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

Sargolzahi, Iman; Mirafzali, Sayyed Yahya

doi:10.1142/s0219749917500435

Cited by 4 publications

(10 citation statements)

References 14 publications

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“…First, using the results of Refs. [18,19], we have emphasized that the phenomenon of entanglement exceeding in the system, under local interactions with the environment, can occur only when the initial state of the whole system-environment is not a Markov state as Eqs. (6) or (9).…”

Section: Discussionmentioning

confidence: 99%

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

Sargolzahi

Mirafzali

2018

Phys. Rev. A

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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. arXiv:1706.05600v3 [quant-ph]

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Section: Discussionmentioning

confidence: 99%

“…Finding this interesting case is, to some extent, due to our previous results in Refs. [18,19]. Especially, we will use the following result of Ref.…”

Section: Introductionmentioning

confidence: 99%

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

Sargolzahi

Mirafzali

2018

Phys. Rev. A

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“…The strategy employed in this paper is to analyze the states rankwise. Similar approaches have been employed successfully earlier [20][21][22][23][24][25][26][27]; however, there are differences between those works and ours in several aspects. Some of them employ numerical or nondeterministic approach [23,24].…”

Section: Introductionmentioning

confidence: 97%

“…Similar approaches have been employed successfully earlier [20][21][22][23][24][25][26][27]; however, there are differences between those works and ours in several aspects. Some of them employ numerical or nondeterministic approach [23,24]. The very interesting result in [20] that measurements on very few observables are required to determine entanglement of formation, requires joint measurements of subsystems while our approach focusses on local measurements unless absolutely is necessary.…”

Section: Introductionmentioning

confidence: 97%

Optimal observables to determine entanglement of a two qubit state

Chaudhary

Ravishankar

2016

Eur. Phys. J. D

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Experimental determination of entanglement is important not only to characterize the state and use it in quantum information, but also in understanding complicated phenomena such as phase transitions. In this paper we show that in many cases, it is possible to determine entanglement of a two qubit state, as represented by concurrence, with a few observables, most of which are local. In particular, rank 1 and rank 2 states need exclusively measurement of local observables while rank 3 states need measurement of just one correlation observable in addition to local observables. Only the rank 4 states are shown to require a more detailed tomography. The analysis also sheds light on the other measure, non separability since it is a lower bound on concurrence.PACS. PACS-key discribing text of that key -PACS-key discribing text of that key arXiv:1403.5767v4 [quant-ph]

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“…During the proof of the above result in [6], it has been assumed that the dimensions of the Hilbert spaces of the system H S and the environment H E can vary during the system-environment evolution U , in general. In [11], we have questioned whether this assumption can be relaxed or not. In Sec.…”

Section: Introductionmentioning

confidence: 99%

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

Sargolzahi

Mirafzali

2019

Phys. Rev. A

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Consider the set S = {ρSE} of possible initial states of the system-environment, steered from a tripartite reference state ωRSE. Buscemi [F. Buscemi, Phys. Rev. Lett. 113, 140502 (2014)] showed that the reduced dynamics of the system, for each ρS ∈ TrES, is always completely positive if and only if ωRSE 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 ωRSE 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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Structure of states for which each localized dynamics reduces to a localized subdynamics

Cited by 4 publications

References 14 publications

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

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

Optimal observables to determine entanglement of a two qubit state

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

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