Probing Rényi entanglement entropy via randomized measurements

By T. Brydges, Andreas Elben, P. Jurcevic, B. Vermersch, C. Maier, B. Lanyon, Peter Zoller, Rainer Blatt, C. F. Roos. Science, 2018

670 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/fa9c7a152a349c7ba218b7b892bfe8f5a62840c2

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Citations in the corpus

The randomized measurement toolbox (2022, methodology): “Asymptotic scalings M ∝ 2 w / ε 2 have been rigorously shown for equation (4) 24,36 and also observed for equation (3) 23,35,44 .”
Quantum simulation and computing with Rydberg-interacting qubits (2020, background): “However recent ideas, such as self-verifying quantum simulations 11 and randomized benchmarking protocols 72,100 would be interesting to implement Rydberg quantum systems (particularly as we approach regimes that cannot be simulated on classical computers).”
Logical quantum processor based on reconfigurable atom arrays (2023, background): “See sections ‘Surface code and its implementation’ and ‘Correlated decoding in the surface code’ for further discussion on the surface code in particular.”
Practical quantum advantage in quantum simulation (2022, methodology): “This is already progressing 98 , with random operations applied digitally being used for platform verification in analogue simulators 76 , or the measurement of many-body entanglement in quench dynamics 98,102,103 .”
Self-verifying variational quantum simulation of lattice models (2018, methodology): “4b, the second-order Rényi entropy 32 , ρ =− S log tr( ) A(2) 2 A2 , where ρ A is the reduced density matrix in the bipartition A–”