Quantum physics has remarkable characteristics such as quantum correlations, uncertainty relations, no cloning, which give rise to an interpretative and conceptual gap between the classical and the quantum world. To provide more unified framework generalized probabilistic theories were formulated. Recently, it turned out that such theories include so called postquantum ones which share many of the typical quantum characteristics but predict supraquantum effects such as correlations stronger than quantum ones. As a result one faces even more dramatic gap between classical/quantum and post-quantum world. Therefore it is imperative to search for information principles characterizing physical theories. In recent years, several principles has been proposed, however all of the principles considered so far do not involve uncertainty constraints.
Here, we introduce an elementary system information content principle (ICP) whose basic ingredient is the phenomenon of Heisenberg uncertainty. The principle states that the amount of non-redundant information which may be extracted from a given system is bounded by a perfectly decodable information content of the system. We show that this new principle is respected by classical and quantum theories and is violated by hidden variable theories as well as post-quantum ones: p-GNST and polygon theories. We also illustrate how the principle can be applied to composite systems. Remarkably, ICP can be more sensitive than Tsirelson's bound: it allows to rule out even some theories which do not violate Tsirelson's bound. The elementary system character of ICP suggests that it might be one of the fundamental bricks of Nature.
Quantum physics has remarkable characteristics such as quantum correlations, uncertainty relations, no cloning, which give rise to an interpretative and conceptual gap between the classical and the quantum world. To provide more unified framework generalized probabilistic theories were formulated. Recently, it turned out that such theories include so called postquantum ones which share many of the typical quantum characteristics but predict supraquantum effects such as correlations stronger than quantum ones. As a result one faces even more dramatic gap between classical/quantum and post-quantum world. Therefore it is imperative to search for information principles characterizing physical theories. In recent years, several principles has been proposed, however all of the principles considered so far do not involve uncertainty constraints.
Here, we introduce an elementary system information content principle (ICP) whose basic ingredient is the phenomenon of Heisenberg uncertainty. The principle states that the amount of non-redundant information which may be extracted from a given system is bounded by a perfectly decodable information content of the system. We show that this new principle is respected by classical and quantum theories and is violated by hidden variable theories as well as post-quantum ones: p-GNST and polygon theories. We also illustrate how the principle can be applied to composite systems. Remarkably, ICP can be more sensitive than Tsirelson's bound: it allows to rule out even some theories which do not violate Tsirelson's bound. The elementary system character of ICP suggests that it might be one of the fundamental bricks of Nature.
To explain the conceptual gap between classical and quantum and other, hypothetical descriptions of the world, several principles have been proposed. So far, all these principles have not explicitly included the uncertainty relation. Here we introduce an information content principle (ICP) which represents a constrained uncertainty principle. The principle, by taking into account the encoding and decoding properties of a single physical system, is capable of separation, both classicality and quanta from a number of potential physical theories, including hidden variable theories. The ICP, which is satisfied by both classical and quantum theory, states that the amount of nonredundant information which may be extracted from a given system is bounded by a perfectly decodable information content of the system. We show that ICP allows one to discriminate theories which do not allow for correlations stronger than Tsirelson's bound. We show also how to apply the principle to composite systems, ruling out some theories despite that their elementary constituents behave quantumly.
Classical physics is traditionally characterized as deterministic and founded on the real number continuum, while quantum mechanics is distinguished by its indeterminism and fundamental uncertainty relations. This apparent dichotomy, however, obscures a deeper continuity. We argue that both frameworks embody a common ontological principle: the physical prohibition of absolute precision. In classical physics, this prohibition is implicit, manifesting in information-theoretic bounds, the non-physicality of infinite-precision initial conditions (chaos theory), and the breakdown of determinism in singular configurations (Norton's dome). These phenomena reveal that the classical reliance on mathematical real numbers with infinite information content is an unphysical idealization. Quantum mechanics, by contrast, does not merely reflect this prohibition; it provides its precise quantitative expression. The Heisenberg uncertainty principle σxσp≥ℏ/2 and the non-commutative structure of observables are the exact mathematical formulation of the fact that physical information is fundamentally finite. The Planck constant ℏ is the universal scale that quantifies the minimal phase space volume—the “atom” of information—below which no further refinement is possible. Thus, quantum mechanics is not a separate theory but the completion of classical physics: it supplies the missing quantification of the principle that nature admits no infinite information density, and consequently, no absolutely precise physical quantities.
Information causality A broad class of theories exist which share the distinguishing characteristics of quantum mechanics, but allow even stronger correlations. Therefore a criterion that could be used to distinguish physical theories from non-physical ones would be of considerable value. The principle of 'information causality', introduced here by Marcin Pawłowski et al., may provide just this. The principle states that communication of m classical bits causes information gain of at most m bits. The authors show that it is respected by classical and quantum physics, but violated by other models that resemble quantum mechanics but with stronger correlations. The principle is a generalization of the no-signalling condition (information cannot be transmitted faster than light) and may be a foundational property of nature.
The uncertainty principle of quantum mechanics is often regarded as a fundamental postulate or an ontological property of the microscopic world. This paperproposes a unified interpretative framework based on information constraints, arguing that uncertainty relations are essentially an inevitable consequence of thetwo operational boundaries in the process of physical cognition: finite informationcapacity and feasibility of finite steps. By introducing the Noetherian property ofalgebraic structures and the discretization of information hierarchies, a rigorouscorrespondence from operational constraints to subfactor towers and informationgeometry is constructed. Within this framework, uncertainty relations naturallyemerge from the geometric rigidity of the information hierarchical structure, andtheir mathematical form is locked by algebraic invariants such as the Jones index. The theory not only coherently derives the standard Heisenberg relations butalso predicts testable modifications at extremely high energies and in strong gravitational fields, providing a clear mechanism for the quantum-classical transitionbased on information accumulation phase transitions. This work indicates that uncertainty is not an inherent fuzziness of nature but a structural boundary of physicaldescription under information constraints, thereby establishing a new foundationfor understanding the continuity between quantum theory and classical physics.
The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in quantum technologies. However, neither the uncertainty principle nor uncertainty relations can fully describe the complementarity between quantum measurements. As an attempt to advance the efforts of complementarity in quantum theories, we formally propose a complementary information principle, significantly extending the one introduced by Heisenberg. First, we build a framework of black box testing consisting of pre- and post-testing with two incompatible measurements, introducing a rigorous mathematical expression of complementarity with definite information causality. Second, we provide majorization lower and upper bounds for the complementary information by utilizing the tool of semidefinite programming. In particular, we prove that our bounds are optimal under majorization due to the completeness of the majorization lattice. Finally, as applications to our framework, we present a general method to outer-approximating all uncertainty regions and also establish fundamental limits for all qualified joint uncertainties.
We often marvel at the beautiful randomness in quantum mechanics, but what if it is simply entropy fulfilling its role as dictated by causality? This paper explores the idea that Heisenberg’s uncertainty principle may not represent an intrinsic limitation, but rather a thermodynamic outcome, a cost we pay for achieving precision. We examine Gaussian wavefunctions, investigate entropic uncertainty, and demonstrate that increased knowledge of one variable (such as position) leads to a corresponding increase in entropy in its complementary variable (such as momentum). Nature does not conceal the truth; rather, the process of acquiring knowledge alters the equilibrium. By associating entropy with quantum uncertainty, we are not simply reinterpreting mathematics; We are redefining the implications of quantum indeterminacy. Perhaps the universe is not inherently uncertain; it is simply economical with certainty. We propose that the Heisenberg Uncertainty Principle can be interpreted through the concept of entropy, framing it as an emergent characteristic of the system’s overall information content rather than merely a constraint imposed by quantum mechanics. Investigating this relationship may yield profound insights into the essence of quantum systems and their relationship with the macroscopic realm governed by thermodynamics. This paper offers both a philosophical and mathematical framework that unifies the ideas of entropy and uncertainty, providing a novel viewpoint on one of the most essential principles of quantum mechanics. By analyzing the influence of entropy on quantum uncertainty, this study contests traditional interpretations and encourages a renewed dialogue regarding the foundational principles of physics. It posits that uncertainty transcends mere measurement concerns and may be embedded in the very structure of the universe, prompting a reevaluation of how quantum mechanics integrates into the wider context of physical laws.