Entanglement for a two-parameter class of states in 2  <i>n</i>quantum system

Pyo, Dong; Lee, Soojoon

doi:10.1088/0305-4470/36/45/010

Cited by 30 publications

(41 citation statements)

References 19 publications

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“…This recovers previous results obtained by the authors in [19], where Λ = max[ ρ TA , R(ρ) ], and others in [29], where Λ = ρ TA . In addition Eq.…”

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confidence: 91%

Entanglement of Formation of Bipartite Quantum States

2005

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We give an explicit tight lower bound for the entanglement of formation for arbitrary bipartite mixed states by using the convex hull construction of a certain function. This is achieved by revealing a novel connection among the entanglement of formation, the well-known Peres-Horodecki and realignment criteria. The bound gives a quite simple and efficiently computable way to evaluate quantitatively the degree of entanglement for any bipartite quantum state.PACS numbers: 03.67. Mn, 03.65.Ud, 89.70.+c Quantum entangled states are used as key resources in quantum information processing and communication, such as in quantum cryptography, quantum teleportation, dense coding, error correction and quantum computation [1]. A fundamental problem in quantum information theory is how to quantify the degree of entanglement in a practical and operational way [2,3]. One of the most meaningful and physically motivated measures is the entanglement of formation (EOF) [2,3], which quantifies the minimal cost needed to prepare a certain quantum state in terms of EPR pairs. Related to the EOF the behavior of entanglement has recently been shown to play important roles in quantum phase transition for various interacting quantum many-body systems [4] and may significantly affect macroscopic properties of solids [5]. Moreover, it has been shown that there is a remarkable connection between entanglement and the capacity of quantum channels [6]. A quantitative evaluation of EOF is thus of great significance both theoretically and experimentally.Considerable efforts have been spent on deriving EOF or its lower bound through analytical and numerical approaches, for some limited sets of mixed states [7,8,9,10,11,12,13,14,15,16,17]. Among them, the most noteworthy results are an elegant analytical formula for two qubits [7,8] [18,19] in giving analytic lower bounds [that can be optimized further numerically [18]] for the concurrence, which permits to furnish a lower bound of EOF for a generic mixed state. However, this lower bound is not explicit except for the case of 2 ⊗ n systems [19]. For low dimensional systems, numerical methods [10] can be used to estimate EOF. Nevertheless, they are generally time-consuming and often not very efficient. The notorious difficulty of evaluation for EOF is due to the complexity to solve a high dimensional optimization problem, which becomes a formidable task, as the dimensionality of the Hilbert space grows.In this Letter, we present the first analytical calculation of a tight lower bound of EOF for arbitrary bipartite quantum states. An explicit expression for the bound is obtained from the convex hull of a simple function, based on a known result in [9]. This is achieved by establishing a key connection between EOF and two strong separability criteria, the Peres-Horodecki criterion [20,21] and the realignment criterion [22,23]. The bound is shown to be exact for some special states such as isotropic states [9,24] and permits to provide EOF estimations for many bound entangled states (BES). It provi...

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“…This recovers previous results obtained by the authors in [19], where Λ = max[ ρ TA , R(ρ) ], and others in [29], where Λ = ρ TA . In addition Eq.…”

supporting

confidence: 91%

Entanglement of Formation of Bipartite Quantum States

2005

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“…We outline here the main arguement from Ref. [33]. It was shown that there exist unitary operators U k and probabilities p k such that…”

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confidence: 94%

Quantum discord for a two-parameter class of states in 2⊗dquantum systems

Ali¹

2010

J. Phys. A: Math. Theor.

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Abstract.Quantum discord witnesses the nonclassicality of quantum states even when there is no entanglement in these quantum states. This type of quantum correlation also has some interesting and significant applications in quantum information processing. Quantum discord has been evaluated explicitly only for certain class of two-qubit states. We extend the previous studies to 2 ⊗ d quantum systems and derive an analytical expression for quantum discord for a two-parameter class of states for d ≥ 3. We compare quantum discord, classical correlation, and entanglement for qubit-qutrit systems to demonstrate that different measures of quantum correlation are not identical and conceptually different.

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“…The class of quantum states with two real parameters α and γ in a 2 ⊗ d quantum system [50] is given as…”

Section: Two Parameter Class Of Statesmentioning

confidence: 99%

Qubit-Qutrit (2 ⊗ 3) Quantum Systems: an Investigation of Some Quantum Correlations Under Collective Dephasing

Ali

2019

Braz J Phys

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We revisit qubit-qutrit quantum systems under collective dephasing and answer some of the questions which have not been asked and addressed so far in the literature. In particular, we examine the possibilities of non-trivial phenomena of time-invariant entanglement and freezing dynamics of entanglement for this dimension of Hilbert space. Interestingly, we find that for qubit-qutrit systems both of these peculiar features coexist, that is, we observe not only time-invariant entanglement for certain quantum states but we find also find evidence that many quantum states freeze their entanglement after decaying for some time. To our knowledge, the existance of both these phenomena for one dimension of Hilbert space is not found so far. All previous studies suggest that if there is freezing dynamics of entanglement, then there is no time-invariant entanglement and vice versa. In addition, we study local quantum uncertainity and other correlations for certain families of states and discuss the interesting dynamics. Our study is an extension of similar studies for qubit-qubit systems, qubit-qutrit, and multipartite quantum systems.

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Entanglement for a two-parameter class of states in 2 nquantum system

Cited by 30 publications

References 19 publications

Entanglement of Formation of Bipartite Quantum States

Entanglement of Formation of Bipartite Quantum States

Quantum discord for a two-parameter class of states in 2⊗dquantum systems

Qubit-Qutrit (2 ⊗ 3) Quantum Systems: an Investigation of Some Quantum Correlations Under Collective Dephasing

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