arXiv subjects

Sayyed Yahya Mirafzali

Publications and source records attributed to Sayyed Yahya Mirafzali.

8 recordsLinked to original sources

arXiv2019

Markovianity of the reference state, complete positivity of the reduced dynamics, and monotonicity of the relative entropy

Consider the set $\mathcal{S}=\lbraceρ_{SE}\rbrace$ of possible initial states of the system-environment, steered from a tripartite reference state $ω_{RSE}$. Buscemi [F. Buscemi, Phys. Rev. Lett. 113, 140502 (2014)] showed that the reduced dynamics of the system, for each $ρ_{S}\in \mathrm{Tr}_{E}\mathcal{S}$, is always completely positive if and only if $ω_{RSE}$ is a Markov state. There, during the proof, it has been assumed that the dimensions of the system and the environment can vary through the evolution. Here, we show that this assumption is necessary: we give an example for which, though $ω_{RSE}$ is not a Markov state, the reduced dynamics of the system is completely positive, for any evolution of the system-environment during which the dimensions of the system and the environment remain unchanged. As our next result, we show that the result of Muller-Hermes and Reeb [A. Muller-Hermes and D. Reeb, Ann. Henri Poincare 18, 1777 (2017)], of monotonicity of the quantum relative entropy under positive maps, cannot be generalized to the Hermitian maps, even within their physical domains.

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arXiv2018

When the assignment map is completely positive

Finding the general set of system-environment states for which the reduced dynamics of the system is completely positive (CP) is the subject of some recent works. An advance in this context appeared in [X. Lu, Phys. Rev. A 93, 042332 (2016)], where the problem has been solved for the case of CP assignment map. Here, we restate this result using the framework introduced in [J. M. Dominy et al., Quantum Inf. Process. 15, 465 (2016)]. This, we think, clarifies the mentioned result better and so leads to a generalization of it, straightforwardly.

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arXiv2018

Entanglement increase from local interaction in the absence of initial quantum correlation in the environment and between the system and the environment

We consider a bipartite quantum system S=AB such that the part A is isolated from the environment E and only the part B interacts with E. Under such circumstances, entanglement of the system may experience decreases and increases, during the evolution of the system. Here, we show that the entanglement of the system can exceed its initial value, under such local interaction, even though, at the initial moment, there is no entanglement in the environment and the system and the environment are only classically correlated. The case which is studied in this paper possesses another interesting feature too: The reduced dynamics of the system can be modeled as a completely positive map. In addition, we introduce the concept of inaccessible entanglement to explain why entanglement can exceed its initial value, under local interactions, in open quantum systems.

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arXiv2017

Structure of states for which each localized dynamics reduces to a localized subdynamics

We consider a bipartite quantum system $S$ (including parties $A$ and $B$), interacting with an environment $E$ through a localized quantum dynamics $\mathcal{F}_{SE}$ . We call a quantum dynamics $\mathcal{F}_{SE}$ localized if, e.g., the party $A$ is isolated from the environment and only $B$ interacts with the environment: $\mathcal{F}_{SE}=id_{A}\otimes \mathcal{F}_{BE}$, where $id_{A}$ is the identity map on the part $A$ and $\mathcal{F}_{BE}$ is a completely positive (CP) map on the both $B$ and $E$. We will show that the reduced dynamics of the system is also localized as $\mathcal{E}_{S}=id_{A}\otimes \bar{\mathcal{E}}_{B}$, where $\bar{\mathcal{E}}_{B}$ is a CP map on $B$, if and only if the initial state of the system-environment is a Markov state. We then generalize this result to the two following cases: when both $A$ and $B$ interact with a same environment, and when each party interacts with its local environment.

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arXiv2011

Measurement-induced nonlocality for an arbitrary bipartite state

Measurement-induced nonlocality is a measure of nonlocalty introduced by Luo and Fu [Phys. Rev. Lett \textbf{106}, 120401 (2011)]. In this paper, we study the problem of evaluation of Measurement-induced nonlocality (MIN) for an arbitrary $m\times n$ dimensional bipartite density matrix $ρ$ for the case where one of its reduced density matrix, $ρ^{a}$, is degenerate (the nondegenerate case was explained in the preceding reference). Suppose that, in general, $ρ^{a}$ has $d$ degenerate subspaces with dimension $m_{i} (m_{i} \leq m, i=1, 2, ..., d)$. We show that according to the degeneracy of $ρ^{a}$, if we expand $ρ$ in a suitable basis, the evaluation of MIN for an $m\times n$ dimensional state $ρ$, is degraded to finding the MIN in the $m_{i}\times n$ dimensional subspaces of state $ρ$. This method can reduce the calculations in the evaluation of MIN. Moreover, for an arbitrary $m\times n$ state $ρ$ for which $m_{i}\leq 2$, our method leads to the exact value of the MIN. Also, we obtain an upper bound for MIN which can improve the ones introduced in the above mentioned reference. In the final, we explain the evaluation of MIN for $3\times n$ dimensional states in details.

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arXiv2011

Measurable lower bounds on concurrence

We derive measurable lower bounds on concurrence of arbitrary mixed states, for both bipartite and multipartite cases. First, we construct measurable lower bonds on the purely algebraic bounds of concurrence [F. Mintert et al. (2004), Phys. Rev. lett., 92, 167902]. Then, using the fact that the sum of the square of the algebraic bounds is a lower bound of the squared concurrence, we sum over our measurable bounds to achieve a measurable lower bound on concurrence. With two typical examples, we show that our method can detect more entangled states and also can give sharper lower bonds than the similar ones.

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arXiv2010

Factorization Law for Two Lower Bounds of Concurrence

We study the dynamics of two lower bounds of concurrence in bipartite quantum systems when one party goes through an arbitrary channel. We show that these lower bounds obey the factorization law similar to that of [Konrad et al., Nat. Phys. 4, 99 (2008)]. We also, discuss the application of this property, in an example.

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arXiv2008

Thermal entanglement in a two-qutrit system with nonlinear coupling under nonuniform external magnetic field

We study the thermal entanglement of a 2-qutrit spin chain with nonlinear coupling in the presence of nonuniform magnetic field. Thermal entanglement of an arbitrary (finite dimensional) m-partite system vanishes at some finite threshold temperature T_s. We investigate the dependence of T_s on the system's parameters, i.e. the nonlinear coupling and the magnetic field, for this 2-qutrit system. In addition, we compare two lower bounds of I-concurrence for this system and also study its dense coding capacity as a function of system's parameters.

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