Entanglement of four-qubit rank-2 mixed states

Jung, Eylee; Park, DaeKil

doi:10.1007/s11128-015-1039-4

Cited by 2 publications

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“…Two particularly common monotones obtained in this way are the concurrence for two qubits [20,21] and the three-tangle for three qubits [22]. Notably, the convex roof extension of the concurrence can be quantified exactly for any system of two qubits [21], although analytical solutions for the convex roof of the threetangle have been found only in very special cases [23][24][25][26][27][28][29][30][31] and the first insights into the solutions of the even more complicated case of the convex roof of four-qubit polynomial measures have been obtained only recently [32].…”

Section: Introductionmentioning

confidence: 99%

Geometric approach to entanglement quantification with polynomial measures

Regula

Adesso

2016

Phys. Rev. A

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We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach provides insight into the properties of entanglement and allows us to relate different polynomial measures to each other, simplifying their quantification. In particular, unveiling and exploiting the geometric structure of the concurrence for two qubits, we show that the convex roof of any polynomial measure of entanglement can be quantified exactly for all rank-2 states of an arbitrary number of qubits which have only one or two unentangled states in their range. We give explicit examples by quantifying the three-tangle exactly for several representative classes of three-qubit states. We further show how our methods can be used to obtain analytical results for entanglement of more complex states if one can exploit symmetries in their geometric representation.

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Section: Introductionmentioning

confidence: 99%

Geometric approach to entanglement quantification with polynomial measures

Regula

Adesso

2016

Phys. Rev. A

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“…1, 2, 3) and the corresponding linear monotones 5 G (4) j (j = 1, 2, 3) for the rank-2 mixtures consist of one of the maximally entangled state and |W 4 are explicitly computed[27].…”

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confidence: 99%

Testing the monogamy relations via rank-2 mixtures

Jung

Park

2016

Phys. Rev. A

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We introduce two tangle-based four-party entanglement measures t 1 and t 2 , and two negativitybased measures n 1 and n 2 , which are derived from the monogamy relations. These measures are computed for three four-qubit maximally entangled and W states explicitly. We also compute these measures for the rank-2 mixture ρ 4 = p|GHZ 4 GHZ 4 |+(1 − p)|W 4 W 4 | by finding the corresponding optimal decompositions. It turns out that t 1 (ρ 4 ) is trivial and the corresponding optimal decomposition is equal to the spectral decomposition. Probably, this triviality is a sign of the fact that the corresponding monogamy inequality is not sufficiently tight. We fail to compute t 2 (ρ 4 ) due to the difficulty for the calculation of the residual entanglement. The negativity-based measures n 1 (ρ 4 ) and n 2 (ρ 4 ) are explicitly computed and the corresponding optimal decompositions are also derived explicitly. arXiv:1607.00135v2 [quant-ph]

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Entanglement of four-qubit rank-2 mixed states

Cited by 2 publications

References 50 publications

Geometric approach to entanglement quantification with polynomial measures

Geometric approach to entanglement quantification with polynomial measures

Testing the monogamy relations via rank-2 mixtures

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