q-entropies and the entanglement dynamics of two-qubits interacting with an environment

Hamadou-Ibrahim, A.; Plastino, A.; Plastino, A.

doi:10.1590/s0103-97332009000400010

Cited by 8 publications

(5 citation statements)

References 38 publications

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“…The recent study by Bellomo et al [12] of the violation of Bell inequalities by two qubits interacting with an environment constituted a notable contribution, within the context of the entanglement dynamics of open systems, to the above-mentioned line of inquiry. On a similar vein, nonclassical entropic inequalities satisfied by the time-dependent state of two qubits evolving according to (5) was examined in [15].…”

Section: Behavior Of Some Entanglement Indicators For Two-qubits Statesmentioning

confidence: 99%

“…The amount of entanglement between the different constituent parts of a multi-partite quantum system tends to decrease as the alluded composite system undergoes decoherence. This decay of entanglement has recently attracted the interest of many researchers [8][9][10][11][12][13][14][15][16][17] because it constitutes one of the most difficult obstacles that have to be overcome to develop quantum technologies requiring the controlled manipulation of entangled states [3]. A remarkable recent discovery is that, in some cases, entanglement can disappear completely in finite times.…”

Section: Introductionmentioning

confidence: 99%

“…A remarkable recent discovery is that, in some cases, entanglement can disappear completely in finite times. This effect is known as entanglement sudden death (ESD) [8][9][10][11][12][13][14][15] and has been observed experimentally by Almeida et al [16]. Besides its theoretical importance, ESD is also a phenomenon of considerable relevance from the practical point of view because the actual implementation of quantum computation and other quantum information tasks crucially depends on the longevity of entanglement in multi-qubit systems.…”

Section: Introductionmentioning

confidence: 99%

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Some entanglement features exhibited by two, three and four qubits interacting with an environment in a non-Markovian regime

Hamadou-Ibrahim¹,

Plastino²,

Zander³

2010

J. Phys. A: Math. Theor.

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We explore various aspects of the quantum entanglement dynamics of systems of two, three and four qubits interacting with an environment at zero temperature in a non-Markovian regime, as described by the paradigmatic model recently studied by Bellomo, Lo Franco, and Compagno [Bellomo et al. Phys. Rev. Lett. 99 (2007) 160502]. We consider important families of initial states for the alluded systems. The average, typical entanglement evolution associated with each of these families is determined, and its relation with the evolution of the global degree of mixedness of the multi-qubit system is explored. For three and four qubits we consider the family of initial states equivalent under local unitary transformations to the |GHZ and |W states, and compare their average behavior with the average behavior exhibited by initial maximally entangled twoqubits states. Furthermore, in the case of two qubits, the evolution of other manifestations of entanglement, related to measurable quantities, is also investigated. In particular, we consider the Mintert-Buchleitner concurrence lower bound and an entanglement indicator based upon the violation of local uncertainty relations.

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Section: Behavior Of Some Entanglement Indicators For Two-qubits Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Some entanglement features exhibited by two, three and four qubits interacting with an environment in a non-Markovian regime

Hamadou-Ibrahim¹,

Plastino²,

Zander³

2010

J. Phys. A: Math. Theor.

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“…A particularly interesting feature of this process, first pointed out by Zyczkowski and the Horodeckis in a pioneering effort almost ten years ago [21], is that sometimes entanglement vanishes completely in a finite time. This remarkable phenomenon, known as entanglement sudden death (ESD), has been the subject of several theoretical and experimental studies [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Typical Behavior of the Global Entanglement of an Open Multiqubit System in a Non-Markovian Regimen

Majtey

Plastino

2012

Int. J. Quantum Inform.

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We investigate the decay of the global entanglement, due to decoherence, of multiqubit systems interacting with a reservoir in a non-Markovian regime. We assume that during the decoherence process each qubit of the system interacts with its own, independent environment. Most previous works on this problem focused on particular initial states or families of initial states amenable of analytical treatment. Here we determine numerically the typical, average behavior of the system corresponding to random initial pure states uniformly distributed (in the whole Hilbert space of n-qubit pure states) according to the Haar measure. We study systems consisting of 3, 4, 5, and 6 qubits. In each case we consider also the entanglement dynamics corresponding to important particular initial states, such as the GHZ states or multiqubit states maximizing the global entanglement, and determine in which cases any of these states is representative of the average behavior associated with general initial states.

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“…H q plays a fundamental role in recent developments of statistical mechanics [15][16][17][18]20]. The generalization has indeed received a lot of attention in the last years, with about 2000 papers containing interesting results and useful applications, many of them in the complex systems' area [15][16][17][18]20] but also in connection with a variegated family of quantum mechanical settings (see, for example [21][22][23][24][25][26][27][28][29][30][31][32]). In what follows we retrace the developments of Ref.…”

Section: Introductionmentioning

confidence: 99%

New features of quantum discord uncovered by q-entropies

Majtey,

Plastino,

Plastino

2011

Preprint

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The notion of quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett 88, 017901 (2001)] (see also Henderson and Vedral [J. Phys. A 34, 6899 (2001)]) has attracted increasing attention, in recent years, as an entropic quantifier of non-classical features pertaining to the correlations exhibited by bipartite quantum systems. Here we generalize the notion so as to encompass powerlaw q-entropies (that reduce to the standard Shannon entropy in the limit q → 1) and study the concomitant consequences. The ensuing, new discord-like measures we advance describe aspects of non-classicality that are different from those associated with the standard quantum discord. A particular manifestation of this difference concerns a feature related to order. Let D1 stand for the standard, Shannon-based discord measure and Dq for the q = 1 one. If two quantum states A, B are such that D1(A) > D1(B), this order-relation does not remain invariant under a change from D1 to Dq.

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q-entropies and the entanglement dynamics of two-qubits interacting with an environment

Cited by 8 publications

References 38 publications

Some entanglement features exhibited by two, three and four qubits interacting with an environment in a non-Markovian regime

Some entanglement features exhibited by two, three and four qubits interacting with an environment in a non-Markovian regime

Typical Behavior of the Global Entanglement of an Open Multiqubit System in a Non-Markovian Regimen

New features of quantum discord uncovered by q-entropies

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