A R P Rau 2009 J. Phys. A: Math. Theor. 42 412002 doi:10.1088/1751-8113/42/41/412002
Algebraic characterization of X-states in quantum information
FREE ARTICLEA R P Rau
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A class of two-qubit states called X-states are increasingly being used to discuss entanglement and other quantum correlations in the field of quantum information. Maximally entangled Bell states and 'Werner' states are subsets of them. Apart from being so named because their density matrix looks like the letter X, there is not as yet any characterization of them. The su(2) × su(2) × u(1) subalgebra of the full su(4) algebra of two qubits is pointed out as the underlying invariance of this class of states. X-states are a seven-parameter family associated with this subalgebra of seven operators. This recognition provides a route to preparing such states and also a convenient algebraic procedure for analytically calculating their properties. At the same time, it points to other groups of seven-parameter states that, while not at first sight appearing similar, are also invariant under the same subalgebra. And it opens the way to analyzing invariant states of other subalgebras in bipartite systems.
- PACS
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03.67.Lx Quantum computation architectures and implementations
- MSC
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81R15 Operator algebra methods (See also 46Lxx, 81T05)
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
- Subjects
- Dates
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Issue 41 (16 October 2009)
Received 24 July 2009, in final form 31 August 2009
Published 22 September 2009
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Algebraic characterization of X-states in quantum information
A R P Rau 2009 J. Phys. A: Math. Theor. 42 412002
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