Security trade-offs in ancilla-free quantum bit commitment in the presence of superselection rules

Abstract

Security trade-offs have previously been established for one-way bit commitment. We study this trade-off in two superselection settings. We show that for an [lsquo]abelian[rsquo] superselection rule (exemplified by particle conservation), the standard trade-off between sealing and binding properties still holds. For the non-abelian case (exemplified by angular momentum conservation), the security trade-off can be more subtle, which we illustrate by showing that if the bit commitment is forced to be ancilla-free, an asymptotically secure quantum bit commitment is possible.