What Is Quantum Information? Information Symmetry and Mechanical Motion

Vasil Dinev Penchev

The concept of quantum information is introduced as both normed superposition of two orthogonal subspaces of the separable complex Hilbert space and invariance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen.The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a wave function describing a state of a quantum system) as its value as the bound variable.A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is representable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above.Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and invariance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper.Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries 𝑈𝑈(1), 𝑆𝑆𝑆 (2), and 𝑆𝑆𝑆 (3) of the Standard model.

Jeffrey Bub

Dongsheng Wang

Quantum mechanics is a special kind of description of motion. The concept of wave function itself implies the openness of quantum system. We show that quantum mechanics describes the quantum correlation, i.e., entanglement, and information in a new kind of space, tangnet T^2, where exist the basic quantum structure of qubit and the universal out-in symmetry. This work tries to form a new view to the fundamental problems of the foundation of quantum mechanics.

David Peter Divincenzo, Daniel Loss

Jincheng Zhang

This paper introduces and formalizes the theory of the Information Potential of Quantum Interaction (IPQI), a novel theoretical framework proposing that quantum information correlation gradients between interacting quantum systems give rise to an effective potential energy and an associated dynamical force. Conventionally, physical forces are mediated by gauge fields, particle exchange, or spatial overlaps of wavefunctions governed by symmetry principles. In contrast, IPQI posits that the mutual information shared between quantum subsystems acts as a fundamental scalar field source capable of driving physical motion and altering system dynamics independently of standard exchange interactions. We define the information potential as V_I = - lambda * I(A:B), where I(A:B) represents the quantum mutual information between subsystems A and B, and lambda is a coupling constant. The corresponding effective force is derived as F_I = - grad V_I = lambda * grad I(A:B). We establish the foundational equations of motion under this potential, demonstrate its independence from conventional exchange mechanisms through rigorous state-space analysis, and explore its theoretical implications across microscopic quantum configurations and broader physical settings.

Olímpia Lombardi, Federico Holik, Leonardo Vanni