Decoherence-Free Subspaces in Supersymmetric Oscillator Networks

Abstract

Quantum superpositions can be used for parallel information processing, but only if protected against decoherence. A two-particle four-state system may have two-dimensional subspaces that are partially or completely decoherence-free, e.g., the symmetric triplet state as an example of the former, the anti-symmetric singlet state of the latter. By extension, a multiparticle system that in the laboratory basis is plagued by decoherence may in some other basis exhibit the symmetries that yield such decoherence-free subspaces (DFS's). Fully-interacting many-fermion spin 1/2 networks may be mathematically transformed to a more tractable many-to-one (or -to-some) variant. This paper applies such a transformation to a hypothetical network of boson-like operators and then argues that a fully-interacting particle number-preserving network of bosons plus fermions with supersymmetric degrees of freedom may be more plausibly exploited so as to contain DFS's. Physical systems that in some basis are inherently anti-symmetric are already known to be useful for quantum information processing. Supersymmetric systems may be likewise.