David W Lyons and Scott N Walck 2006 J. Phys. A: Math. Gen. 39 2443 doi:10.1088/0305-4470/39/10/013
David W Lyons1 and Scott N Walck2
Show affiliationsThe group of local unitary transformations acts on the space of n-qubit pure states, decomposing it into orbits. In a previous paper we proved that a product of singlet states (together with an unentangled qubit for a system with an odd number of qubits) achieves the smallest possible orbit dimension, equal to 3n/2 for n even and (3n + 1)/2 for n odd, where n is the number of qubits. In this paper we show that any state with minimum orbit dimension must be of this form, and furthermore, such states are classified up to local unitary equivalence by the sets of pairs of qubits entangled in singlets.
03.67.Lx Quantum computation architectures and implementations
03.67.Mn Entanglement measures, witnesses, and other characterizations
81Rxx Groups and algebras in quantum theory
22D10 Unitary representations of locally compact groups
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
Issue 10 (10 March 2006)
Received 27 October 2005, in final form 20 January 2006
Published 22 February 2006
David W Lyons and Scott N Walck 2006 J. Phys. A: Math. Gen. 39 2443
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