Measuring entanglement entropy through the interference of quantum many-body twins (1509.01160v1)

Abstract: Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is rapidly gaining prominence in diverse fields ranging from condensed matter to quantum gravity. Despite this generality, measuring entanglement remains challenging. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Leveraging our single-site resolved control of ultra-cold bosonic atoms in optical lattices, we prepare and interfere two identical copies of a many-body state. This enables us to directly measure quantum purity, Renyi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly-correlated many-body systems.

• The paper introduces a novel experimental technique using the interference of quantum many-body twins to directly measure state purity and entanglement entropy.
• It employs a 50-50 beam splitter setup to analyze the Bose-Hubbard model, revealing both bipartite and multipartite entanglement phases.
• The findings offer new insights into quantum phase transitions and pave the way for scalable studies in optical lattices and non-equilibrium dynamics.

Measuring Entanglement Entropy Through the Interference of Quantum Many-Body Twins

The paper, "Measuring entanglement entropy through the interference of quantum many-body twins" presents a novel experimental technique for measuring entanglement in quantum systems. Entanglement, a fundamental aspect of quantum mechanics, represents non-local correlations between quantum entities and has significant implications for quantum information science. Measuring entanglement, particularly in systems of delocalized interacting particles, poses a substantial challenge. This research offers a promising approach by leveraging the precise control and measurement capabilities provided by ultra-cold bosonic atoms in optical lattices.

Key Contributions

The authors utilize quantum interference to achieve direct measurements of quantum purity, second-order Rényi entropy, and mutual information. The experimental setup involves preparing two identical copies of a many-body state and observing their interference. This interference, facilitated by a quantum gas microscope, allows for the quantification of spatial entanglement and the elucidation of underlying quantum states.

1. Quantum Purity Measurement: The methodology involves the interference of two copies of a quantum state via a 50-50 beam splitter, analogous to the Hong-Ou-Mandel interference seen in photon experiments. For an identical pure input state, destructive interference leads to outcomes with even numbers of particles at the outputs. The average parity of particle numbers at the output is used to measure the purity of the initial state, thus providing insights into the state’s entanglement properties.
2. Entanglement in Ground States: The paper investigates the Bose-Hubbard model, tracking entanglement as the system transitions from a Mott insulator phase to a superfluid phase. A notable observation is that spatial subsystem entropies surpass the full system entropy in the superfluid phase, revealing the presence of bipartite entanglement.
3. Detection of Multipartite Entanglement: The experiment measures the second-order Rényi entropy for various subsystem sizes, demonstrating multipartite entanglement. Particularly in the superfluid phase, calculated mutual information reveals the build-up and extension of correlations as the system evolves.
4. Entanglement Dynamics in Non-Equilibrium Systems: Further experiments explore the changes in entanglement as the system undergoes a quench—a sudden change in the Hamiltonian parameters. The resulting oscillations in entanglement dynamics provide insight into transient quantum phenomena.

Implications and Future Directions

This research opens several avenues for practical and theoretical advancements. It offers a reliable method to directly measure entanglement, circumventing the need for state-specific entanglement witnesses or complex state tomography. The ability to probe spatial entanglement in optical lattices gives physicists a new tool for exploring quantum phases and transitions, particularly in strongly-correlated systems.

For future research, scaling this method to larger systems holds promise for more comprehensive studies of quantum phase transitions and the exploration of properties such as topological order. Moreover, the technique could be adapted to investigate fermionic systems or systems with internal degrees of freedom, thereby broadening its applicability. Additionally, the experimental framework can be employed to test theoretical models of non-equilibrium dynamics and many-body localization, further enhancing our understanding of quantum systems far from equilibrium.

Overall, this work provides a robust experimental framework for the paper of quantum entanglement, paving the way for future explorations in quantum many-body physics and quantum information science.