Separability of entangled qutrits in noisy channels

Chęcińska, Agata; Wódkiewicz, K.

doi:10.1103/physreva.76.052306

Cited by 31 publications

(24 citation statements)

References 27 publications

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“…The same value is reported in, e.g., Ref. [13]. The fact that this can be obtained ignoring the condition for admissible n's is a surprising bonus.…”

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confidence: 83%

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Experimentally Friendly Geometrical Criteria for Entanglement

et al. 2008

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A simple geometrical criterion gives experimentally friendly sufficient conditions for entanglement. Its generalization gives a necessary and sufficient condition. It is linked with a family of entanglement identifiers, which is strictly richer than the family of entanglement witnesses.PACS numbers: 03.65.Ud Entanglement is one of the basic features of quantum physics and it is a resource for quantum information science [1]. Thus, detection of entanglement belongs to the mainstream of this field [2]. Today, the most widely used and experimentally feasible detectors of this resource are entanglement witnesses [3]. They are linked with positive but not completely positive maps [4], which are the most universal entanglement identifiers.We present an alternative approach to entanglement detection. It is rooted in an elementary geometrical fact: if a scalar product of two real vectors s and e satisfies s · e < e · e, then s = e. This fact was used in, e.g., [5] to derive a powerful series of Bell inequalities, and in [6] it led to sufficient condition for entanglement. Here, it inspires a new family of entanglement identifiers, which are naturally expressed in terms of the correlation functions [7], easily determined by local measurements. This makes them friendly to experiments. The family of our identifiers is richer than the family of the entanglement witnesses and leads to a necessary and sufficient criterion for entanglement.The bulk of our presentation uses systems of many spin-1 2 particles (qubits), but the method is applicable to composite systems of arbitrary dimensions. For that in our formulae, one needs to substitute Pauli operators by their Gell-Mann-type generalizations. This allows a complete separability analysis of a multi-partite state, and will be illustrated by an example. Even if the underlying system consists of many qubits, analysis of the so-called k-separability (k < N ) requires identification of entanglement in the system partitioned into k parts only [8]. Clearly, at least one part will contain two or more qubits, and can be considered as a multi-level system.

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“…The same value is reported in, e.g., Ref. [13]. The fact that this can be obtained ignoring the condition for admissible n's is a surprising bonus.…”

supporting

confidence: 83%

“…The admissible vectors n obey an additional condition, see e.g. [13]. A state of two qutrits can be expressed in the operator basis made of tensor products of Gell-Mann operators (including the unit operators).…”

mentioning

confidence: 99%

Experimentally Friendly Geometrical Criteria for Entanglement

et al. 2008

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“…For example, the transposition map can be implemented as Following [31] (see also [32], QI package provides a definition of a spontaneous emission channel for a three-level system (qutrit).…”

Section: Quantum Channelsmentioning

confidence: 99%

Singular Value Decomposition and Matrix Reorderings in Quantum Information Theory

Miszczak

2011

Int. J. Mod. Phys. C

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We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyse the correspondence between quantum states and operations with the help of Jamio lkowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations we utilize a package for the Mathematica computing system implementing basic functions used in the calculations related to quantum information theory.

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“…This phenomenon is called entanglement sudden death (ESD). The surprising phenomenon of ESD, contrary to intuition which is based on experience about qubit decoherence, has attracted much attention recently [7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

The sudden death of entanglement in constructed Yang–Baxter systems

Sun

Xue

2009

Quantum Inf Process

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Some Hamiltonians are constructed from the unitaryŘ i,i+1 (θ, ϕ)-matrices, where θ and ϕ are time-independent parameters. We show that the entanglement sudden death (ESD) can happen in these closed Yang-Baxter systems. It is found that the ESD is not only sensitive to the initial condition, but also has a great connection with different Yang-Baxter systems. Especially, we find that the meaningful parameter ϕ has a great influence on ESD.

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Separability of entangled qutrits in noisy channels

Cited by 31 publications

References 27 publications

Experimentally Friendly Geometrical Criteria for Entanglement

Experimentally Friendly Geometrical Criteria for Entanglement

Singular Value Decomposition and Matrix Reorderings in Quantum Information Theory

The sudden death of entanglement in constructed Yang–Baxter systems

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