Image credit: Helene Hainzer
Entanglement is the backbone of quantum information science. Quantum computers and simulators can outperform classical calculations when simulating complex many-body quantum states. In modern times, characterizing entanglement in quantum simulations is a tricky task. Due to the fragile nature of entanglement and the exponentially increasing number of measurements required for characterizing entanglement with the system sizes, experimental techniques and analysis methods need to be upgraded to more sample-efficient methods. Here, theoretical ideas originally formulated for conformal field theories come into play. These ideas state that a mixed state, segregated from continuum spatial and temporal systems, can be represented by a Gibbs ensemble. The original concept was formulated for lattice models and has now been tested on a trapped ion quantum simulator.
In our recent research studies, we conducted experimental investigations of entanglement in quantum many-body states. Here we used a 51-ion quantum simulator to study entanglement in the ground and excited states of a one-dimensional XXZ Heisenberg chain. We focused on the entanglement Hamiltonian (EH) as an effective description of the reduced density matrix of a 20 spin subsystem out of 51 ion chain. Through sample-efficient learning, we confirmed a local structure of the EH, providing the first instance of confirming fundamental predictions of quantum field theory. Here, the reduced state of quantum many-body system exhibited a Gibbs ensemble with a spatially varying temperature profile, indicating local structure of entanglement in the Eigen states. The results also demonstrated the transition from area to volume-law scaling of von Neumann entanglement entropies from ground to excited states. The results are now published in Nature [1].
The current study resulted from a collaboration of the experimental team led by Christian Roos and Rainer Blatt with the theory team led by Peter Zoller. The joint collaboration was carried out between the University of Innsbruck and the Institute for Quantum Optics and Quantum Information Innsbruck.
For further studies please follow following articles:
[1] Exploring large-scale entanglement in quantum simulation, M. K. Joshi, C. Kokail, R. van Bijnen et al., Nature (2023).
[2] Entanglement Hamiltonians: from field theory to lattice models and experiments. M. Dalmonte, V. Eisler, M. Falconi & B. Vermersch. Ann. Phys. 534, 2200064 (2022).
[3] Entanglement Hamiltonian tomography in quantum simulation. C. Kokail, R. van Bijnen, A. Elben, B. Vermersch & P. Zoller. Nat. Phys. 17, 936 (2021).
[4] On the duality condition for a Hermitian scalar field. J. J. Bisognano & E. H. Wichmann. J. Math. Phys. 16, 985 (1975).