Entanglement and private information in many-body thermal states

• URL: http://arxiv.org/abs/2502.13218v1
• Date: Tue, 18 Feb 2025 19:00:10 GMT
• Title: Entanglement and private information in many-body thermal states
• Authors: Samuel J. Garratt, Max McGinley,
• Abstract summary: We show how entanglement in many-body mixed states is reflected in correlation functions.<n>We ask whether entanglement in the system can be used as a resource for distilling private keys.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Using concepts from quantum cryptography, we show how entanglement in many-body mixed states is reflected in standard correlation functions. Focusing on systems in thermal equilibrium with an environment, we ask whether the entanglement in the system can be used as a resource for distilling private keys -- random classical bits that are shared by spatially separated observers but hidden from an eavesdropper having access to the environment. Since private keys cannot be generated using separable states, we can infer the presence of entanglement from the success of such protocols. We derive a simple relation between the information accessible to the eavesdropper and the linear response of the system. This relation allows us to determine which spatial correlations can be used to detect entanglement across wide varieties of physical systems, and provides a new experimental probe of entanglement. We also show that strong symmetries of a density matrix imply the existence of correlations that are always hidden from the environment. This result implies that, although grand canonical ensembles are separable above a finite temperature, canonical ensembles are generically entangled at all finite temperatures.

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