Péter Lévay 2005 J. Phys. A: Math. Gen. 38 9075 doi:10.1088/0305-4470/38/41/016
On the geometry of a class of N-qubit entanglement monotones
Péter Lévay
Show affiliationsA family of N-qubit entanglement monotones invariant under stochastic local operations and classical communication (SLOCC) is defined. This class of entanglement monotones includes the well-known examples of the concurrence, the 3-tangle and some of the four-, five- and N-qubit SLOCC invariants introduced recently. The construction of these invariants is based on bipartite partitions of the Hilbert space in the form 
with L = 2N−n ≥ l = 2n. Such partitions can be given a nice geometrical interpretation in terms of Grassmannians Gr(L, l) of l-planes in CL that can be realized as the zero locus of quadratic polynomials in the complex projective space of suitable dimension via the Plücker embedding. The invariants are neatly expressed in terms of the Plücker coordinates of the Grassmannians.
- PACS
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03.67.Lx Quantum computation architectures and implementations
03.65.Ta Foundations of quantum mechanics; measurement theory
03.67.Mn Entanglement measures, witnesses, and other characterizations
- MSC
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81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
- Subjects
- Dates
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Issue 41 (14 October 2005)
Received 1 August 2005, in final form 1 September 2005
Published 28 September 2005
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On the geometry of a class of N-qubit entanglement monotones
Péter Lévay 2005 J. Phys. A: Math. Gen. 38 9075
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