Quantum Information and Entropy

Nilanjana Datta

Wen-Ran Zhang, Hengyu Zhang

While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) are reviewed and distinguished for quantum emergence/submergence of quantum agent (QA) and quantum intelligence (QI) in algebraic terms. This work refers to QA as an entangled bipolar string/superstring in bipolar dynamic equilibrium (BDE) and QI being centered on logically definable causality in regularity, mind-light-matter unity, and brain-universe similarity. ER = EPR is extended to ER ≥≥ EPR for the mathematical scalability of bipolar strings and their collective entanglement. The extension leads to a number of conjectures, testable predictions, and theorems. The term “equilibraton” is proposed as a type of EPR or bipolar generic string to serve as an entropic stitch to collectively hold the universe together as a quantum entanglement in BDE with ubiquitous, regulated local emergence and submergence of QA&QI. Equilibraton leads to the concept of bipolar entropy square—a complete entropic solution to the background issue in quantum gravity. With complete background independence, energy/information conservational bipolar entropy, energy/information invariance, bipolar entropy non-additivity, and equilibrium-based plateau concavity are introduced. The nature of the one-dimensional arrow of time is conjectured. As a unification of order and disorder for equilibrium-based regulation, bipolar entropy bridges QA&QI to agentic AI, where quantum-bio-economics can be viewed as a topological intervention of a natural dynamic equilibrium in a social or natural world. Use cases are reviewed to illustrate the practical and theoretical aspects of bipolar entropy in business management, quantum-bio-economics, quantum cryptography, physics, and biology. Eddington–Einstein’s comments on entropy are revisited. It is expected that bipolar entropy will bring quantum emergence/submergence to agentic AI&QI for entangled machine thinking and imagination as a naturally scalable and testable foundation of real-world quantum gravity, quantum information science (QIS), quantum cognition and quantum biology (QCQB) to enhance Large Language AI Models (LLMs) and machine intelligence.

Jincheng Zhang

This paper introduces a generalized definition of quantum information entropy, aiming to provide a more comprehensive framework for quantifying information in complex quantum systems. The core of this work lies in extending the conventional concept of entropy, traditionally applied to classical information, to the realm of quantum mechanics. We explore various types of quantum entropy, including von Neumann entropy, relative entropy, and a newly proposed generalized entropy, denoted as *Eg*. The definition of *Eg* is based on a novel approach that considers the entanglement structure and correlations within quantum states. We establish relationships between these different entropy measures, demonstrating their interconnectedness within the broader context of quantum information theory. The paper further outlines a mathematical formalism for calculating *Eg*, providing a tool for analyzing and characterizing quantum information. Our generalized entropy provides a more flexible and potentially more accurate measure of quantum information, particularly in scenarios involving complex quantum correlations and multi-partite quantum systems. ---

Göran Lindblad

Richard Jozsa

Jincheng Zhang

This paper proposes a novel information encoding scheme, termed Quantum Information Entropy Encoding (QIE), leveraging quantum entanglement and coherence to potentially surpass the entropy limits established by classical information theory. QIE utilizes multi-qubit entanglement states, precisely manipulating their coherence, to establish highly correlated information representations between quantum bits. The encoding process employs quantum gate operations to transform these entangled states, facilitating information compression and transmission. Decoding relies on measurements of the entangled states to recover the original information. The core claim is the potential for QIE to achieve higher compression rates and faster transmission speeds compared to conventional entropy coding methods. This approach represents a departure from traditional information theory, exploring the utilization of quantum mechanical phenomena for enhanced information processing. The theoretical framework presented here lays the groundwork for future investigations into the feasibility and limitations of QIE.