Measuring Rényi entropy using a projected Loschmidt echo

• URL: http://arxiv.org/abs/2504.05237v1
• Date: Mon, 07 Apr 2025 16:21:53 GMT
• Title: Measuring Rényi entropy using a projected Loschmidt echo
• Authors: Yi-Neng Zhou, Robin Löwenberg, Julian Sonner,
• Abstract summary: We present efficient and practical protocols to measure the second R'enyi entropy (RE), whose exponential is known as the purity.<n>We achieve this by establishing a direct connection to a Loschmidt echo (LE) type measurement sequence, applicable to quantum many-body systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present efficient and practical protocols to measure the second R\'enyi 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.

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