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Quantum simulators—carefully engineered and programmable quantum systems—provide an exciting avenue to explore the laws of nature and to realize complex physical phenomena. However, current quantum simulators still lack the sophisticated controls needed to interrogate a prepared state in depth, limiting the information that can be extracted by measurements. Here, we propose a novel measurement protocol that completely overcomes this difficulty, allowing for the extraction of arbitrary physical information. Excitingly, the protocol can be implemented with present-day technologies.
Our protocol involves introducing ancillary degrees of freedom prepared in a known state to a system of interest, letting them evolve naturally under joint quantum dynamics, then performing global measurements in a standard basis. Even though only a single, fixed basis is measured, we show how our protocol enables any property of the original quantum state to be estimated. The key ingredient of our protocol is ergodicity—the natural randomness in general quantum dynamics—which ensures that all information of the original system, even complicated observables, manifest over the ancillary system and can be observed. We demonstrate our protocol with extensive numerical simulations showcasing the extraction of elusive properties like topological numbers and entanglement entropies, assuming only the capabilities of existing experimental platforms.
Our protocol empowers quantum simulators to make previously impossible measurements, significantly advancing near-term quantum technologies. Further, our work heralds a paradigm shift in quantum protocol design, where we harness ergodicity—a ubiquitous feature of quantum dynamics—to aid scientific discoveries.
Figure 1 Our method allows experimentalits to extract arbitrary physical properties of quantum states produced in laboratory for scientific investigation by utilizing the ergodic nature of interacting quantum many-body dynamics. (AI generated image)