Security Trade-offs in Ancilla-Free Quantum Bit Commitment in the Presence of Selection Rules

Security trade-offs have been established for one-way bit commitment in Ref. [1]. We study this trade-off in two selection settings. We show that for an ‘abelian’ selection rule (exemplified by particle conservation) the standard trade-off between sealing and binding properties still holds. For the nonabelian 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.