  We construct a quantum reference frame, which can be used to approximately
implement arbitrary unitary transformations on a system in the presence of any
number of extensive conserved quantities, by absorbing any back action provided
by the conservation laws. Thus, the reference frame at the same time acts as a
battery for the conserved quantities.
  Our construction features a physically intuitive, clear and
implementation-friendly realisation. Indeed, the reference system is composed
of the same types of subsystems as the original system and is finite for any
desired accuracy. In addition, the interaction with the reference frame can be
broken down into two-body terms coupling the system to one of the reference
frame subsystems at a time. We apply this construction to quantum thermodynamic
setups with multiple, possibly non-commuting conserved quantities, which allows
for the definition of explicit batteries in such cases.

Quantum Physics