Nature Physics Using ultracold atoms to reconstruct quantum information
Recently, a multinational joint team of New York University, the Max Planck Institute for Quantum Optics, and the ETH has successfully measured entanglement entropy in quantum bit systems using ultracold atoms with a quantum field simulator.
The research results were published in the journal Nature Physics on April 24 under the title "Verification of the area law of mutual information in a quantum field simulator".
Quantitative insight into physiological systems can be obtained through "information measurements". For example, entropy is a measure of information that can be used to quantify the order in a system. Another example is mutual information, which tells us how much we can learn about the whole picture by looking at one part of a system.
A fundamental property of many-body subsystems is the area law of mutual information. This states that the information shared between subsystems is proportional to the size of the boundary between them, rather than their volume. This is analogous to the area law in gravitational physics - that is, the entropy of a black hole is proportional to the surface area of its event horizon, rather than its volume. This theoretical prediction about quantum systems has been around for nearly 20 years.
However, it has not been experimentally verified so far due to the difficulty of measuring the von Neumann entropy (the quantum extension of Gibbs' entropy) in an extended continuum system: it requires a full tomography of quantum states through exponentially many measurements.
The research team, which includes scientists from the Vienna University of Technology, ETH Zurich, Freie Universität Berlin and the Max Planck Institute for Quantum Optics, performed tomography of quantum systems: specific quantum state reconfigurations with the aim of finding experimental evidence for the above theory.
In this regard, Dries Sales, associate professor in the Department of Physics at New York University and author of the study, explains, "The item of work reconstructs the entire state of the quantum fluid based on the predictions of quantum field theory - similar to the predictions describing the fundamental particles of our universe."
"Quantum computing relies on being able to generate entanglement between different subsystems, and that's exactly what we can test with our method. The ability to do this precise characterization could also lead to better quantum sensors, another area of application for quantum technology."
The experimental team created a system of two parallel, one-dimensional, tunnelling-coupled (TCC) superfluids on an atomic chip. The device simulates the thermal state of Klein-Gordon field theory (one of the fundamental models of quantum field theory) and allows the effective mass and temperature of the system to be tuned.
Schematic diagram of the experimental scheme
In order to measure the von Neumann entropy, we need to reconstruct the full low-energy density matrix of the initial Gaussian state based on the measurement of the two-point relation. Eventually, using tomographic methods, the experimental team estimated the von Neumann entropy and mutual information of the quantum system.
Von Neumann entropy and mutual information of coupled superfluids on an atomic chip
In their work, the scientists created two "versions" of this quantum system: cigar-shaped clouds of atoms that evolve over time without interacting with each other. At different stages of the process, the team conducted a series of experiments that revealed the connections between the two versions.
"By establishing a complete history of these connections, we can infer what the initial quantum state of the system was and extract its properties," Sales explained. "Initially, we had a very tightly bound quantum fluid, which we split in two and evolved into two separate fluids. then recombine them and detect the waves in the fluid."
"It's like looking at the ripples in a pond after a rock has been thrown and inferring the properties of the rock, such as its size, shape and weight."
Information content shared between two spatially separated subsystems
The research provides a sophisticated understanding of a complex phenomenon that underlies quantum computing and allows certain computational operations to be performed more efficiently than traditional computing.
In the future, the team says the next goal is to measure quantum field theory and extend the entanglement of many-body quantum systems. Another interesting direction is to simulate quantum information in systems with interacting Hamiltonians in quantum field theory.
Reference links:
[1] https://www.nature.com/articles/s41567-023-02050-2
[2]https://www.nature.com/articles/s41567-023-02027-1
[3]https://www.theclevelandamerican.com/science-the-complete-state-of-the-quantum-fluid-is-reconstructed-publimetro-mexico/
