Quantum coherence in the presence of unobservable quantities

State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on any observable data. We demonstrate that the inference-free subspace may be extracted whenever the quantity's unobservability is guaranteed by a global conservation law. This result can generalize even without such a guarantee. In particular, we examine the coherent-state representation of a laser where the absolute phase of the electromagnetic field is believed to be unobservable. We show that experimental coherent states may be separated from the inference-free subspaces induced by this unobservable phase. These physical states may then be approximated by coherent states in a relative-phase Hilbert space.