**Using classical electrical circuits as stand-ins for complex quantum systems, researchers have successfully demonstrated negative entanglement entropy, providing a practical model for exploring exotic quantum phenomena and developing quantum information technology.**

Entanglement entropy is a measure of the degree of entanglement between different parts of a quantum system. It indicates how much information about one part reveals about another, revealing hidden interactions between particles. This concept is essential for progress Quantum computing and quantum communication technologies.

To understand what negative entanglement entropy is, we must first understand what entanglement and entropy are.

#### Complexity and entropy in abstraction

Imagine you have two coins. Generally, if you flip one coin, it doesn’t affect the outcome of flipping another. But in the quantum world, particles can become „entangled,” meaning their states are entangled. If two coins are thrown, the rule of thumb is that if one coin is flipped heads, the other coin must show tails. In essence, knowing the outcome of one limits the possible outcomes of the other.

Entropy, on the other hand, is a statistical physics concept that measures the disorder or uncertainty of a system. For example, a chaotic room has high entropy because objects are scattered everywhere and it is difficult to predict where any particular object is. A tidy room has low entropy because everything is in its place, making it easy to find things.

#### Entanglement entropy

Taken together, „entanglement entropy” measures how much information you lose about one part of a system if another part of the system suddenly becomes inaccessible, i.e. disconnected due to a so-called „entanglement cut”. Intuitively, the more the two parts are entangled, the more information is lost.

A simple analogy to understand entanglement entropy is to imagine a pair of socks. You put one sock in one drawer and the other sock in another drawer. If socks are a „trouble,” knowing the color of the socks in one drawer immediately tells you the color of the socks in the other drawer. Here, two situations can occur:

- High difficulty: If the colors of two socks are almost perfectly correlated, then knowing the color of one sock gives you complete information about the other. In particular, if one sock suddenly becomes inaccessible, one may also lose knowledge of the color of another sock.
- A lesser problem: if the colors of the socks are essentially unrelated, knowing the color of one sock cannot be certain about the color of another. In particular, if one sock suddenly becomes inaccessible, there is no uncertainty, or entropy, about the color of the other sock.

#### Negative entanglement entropy

Conventional quantum mechanics is concerned only with particles and conservative systems in which energy is neither destroyed nor created. However, intriguing new physics arise when this constraint is removed—in the sock analogy, socks can be removed or added to the system. Such systems are called „non-Hermitian” systems.

In non-Hermitian systems, the concept of entanglement must be modified because information can also be lost when the number of particles changes. Specifically, receiving new socks and their information can be viewed as providing others with a negative amount of sock information. This leads to the new concept of negative entanglement entropy.

A theoretical recipe for achieving negative entanglement entropy in a non-Hermitian quantum system has been considered since a few years ago, and in reality observing negative entanglement in quantum experiments is not easily done. This is due to the significant challenges of manipulating complex quantum states in the way they gain or lose energy, while also measuring how entangled they are.

#### Exceptional bonding states and negative entanglement entropy in electric circuits

Reporting in *Scientific Bulletin*Physicists from Singapore and China have experimentally observed entanglement states that have mathematically negative entanglement entropy. Instead of using a quantum system, the research team used a non-quantum (or classical) circuit to create a 'sandbox’ system, similar to a negative-complex computer, but without the challenges that come with true quantum systems. Such classical electrical circuits are built with readily available electronic components such as resistors, capacitors and operational amplifiers, without the need for ultralow cryogenic cooling and high-precision lasers required in a quantum system.

„EB states are very robust and exhibit important measurable signatures, thus greatly simplifying their physical realization in relatively simple classical networks such as circuits,” said Professor Xiangdong Zhang from the Beijing Institute of Technology. Experimental measurements of EB levels using electrical circuits.

„The most pertinent question we always want to answer is: can the behavior of esoteric negative entanglement manifest itself in realistic experiments? In this work, we provide a resounding „yes” through the new concept of exceptional bounded states (EB) states,” said Project Leader Assistant Professor Ching Hua of the National University of Singapore. Lee said.

„EB levels are special levels that provide important fingerprints for negative entanglement,” said Professor Haiyu Meng from Xiangtan University, co-author of the work. Whenever the host system becomes highly sensitive due to non-hermeticity, EB levels may emerge as a direct result of negative entanglement.

„This work suggests classical electrical circuits as a new hunting ground to search for exotic quantum phenomena that are challenging to realize using atoms and material crystals. Due to the ease of fabrication, electrical circuits may provide a low-cost sandbox for designing and prototyping devices useful for future quantum technology,” said the Singapore University of Technology and Design. said Assistant Professor Yee Chin Aung.

The proof of negative entanglement entropy will have a profound impact on many areas of physics and engineering, especially quantum information technology. Going forward, EB states and circuits can be used to probe exotic physics in higher dimensions, thereby creating a new rich arena for the triple interplay of topological, non-Hermitian and EB physics.

Reference: „Experimental Observation of Exceptional Bounded States in a Classical Circuit Network” Deyuan Zhu, Tian Chen, Haiu Meng, Yee Xin Ang, Xiangdong Zhang, and Tsing Hua Lee, 29 May 2024, *Scientific Bulletin*.

DOI: 10.1016/j.scib.2024.05.036

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