We investigate the distribution of bipartite and multipartite entanglement in multiqubit states. In particular we define a set of monogamy inequalities sharpening the conventional Coffman-Kundu-Wootters constraints, and we provide analytical proofs of their validity for relevant classes of states. We present extensive numerical evidence validating the conjectured strong monogamy inequalities for arbitrary pure states of four qubits.

May 15, 20140 citations

Strong Monogamy Conjecture for Multiqubit Entanglement: The Four-Qubit Case

Bartosz Regula, Sara Di Martino, Soojoon Lee +1 more

We investigate the distribution of bipartite and multipartite entanglement in multiqubit states. In particular, we define a set of monogamy inequalities sharpening the conventional Coffman-Kundu-Wootters constraints, and we provide analytical proofs of their validity for relevant classes of states. We present extensive numerical evidence validating the conjectured strong monogamy inequalities for arbitrary pure states of four qubits.

arXiv:1405.3989Physical Review LettersSep 10, 201493 citations

arXiv:2002.00701 · Quantum Information Processing

Monogamy constraints on entanglement of four-qubit pure states

S. Shelly Sharma, N. K. Sharma

Published Aug 13, 2022• 0 citations

arXiv HTML PDF

DOI: 10.1007/s11128-022-03610-w

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We report a set of monogamy constraints on one-tangle, two-tangles, three-tangles and four-way correlations of a general four-qubit pure state. It is found that given a two-qubit marginal

\rho

of an

N

qubit pure state $\left\vert \Psi_{N}\right\rangle $, the non-Hermitian matrix

\rho \widetilde{\rho}

where

\widetilde{\rho}

$=\left( \sigma_{y}\otimes \sigma_{y}\right) \rho^{\ast}\left( \sigma_{y}\otimes\sigma_{y}\right) $, contains information not only about the entanglement properties of the two-qubits in that state but also about the correlations of the pair of qubits with $\left( N-2\right) $ qubits in $\left\vert \Psi_{N}\right\rangle $. To extract information about tangles of a four-qubit state $\left\vert \Psi_{4}\right\rangle $, the coefficients in the characteristic polynomial of matrix

\rho\widetilde{\rho}

are analytically expressed in terms of

2\times2

matrices of state coefficients. A general monogamy relation satisfied by one-tangle, two-tangles, three-tangles, and residual correlations in a multiqubit state $\left\vert \Psi_{N}\right\rangle $ is also given.