Classification of n-qubit states with minimum orbit dimension

Details Classification of n-qubit states with minimum orbit dimension Classification of n-qubit states with minimum orbit dimension

2005-06-28

arxiv.org/abs/quant-ph/0506241v3

J. Phys. A: Math. Gen. 39 (2006) 2443-2456

Physics

Quantum Physics

15 pages, latex, revision 2, conclusion added, some proofs shortened

Scientific paper

10.1088/0305-4470/39/10/013

The 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.

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