  We formulate limits to perception under continuous quantum measurements by
comparing the quantum states assigned by agents that have partial access to
measurement outcomes. To this end, we provide bounds on the trace distance and
the relative entropy between the assigned state and the actual state of the
system. These bounds are expressed solely in terms of the purity and von
Neumann entropy of the state assigned by the agent, and are shown to
characterize how an agent's perception of the system is altered by access to
additional information. We apply our results to Gaussian states and to the
dynamics of a system embedded in an environment illustrated on a quantum Ising
chain.
