On Monogamy of four qubit entanglement
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.
Keywords
Cite
@article{arxiv.1703.09861,
title = {On Monogamy of four qubit entanglement},
author = {S. Shelly Sharma and N. K. Sharma},
journal= {arXiv preprint arXiv:1703.09861},
year = {2018}
}
Comments
14 pages, one figure, This revision further improves readability and corrects typos