# Limits to Perception by Quantum Monitoring with Finite Efficiency

## TL;DR

This paper investigates the fundamental limits of how well agents can perceive quantum systems through continuous measurements with finite efficiency, providing bounds based on accessible information and applying them to Gaussian states and quantum Ising chains.

## Contribution

It introduces bounds on perception accuracy in quantum monitoring based on purity and entropy, highlighting the impact of information access on quantum state estimation.

## Key findings

- Bounds relate perception accuracy to state purity and entropy.
- Perception limits depend on measurement efficiency and information access.
- Application to Gaussian states and quantum Ising chains demonstrates practical relevance.

## Abstract

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.