Detecting some three-qubit MUB diagonal entangled states via nonlinear optimal entanglement witnesses

@article{Jafarizadeh2008DetectingST,
  title={Detecting some three-qubit MUB diagonal entangled states via nonlinear optimal entanglement witnesses},
  author={M. Jafarizadeh and M. Mahdian and A. Heshmati and K. Aghayar},
  journal={The European Physical Journal D},
  year={2008},
  volume={50},
  pages={107-121}
}
The three qubits mutually unbiased bases (MUB) diagonal density matrices with maximally entanglement in Greenberger-Horne-Zeilinger (GHZ) basis are studied. These are a natural generalization of Bell-state diagonal density matrices. The linearity of positive partial transpose (PPT) conditions allows one to specify completely PPT states or feasible region (FR) which form a polygon, where the projection of the feasible region to some two dimensional planes has lead to better visualization. To… Expand
8 Citations

Tables from this paper

Nonlinear entanglement witnesses for four qubits in mutually unbiased bases
Entanglement witness is a Hermitian operator that is useful for detecting the genuine multipartite entanglement of mixed states. Nonlinear entanglement witnesses have the advantage of a widerExpand
Entanglement witnesses for families of the bound entangled three-qubit states
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 moreExpand
Beating detection loophole in nonlinear entanglement witnesses
Detectors in the laboratory are often unlike their ideal theoretical cousins. They have non-ideal efficiencies, which may then lead to non-trivial implications. We show how it is possible to predictExpand
Measurement-device-independent nonlinear entanglement witnesses
Entanglement witnesses are one of the most effective methods to detect entanglement. It is known that nonlinear entanglement witnesses provide better entanglement detection than their linearExpand
Optimization of device-independent witnesses of entanglement depth from two-body correlators
In a recent work [A. Aloy et al., Phys. Rev. Lett. 123, 100507 (2019)] we have considered the characterization of entanglement depth, from a device-independent perspective, in a quantum many-bodyExpand
General algorithm for manipulating nonlinear and linear entanglement witnesses by using exact convex optimization
We consider the problem of obtaining the entanglement witnesses for a given quantum system. We present a method to convert this problem to a standard convex optimization problem by defining aExpand
Entanglement classification in the noninteracting Fermi gas
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 onExpand
Relativistic entanglement in single-particle quantum states using non-linear entanglement witnesses
TLDR
It is shown that by using Non-Linear entanglement witnesses (NLEWs), the effect of Lorentz transformation would decrease both the amount and the region ofEntanglement. Expand

References

SHOWING 1-10 OF 68 REFERENCES
Investigating a class of 2⊗2⊗d bound entangled density matrices via linear and nonlinear entanglement witnesses constructed by exact convex optimization
Here we consider a class of $2\otimes2\otimes d$ chessboard density matrices starting with three-qubit ones which have positive partial transposes with respect to all subsystems. To investigate theExpand
Local transformation of mixed states of two qubits to Bell diagonal states
The optimal entanglement manipulation for a single copy of mixed states of two qubits is to transform it to a Bell diagonal state. In this paper we derive an explicit form of the local operation thatExpand
Bell-state diagonal entanglement witnesses for relativistic and nonrelativistic multispinor systems in arbitrary dimensions
Two kinds of Bell-state diagonal (BSD) entanglement witnesses (EWs) are constructed by using the algebra of Dirac $\ensuremath{\gamma}$ matrices in a space-time of arbitrary dimension $d$, where theExpand
Manipulating multiqudit entanglement witnesses by using linear programming
A class of entanglement witnesses (EWs) called reduction-type entanglement witnesses is introduced, which can detect some multipartite entangled states including positive partial transpose ones withExpand
Mutually unbiased phase states, phase uncertainties, and Gauss sums
Abstract.Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to $1/\sqrt{d}$, with d the dimension of theExpand
Multi-qubit stabilizer and cluster entanglement witnesses
Abstract.One of the problems concerning entanglement witnesses (EWs) is the construction of them by a given set of operators. Here several multi-qubit EWs called stabilizer EWs are constructed byExpand
Bell-state diagonal-entanglement witnesses
It has been shown that finding generic Bell-state diagonal-entanglement witnesses for d{sub 1}xd{sub 2}x{center_dot}{center_dot}{center_dot}xd{sub n} systems reduces to linear programming if theExpand
Mixed-state entanglement and quantum error correction.
TLDR
It is proved that an EPP involving one-way classical communication and acting on mixed state M (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa, and it is proved Q is not increased by adding one- way classical communication. Expand
Classification of mixed three-qubit states.
TLDR
A classification of mixed three-qubit states is introduced, in which the classes of separable, biseparable, W, and Greenberger-Horne-Zeilinger states are successively embedded into each other. Expand
Generalized qudit Choi maps
Following the linear programming prescription of Jafarizadeh et al. [Phys. Rev. A 72, 062106 (2005)], the $d\ensuremath{\bigotimes}d$ Bell diagonal entanglement witnesses are provided. By usingExpand
...
1
2
3
4
5
...