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Probing Rényi entanglement entropy via randomized measurements

An entropic look into entanglement Quantum systems are predicted to be better at information processing than their classical counterparts, and quantum entanglement is key to this superior performance. But how does one gauge the degree of entanglement in a system? Brydges et al. monitored the build-up of the so-called Rényi entropy in a chain of up to 10 trapped calcium ions, each of which encoded a qubit. As the system evolved, interactions caused entanglement between the chain and the rest of the system to grow, which was reflected in the growth of the Rényi entropy. Science, this issue p. 260 The buildup of entropy in an ion chain reflects a growing entanglement between the chain and its complement. Entanglement is a key feature of many-body quantum systems. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a protocol for measuring the second-order Rényi entropy based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator with partition sizes of up to 10 qubits, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts, in both the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, which is applicable to arbitrary quantum states of up to several tens of qubits.