Construct New Form of Maximally Nine-Qubit Entangled State Via Recurrence Relation

Che, Junling; Zhao, Peilin; Wen, Feng

doi:10.1007/s10773-020-04648-1

Cited by 2 publications

(4 citation statements)

References 17 publications

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“…is not a pure 3-qubit density matrix but it is similar as an n-qubit entangled state, as shown in equation (12). The square of the reduced density matrix of equation (19) also cannot equal the reduced density matrix itself.…”

Section: Discussionmentioning

confidence: 99%

“…The square of the reduced density matrix of equation (19) also cannot equal the reduced density matrix itself. In addition, pqr 2 r is complicated mathematically as well as equation (12) in different coefficients, i.e., equations (1) and (14). Therefore, the invariant Tr pqs pqs pqs 2 r P = is similar as equation (13).…”

Section: Discussionmentioning

confidence: 99%

“…The evaluation of the entanglement pattern was also performed by Purwanto et al [15] in different method, i.e., by using rank of reduced density matrix. In addition, the previous research [10][11][12][13][14] did not provide complete invariants to determine the entanglement pattern for n 4. …”

mentioning

confidence: 98%

“…This invariant was utilized to analyze the characteristic of maximally multipartite entangled state (MMES) [10][11][12][13][14].…”

mentioning

confidence: 99%

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Invariants for determining entanglements pattern

Artawan¹,

Purwanto²,

Yuwana³

2022

Phys. Scr.

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We propose invariant, i.e., trace of the square of reduced density matrix, to determine the entanglement pattern of n-qubits state. The substate is separable from its complement substate if the invariant of this substate equals one. Meanwhile, the substate is entangled if the invariant is less than one. Only two types of states that the number of evaluations can be determined. Firstly, a completely separable state can be determined after evaluating n-1 invariants of reduced single qubit. Secondly, a completely separable state can be indicated after 2n-1-1 consecutive calculations of invariants, which started from reduced single state, then followed with reduced double state, reduced triple state, etc., where each invariant is less than one. On the other hand, the number of evaluations of invariants cannot be determined and depend on the pattern of the compound entangle state.

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Section: Discussionmentioning

confidence: 99%