The Intrinsic Connection Between Coherence and Entanglement: MicroCloud Holography (NASDAQ: HOLO) Analyzes the Resource Logic of Quantum Measurement

In quantum systems, quantum states have non-classical properties such as superposition and entanglement, while classical states exhibit definite physical attributes. Quantum measurement is precisely the key link between these two types of states—it interacts with the quantum system through specific measurement apparatuses, transforming the non-classical information of the quantum system into observable and recordable classical signals. However, for a long time, the rules governing the conversion of quantum resources (such as coherence and entanglement) during quantum measurement have not been clearly explained, and this question has also become a crucial breakthrough in understanding the essence of quantum measurement.

MicroCloud Holography (NASDAQ: HOLO), focusing on the resource interpretation problem in quantum measurement, has proposed a relative-entropy–based quantity to quantify and analyze quantum resources in quantum measurement. As an important tool in information theory, relative entropy can describe the difference between two probability distributions. MicroCloud Holography extends this application to the quantum domain, and the constructed relative-entropy–based quantity can be used to measure the degree of change in quantum resources during the process of quantum measurement. Specifically, this relative-entropy–based quantity compares the quantum states (or resource states) of the system before and after the quantum measurement, and calculates the gain or loss of resources, thereby providing a unified quantitative standard for resources such as quantum coherence and quantum entanglement. The core value of this idea is that it overcomes the limitations of independently quantifying different quantum resources in the past, offering a unified framework for simultaneously analyzing the roles of coherence and entanglement in quantum measurement, making research on the interrelation between the two resources more systematic and rigorous.

Within the theoretical framework of the relative-entropy–based quantity, MicroCloud Holography further reveals the transformation pathway in which coherence is converted into entanglement during quantum measurement: the quantum coherence in quantum measurement can be transformed into entanglement in a two-quantum measurement scenario via coherence non-generating transformations. Coherence non-generating transformations are a special class of quantum operations: their characteristic is that they do not generate any new coherence during the transformation process; they only redistribute or convert the system’s existing coherence resources. In the measurement of a single quantum system, the system’s coherence exists in the form of a superposition state. When a second quantum system is introduced to form a two-quantum measurement scenario, through coherence non-generating transformations, the single-system coherence can be converted into non-local correlations between the two systems—that is, entanglement. The key to this transformation is that coherence non-generating transformations ensure the “conservation” of resource conversion—neither increasing the total coherence resource nor producing additional loss. They only realize the change in resource form from coherence to entanglement, providing theoretical support for the efficient use of resources in quantum measurement.

MicroCloud Holography’s research also confirms the reverse logic of resource conversion in quantum measurement: the monotonicity of quantum entanglement leads to the monotonicity of quantum coherence in quantum measurement. Here, “monotonicity” means that the quantification metric of a quantum resource exhibits stability and regularity in relation to the trend of measurement operations—if the quantification value of quantum entanglement (entanglement monotonicity) follows a particular pattern as the quantum measurement operation changes (such as decreasing or increasing), then the quantification value of quantum coherence (coherence monotonicity) will also show a corresponding trend of change.

This reverse inference indicates that in quantum measurement, coherence and entanglement not only have a one-way conversion relationship, but also share interrelated patterns of change. Their monotonic properties influence and constrain each other. This finding further strengthens the intrinsic connection between the two resources, showing that they are not isolated quantum attributes; rather, they are different aspects of how resources manifest during the process of quantum measurement, jointly reflecting the non-classical nature of quantum systems.

Finally, the coherence–entanglement correlation theory proposed by MicroCloud Holography (NASDAQ: HOLO) in this work has broad applicability. It not only applies to quantum measurement scenarios involving resource gains and losses, but can also explain special cases of resource conservation, providing complete theoretical support for a comprehensive understanding of the resource mechanisms of quantum measurement.

(Editor-in-charge: Guo Jiandong ）

     【Disclaimer】This article only represents the author’s personal views and is not related to Hexun. The Hexun website remains neutral regarding the statements, viewpoints, and judgments made in the text, and does not provide any express or implied guarantees regarding the accuracy, reliability, or completeness of the content included. Readers are requested to treat this as reference only and bear all responsibility themselves. Email: news_center@staff.hexun.com

Report