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We formulate limits to perception under continuous quantum measurements bycomparing the quantum states assigned by agents that have partial access tomeasurement outcomes. To this end, we provide bounds on the trace distance andthe relative entropy between the assigned state and the actual state of thesystem. These bounds are expressed solely in terms of the purity and vonNeumann entropy of the state assigned by the agent, and are shown tocharacterize how an agent's perception of the system is altered by access toadditional information. We apply our results to Gaussian states and to thedynamics of a system embedded in an environment illustrated on a quantum Isingchain.

Limits to Perception by Quantum Monitoring with Finite Efficiency