Large quantum systems are masters at hiding their qualities.
Ultimately, all matter is governed by the laws of quantum mechanics. Intriguing quantum physics is leveraged in various technical applications like high-temperature superconductivity and it fuels high hopes for a revolution in information technology through quantum computation. As it turns out, there are fundamental limitations for our options to probe quantum systems.
While the complexity of a quantum system increases quickly when considering larger and larger system sizes, we usually just have a few knobs in the lab to measure a small set of system properties. A way to find out more about the state of a quantum system is to use dynamical measurement schemes. The idea is to first manipulate the system for some time by imposing external fields or designing interactions before doing one of the standard measurements. In this way, we can observe properties that are not directly accessible.
However, recent results by Thomas Barthel and Jianfeng Lu show that even perfect dynamical control over the system would not be sufficient to uncover all its secrets. The theoretical analysis shows that, for a generic observable, the time needed for its measurement increases exponentially with the size of the quantum system. In analogy to the wheat and chessboard problem, the exponential growth quickly exceeds the patience of the most longanimous experimentalist. So it is a question of clever design to allow for the measurement of the observables of interest through efficient dynamical schemes and a suitable encoding of models in quantum simulation protocols.
Reference: T. Barthel and J. Lu, "Fundamental limitations for measurements in quantum many-body systems", Phys. Rev. Lett. 121, 080406 (2018).