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arXiv · 1703.09861

On Monogamy of four qubit entanglement

S. Shelly Sharma·N. K. Sharma
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Abstract

Our main result is a monogamy inequality satisfied by the entanglement of a focus qubit (one-tangle) in a four-qubit pure state and entanglement of subsystems. Analytical relations between three-tangles of three-qubit marginal states, two-tangles of two-qubit marginal states and unitary invariants of four-qubit pure state are used to obtain the inequality. The contribution of three-tangle to one-tangle is found to be half of that suggested by a simple extension of entanglement monogamy relation for three qubits. On the other hand, an additional contribution due to a two-qubit invariant which is a function of three-way correlations is found. We also show that four-qubit monogamy inequality conjecture of ref. [PRL 113, 110501 (2014)] in which three-tangles are raised to the power (3/2), does not estimate the residual correlations, correctly. A lower bound on residual four-qubit correlations is obtained.

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S. Shelly Sharma, N. K. Sharma. 2018-05-11. On Monogamy of four qubit entanglement. https://doi.org/10.1007/s11128-018-1940-8

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