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[superscript n] + 1)/2|(3[superscript n] - 1)/2) for an n-superqubit system, which contains as a subgroup the local unitary supergroup [UOSp](2|1)][superscript n]. While for 4 > n > 1 the bosonic subgroup in UOSp((3[superscript n] + 1)/2|(3[superscript n] - 1)/2) does not contain the standard global unitary group SU(2[superscript n]), it does have an USp(2[superscript n]) [subset] SU (2[superscript 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>.