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Measuring Rényi entropy using a projected Loschmidt echo
Yi-Neng Zhou, Robin Löwenberg, Julian Sonner·April 7, 2025
Quantum Physicscond-mat.quant-gascond-mat.stat-mechhep-th
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Abstract
We present efficient and practical protocols to measure the second Rényi entropy (RE), whose exponential is known as the purity. We achieve this by establishing a direct connection to a Loschmidt echo (LE) type measurement sequence, applicable to quantum many-body systems. Notably, our approach does not rely on random-noise averaging, a feature that can be extended to protocols to measure out-of-time-order correlation functions (OTOCs), as we demonstrate. By way of example, we show that our protocols can be practically implemented in superconducting qubit-based platforms, as well as in cavity-QED trapped ultra-cold gases.