The structure of superqubit states

Abstract

Superqubits provide a supersymmetric generalisation of the conventional qubit in quantum information theory. After a review of their current status, we address the problem of generating entangled states. We introduce the global unitary supergroup UOSp((3 n + 1)/2|(3 n − 1)/2) for an n-superqubit system, which contains as a subgroup the local unitary supergroup [UOSp(2|1)] n . While for 4 > n > 1 the bosonic subgroup in UOSp((3 n + 1)/2|(3 n − 1)/2) does not contain the standard global unitary group SU(2 n ), it does have an USp(2 n ) ⊂ SU(2 n ) subgroup which acts transitively on the n-qubit subspace, as required for consistency with the conventional multi-qubit framework. For two superqubits the UOSp(5|4) action is used to generate entangled states from the "bosonic" separable state |00 .