Practical Entanglement Estimation for Spin-System Quantum Simulators

Strong entanglement, a quintessential feature of quantum mechanics, is typically a signature of a successfully implemented quantum simulator. Indeed, the aim of these experiments is the preparation and control of systems which show genuine quantum features. For example, recent experiments with trapped ions were designed to implement critical systems – a scenario which is known to become hard to simulate numerically with increasing number of spins due to the presence of large quantum correlations. In order to determine the entanglement in an experiment, one has to take into account that measurements to extract the required information are not only limited by the specifications of the different experimental platforms but, more generally, also by the large dimension of the Hilbert space. A familiar choice to overcome these issues are entanglement witnesses. In our work we determine entanglement witnesses that are quantitative in the sense that they determine lower bounds to the logarithmic negativity, a widely used entanglement measure, that can be obtained to reveal the behavior of entanglement across quantum phase transitions experimentally. In particular, we describe how these witnesses can be measured, e.g., using a short sequence of gate operations and we study the robustness of these measurements in the presence of noise.

Practical Entanglement Estimation for Spin-System Quantum Simulators.png