Weakly Entangled Proton and Neutron Orbitals

This post will discuss what findings concerning weakly entangled proton and neutron orbitals mean for a journey towards quantum internet. The most important term to recap to understand this post is quantum entanglement:

Quantum entanglement is a unique phenomenon in quantum physics where two or more particles become linked, and the state of one particle is immediately connected to the state of the other, no matter how far apart they are. This is a key resource in quantum communication and quantum computing.

The findings I want to explore come from an arxiv paper titled "Quantum entanglement patterns in the structure of atomic nuclei within the nuclear shell model" by A. Pérez-Obiol, S. Masot-Llima, A. M. Romero, J. Menéndez, A. Rios, A. García-Sáez, and B. Juliá-Díaz from 11th of Jul 2023. It explores the entanglement features in the nuclear shell model, focusing on Be, O, Ne, and Ca isotopes.

Artistic visualization of a quantum entanglement generated with "midjourney".

The authors of that paper use different metrics to quantify the importance of entanglement, including single-orbital entropies, orbital-orbital mutual information, and the von Neumann entropies between two equipartitions of the valence space. They find that the entanglement properties are directly related to the number of valence nucleons and the energy structure of the shell.

The study reveals that proton and neutron orbitals are weakly entangled by all measures, and in fact, have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies.

The authors conclude that the proton-neutron partition presents the lowest entanglement and that the proton-neutron entanglement decreases with neutron excess. This indicates that, in order to simulate separately two halves of the valence space, the optimal choice is to split this space in terms of the isospin projection, t_z.

So, let's discuss those findings in the context of quantum internet:

1) Efficiency of Quantum Algorithms: The study finds that the proton-neutron partition presents the lowest entanglement. This insight could guide the design of more efficient quantum algorithms. In quantum computing, the efficiency of an algorithm can often be improved if the quantum system's entanglement properties are well understood and leveraged. Efficient quantum algorithms are crucial for the development of a quantum internet as they could enable faster and more secure data processing and transmission.

2) Quantum Error Correction: Understanding the entanglement properties of atomic nuclei could also help improve quantum error correction techniques. Quantum error correction is a set of methods designed to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is essential for a quantum internet because it helps maintain the integrity of the quantum information while it's being transmitted over long distances.

3) Quantum Network Design: The findings of the study could also inform the design of quantum networks. For example, understanding the entanglement properties of atomic nuclei could help in the development of quantum repeaters, devices that can extend the range of quantum communication by preserving the entanglement of quantum bits (qubits) over long distances.

In classical communication, repeaters work by receiving a signal, amplifying it, and retransmitting it. However, in quantum communication, due to the no-cloning theorem, you can't simply copy and amplify a quantum state. This is where quantum entanglement comes in. Quantum repeaters use entanglement to transmit quantum information over long distances. Here's a simplified explanation of how it works:

a) Two entangled particles are created. One is kept at the repeater station, and the other is sent to the destination.

b) When a quantum bit (qubit) arrives at the repeater station, the repeater performs a special operation that transfers the state of the incoming qubit to the entangled particle that was sent to the destination.

c) Because the two particles are entangled, the state of the incoming qubit is effectively transmitted to the destination, even though the qubit itself didn't travel the whole distance.

Now, coming back to the paper, it discusses the entanglement properties in the nuclear shell model. Understanding these properties could help improve the design and operation of quantum repeaters. For instance, it could provide insights into how to create and maintain entangled states more effectively, or how to better protect these states from noise and other disturbances. This could, in turn, enhance the performance of quantum repeaters, making quantum communication over long distances more reliable and efficient.

4) Quantum Simulation: The study also suggests that the insights gained could lead to more efficient circuit designs to study atomic nuclei across the nuclear chart with quantum simulations. Quantum simulations are a powerful tool for studying quantum systems that are too complex to be studied by classical computers. They could be used to design new materials and drugs, optimize complex systems, and more. These applications could, in turn, support the development of a quantum internet by driving the demand for quantum communication.

Original paper that inspired this post: Arxiv: Quantum entanglement patterns in the structure of atomic nuclei within the nuclear shell model