Universal Uncertainty Entanglement Theory

Jun‐Li Li, Cong‐Feng Qiao

Abstract Employing the lattice theory on majorization, the universal quantum uncertainty relation for any number of observables and general measurement is investigated. It is found that 1) the least bounds of the universal uncertainty relations can only be properly defined in the lattice theory; 2) contrary to variance and entropy, the metric induced by the majorization lattice implies an intrinsic structure of the quantum uncertainty; and 3) the lattice theory correlates the optimization of uncertainty relation with the entanglement transformation under local quantum operation and classical communication. Interestingly, the optimality of the universal uncertainty relation found can be mimicked by the Lorenz curve, initially introduced in economics to measure the wealth concentration degree of a society.

Zhian Jia, Yu-Chun Wu, Guang‐Can Guo

Characterization of nonlocal correlations is one of the most attractive topics in quantum information theory. In this work, we develop the methods of detecting entanglement and steering based on the universal uncertainty relations and fine-grained uncertainty relations. According to the majorization form of the uncertainty relations, the uncertainty quantifier can be constructed by choosing Schur concave functions. Hence a large number of quantifier-independent entanglement and steering criteria are derived, from which many existing criteria based on different quantifiers can be rededuced. Finally, we show that entanglement and steering of pure states and some mixed states such as isotropic states can be always witnessed by some uncertainty quantifier.

Duan Kai-Min, Chuan‐Feng Li

Kai Kai, MinDuan

Moses Rahnama

We propose that uncertainty relations and entanglement are not limited to the handful of conjugate pairs discovered in quantum mechanics, but represent a universal principle governing all boundary creation in reality. Reality is born when perfect symmetry is broken by exactly one physical inequality-any minimal, thermodynamically paid bias between entangled states. There is no privileged numeric ratio; the relevant invariant is the existence of a nonzero inequality Δ ≠ 0 that survives because it is amplified across N ≥ Nc degrees of freedom and pays at least the Landauer cost kB T ln 2 per bit. This framework predicts infinite complementary pairs across all domains-physical, biological, informational, and conscious-each imposing measurement limits and correlation structures. We derive a universal uncertainty formula ΔP × ΔP' ≥ ℏ_domain/2 applicable to any measurable property and its complement, where ℏ_domain represents the fundamental quantum of action for that domain. This theory explains why we've discovered only a small subset of possible uncertainty relations and predicts numerous testable new pairs including Information- Entropy, Growth-Stability, Causality-Correlation, and Self-Other boundaries.