Journal
PHYSICAL REVIEW A
Volume 85, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.85.022301
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Funding
- German Research Foundation [SFB 631, SPP 1386]
- Basque Government [IT-472]
- Belgian F.R.S.-FNRS
- University of Regensburg
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We show that a positive homogeneous function that is invariant under determinant-1 stochastic local operations and classical communication (SLOCC) transformations defines an N-qubit entanglement monotone if and only if the homogeneous degree is not larger than 4. We then describe a common basis and formalism for the N-tangle and other known invariant polynomials of degree 4. This allows us to elucidate the relation of the four-qubit invariants defined by Luque and Thibon [Phys. Rev. A 67, 042303 (2003)] and the reduced two-qubit density matrices of the states under consideration, thus giving a physical interpretation for those invariants. We demonstrate that this is a special case of a completely general law that holds for any multipartite system with bipartitions of equal dimension, e. g., for an even number of qudits.
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