper thumbnail of Quantum correlations of Two-Qubit XXZ Heisenberg Chain with Dzyaloshinsky-Moriya interaction coupled to bath spin as non-Markovian environment

We consider the quantum correlations (entanglement and quantum discord) dynamics of two coupled s... more We consider the quantum correlations (entanglement and quantum discord) dynamics of two coupled spin qubits with Dzyaloshinsky-Moriya interaction influenced by a locally external magnetic field along z-direction and coupled to bath spin-1 2 particles as independent non-Markovian environment. We find that with increasing D z and decreasing J z , the value of entanglement and quantum discord increase for both antiferromagnetic and ferromagnetic materials. Not that, this growth is more for the ferromagnetic materials. In addition, we perceive that entanglement and quantum discord decrease with increased temperature and increased coupling constants between reduced system and bath. But, strong quantum correlations within the spins of bath reduce decoherence effects. We discuss about type of the constituent material of the central spins that it can speedup the quantum information processing and as a result, we perceive that one can improve and control the quantum information processing with correct selection of the properties of the reduced system (J, J z , D z).