From clocks to cloners: Catalytic transformations under covariant operations and recoverability

Understand

There are various physical scenarios in which one can only implement operations with a certain symmetry.

• Under such restriction, a system in a symmetry-breaking state can be used as a catalyst, e.g.
• to prepare another system in a desired symmetry-breaking state.
• This sort of (approximate) catalytic state transformations are relevant in the context of (i) state preparation using a bounded-size quantum clock or reference frame, where the clock or reference frame acts as a catalyst, (ii) quantum thermodynamics, where again a clock can be used as a catalyst to prepare states which contain coherence with respect to the system Hamiltonian, and (iii) cloning of unknown quantum states, where the given copies of state can be interpreted as a catalyst for preparing the new copies.