Maximally genuine multipartite entangled mixed X-states of<i>N</i>-qubits

Mendonça, Paulo E. M. F.; Rafsanjani, Seyed Mohammad Hashemi; Galetti, D.; Marchiolli, Marcelo A.

doi:10.1088/1751-8113/48/21/215304

Cited by 9 publications

(16 citation statements)

References 69 publications

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“…[24] for a discussion on spin-tunneling processes involving an original version of the aforementioned model, where now the discrete Husimi function has been extensively used. Moreover, the active and fruitful field of research on N-qubit X-states [71] represents, nowadays, an interesting scenario of possible applications for discrete Wigner function where the study on maximally genuine multipartite entangled mixed states will take place [72].…”

Section: Discussionmentioning

confidence: 99%

On the discrete Wigner function for $\mathrm{SU(N)}$

Marchiolli¹,

Galetti²

2019

J. Phys. A: Math. Theor.

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We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group SU(N). This general mathematical construction provides a sound pathway to the formulation of a genuinely discrete Wigner function for arbitrary quantum systems described by finite-dimensional state vector spaces. To illustrate our results, we obtain a general discrete Wigner function for the group SU(3) and apply this to the study of a particular three-level system. Moreover, we also discuss possible extensions to the discrete Husimi and Glauber-Sudarshan functions, as well as future investigations on multipartite quantum states.

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Section: Discussionmentioning

confidence: 99%

On the discrete Wigner function for $\mathrm{SU(N)}$

Marchiolli¹,

Galetti²

2019

J. Phys. A: Math. Theor.

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“…For z ∈ C 4 , we will define z σ = (z σ(1) , z σ(2) , z σ(3) , z σ(4) ) ∈ C 4 . It is clear by definition that z σ X = z X when σ is one of the following eight permutations: (15) 1234 , 1324 , 4231 , 4321 , 2143 , 2413 , 3142 , 3412 .…”

Section: Norms Arising From Separability Problemmentioning

confidence: 99%

Separability criterion for three-qubit states with a four dimensional norm

Chen

Han

Kye

2017

J. Phys. A: Math. Theor.

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PAPERSeparability criterion for three-qubit states with a four dimensional norm AbstractWe give a separability criterion for three qubit states in terms of diagonal and anti-diagonal entries. This gives us a complete characterization of separability when all the entries are zero except for diagonal and anti-diagonals. The criterion is expressed in terms of a norm arising from anti-diagonal entries. We compute this norm in several cases, so that we get criteria with which we can decide the separability by routine computations.

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“…Those states arise naturally in quantum information theory in various aspects. See [1,26,29,30,31,32] for example. Notable examples include Greenberger-Horne-Zeilinger diagonal states, which are mixtures of GHZ states with noises.…”

Section: Introductionmentioning

confidence: 99%

The role of phases in detecting three-qubit entanglement

Han

Kye

2017

Journal of Mathematical Physics

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Abstract. We propose separability criteria for three-qubit states in terms of diagonal and anti-diagonal entries to detect entanglement with positive partial transposes. We report that the phases, that is, the angular parts of anti-diagonal entries, play a crucial role in determining whether a given three-qubit state is separable or entangled, and they must obey even an identity for separability in some cases. These criteria are strong enough to detect PPT (positive partial transpose) entanglement with nonzero volume. In several cases when all the entries are zero except for diagonal and anti-diagonal entries, we characterize separability using phases. These include the cases when anti-diagonal entries of such states share a common magnitude, and when ranks are less than or equal to six. We also compute the lengths of rank six cases, and find three-qubit separable states with lengths 8 whose maximum ranks of partial transposes are 7.

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Maximally genuine multipartite entangled mixed X-states ofN-qubits

Cited by 9 publications

References 69 publications

On the discrete Wigner function for $\mathrm{SU(N)}$

On the discrete Wigner function for $\mathrm{SU(N)}$

Separability criterion for three-qubit states with a four dimensional norm

The role of phases in detecting three-qubit entanglement

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