Measuring entanglement at finite temperatures

Relating the entanglement of many-body systems at finite temperature to measurable observables is desirable. In this talk, we provide relations between Renyi moments of an entanglement monotone and measurable observables. First we introduce a new entanglement monotone, the number entanglement entropy [1]. It is an entropy change due to an unselective subsystem charge measurement, and is an entanglement monotone for the systems with a conserved charge. Next, we derive finite temperature equilibrium relations between the Renyi moments of the number entanglement entropy and multi-point charge correlation functions. We exemplify these relations in quantum dot systems where the desired charge correlations can be measured via a nearby quantum point contact. Especially, in the multi-channel Kondo effect, we show that the number entanglement entropy and its Renyi moments have the same nontrivial universal temperature dependence at low temperature, which is now accessible using the proposed methods.