Investigating a class of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>⊗</mml:mo><mml:mn>2</mml:mn><mml:mo>⊗</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math>bound entangled density matrices via linear and nonlinear entanglement witnesses constructed by exact convex optimization

Jafarizadeh, M. A.; Akbari, Y.; Aghayar, K.; Heshmati, A.; Mahdian, M.

doi:10.1103/physreva.78.032313

Cited by 12 publications

(8 citation statements)

References 43 publications

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“…On the other hand, finding the best measurements is one of the significant challenges in quantum computing. Optimal measurements have been used in many context, such as quantum discrimination [2], quantum entanglement [3][4][5], quantum teleportation [6], and superdense coding [7], also in the calculation of quantum correlation [1,[8][9][10][11][12]. We know that quantum correlations play a very critical role in quantum information and computation.…”

Section: Introductionmentioning

confidence: 99%

Toward a quantum computing algorithm to quantify classical and quantum correlation of system states

Mahdian,

Yeganeh

2021

Preprint

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Optimal measurement is required to obtain the quantum and classical correlations of a quantum state, and the crucial difficulty is how to acquire the maximal information about one system by measuring the other part; in other words, getting the maximum information corresponds to preparing the best measurement operators. Within a general setup, we designed a variational hybrid quantum-classical (VHQC) algorithm to achieve classical and quantum correlations for system states under the Noisy-Intermediate Scale Quantum (NISQ) technology. To employ, first, we map the density matrix to the vector representation, which displays it in a doubled Hilbert space, and it's converted to a pure state. Then we apply the measurement operators to a part of the subsystem and use variational principle and a classical optimization for the determination of the amount of correlation. We numerically test the performance of our algorithm at finding a correlation of some density matrices, and the output of our algorithm is compatible with the exact calculation.

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Section: Introductionmentioning

confidence: 99%

Toward a quantum computing algorithm to quantify classical and quantum correlation of system states

Mahdian,

Yeganeh

2021

Preprint

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“…Here, following the method of [11] and [12], we construct entanglement witnesses for three-qubit states. The witnesses have relatively simple structures, but they are nevertheless capable to detect a number of bound entangled states more effectively.…”

Section: Introductionmentioning

confidence: 99%

Entanglement witnesses for families of the bound entangled three-qubit states

Akbari-Kourbolagh

Azhdargalam

2018

Int. J. Quantum Inform.

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We construct three-qubit entanglement witnesses with relatively simple structures. Despite their simplicity, these witnesses are capable of detecting a number of bound entangled states more effectively. To illustrate this, two families of bound entangled three-qubit states, introduced by Kay [Phys. Rev. A 83, 020303 (2011)] and Kye [J. Phys. A: Math. Theor. 48, 235303 (2015)], are considered and it is shown that these witnesses are able to detect the entanglement of all states in the families.

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“…The entanglement of is detected by EW if and only if TrðW Þ 0. [23][24][25][26][27] The characterization of multipartite entanglement is very important in all physical systems specially in solid state models. Researchers are interested for studying the entanglement in the solid state models.…”

Section: Introductionmentioning

confidence: 99%

Entanglement classification in the noninteracting Fermi gas

Jafarizadeh

Eghbalifam

Nami

et al. 2017

Int. J. Quantum Inform.

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In this paper, entanglement classification shared among the spins of localized fermions in the noninteracting Fermi gas is studied. It is proven that the Fermi gas density matrix is block diagonal on the basis of the projection operators to the irreducible representations of symmetric group [Formula: see text]. Every block of density matrix is in the form of the direct product of a matrix and identity matrix. Then it is useful to study entanglement in every block of density matrix separately. The basis of corresponding Hilbert space are identified from the Schur–Weyl duality theorem. Also, it can be shown that the symmetric part of the density matrix is fully separable. Then it has been shown that the entanglement measure which is introduced in Eltschka et al. [New J. Phys. 10, 043104 (2008)] and Guhne et al. [New J. Phys. 7, 229 (2005)], is zero for the even [Formula: see text] qubit Fermi gas density matrix. Then by focusing on three spin reduced density matrix, the entanglement classes have been investigated. In three qubit states there is an entanglement measure which is called 3-tangle. It can be shown that 3-tangle is zero for three qubit density matrix, but the density matrix is not biseparable for all possible values of its parameters and its eigenvectors are in the form of W-states. Then an entanglement witness for detecting non-separable state and an entanglement witness for detecting nonbiseparable states, have been introduced for three qubit density matrix by using convex optimization problem. Finally, the four spin reduced density matrix has been investigated by restricting the density matrix to the irreducible representations of [Formula: see text]. The restricted density matrix to the subspaces of the irreducible representations: [Formula: see text], [Formula: see text] and [Formula: see text] are denoted by [Formula: see text], [Formula: see text] and [Formula: see text], respectively. It has been shown that some highly entangled classes (by using the results of Miyake [Phys. Rev. A 67, 012108 (2003)] for entanglement classification) do not exist in the blocks of density matrix [Formula: see text] and [Formula: see text], so these classes do not exist in the total Fermi gas density matrix.

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Investigating a class of2⊗2⊗dbound entangled density matrices via linear and nonlinear entanglement witnesses constructed by exact convex optimization

Cited by 12 publications

References 43 publications

Toward a quantum computing algorithm to quantify classical and quantum correlation of system states

Toward a quantum computing algorithm to quantify classical and quantum correlation of system states

Entanglement witnesses for families of the bound entangled three-qubit states

Entanglement classification in the noninteracting Fermi gas

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