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We propose the concept of SLOCC-equivalent basis (SEB) in the multiqubitspace. In particular, two special SEBs, the GHZ-type and the W-type basis areintroduced. They can make up a more general family of multiqubit states, theGHZ-W-type states, which is a useful kind of entanglement for quantumteleporatation and error correction. We completely characterize the property ofthis type of states, and mainly classify the GHZ-type states and the W-typestates in a regular way, which is related to the enumerative combinatorics.Many concrete examples are given to exhibit how our method is used for theclassification of these entangled states.Comment: 16 pages, Revte

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Classification of GHZ-type,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>-type, and GHZ-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>-type multiqubit entanglement

Classification of GHZ-type,W-type, and GHZ-W-type multiqubit entanglement