Zeilinger's Foundational Principle

• Zeilinger's Foundational Principle is a theoretical framework asserting that every elementary quantum system carries only one bit of information, thereby defining its Hilbert space structure.
• It connects quantization, objective probabilities, and nonlocal correlations by demonstrating that limited informational capacity leads to irreducible randomness in quantum measurements.
• The principle has sparked debates by contrasting an information-based view with contextual interpretations, influencing both experimental protocols and philosophical discussions in quantum foundations.

Zeilinger's Foundational Principle posits that the irreducible randomness and state structure of quantum mechanics can be derived from a single informational constraint: an elementary system carries only one bit of information. This principle asserts that each quantum system is fundamentally limited to representing the truth value of one yes/no proposition, which formally constrains the dimension and structure of quantum state spaces. Zeilinger’s approach offers an informational synthesis of quantization, objective probability, and quantum nonlocality, but also invites substantial philosophical and technical critique—most notably the contextuality-based alternative, which reframes quantum properties as context-dependent rather than information-bearing. This article surveys the formulation, mathematical consequences, critical debates, and experimental implications of Zeilinger’s Foundational Principle, highlighting its influence and limitations within the quantum foundations literature.

1. Principle Formulation and Motivation

Zeilinger's Foundational Principle can be succinctly stated as: "An elementary system carries one bit of information," or equivalently, "An elementary system represents the truth value of one proposition" (Laurent et al., 2022, Pris, 2021). The essential motivation is to elevate "information" to the same ontological status as "reality," contrasting the classical perspective where physical properties exist independent of observation. The informational constraint is intended to synthesize features such as quantization, objective quantum probabilities, exclusion of local hidden variables, and complementarity, arguing that these all follow from the principle that a system's informational content is bounded (Laurent et al., 2022).

The recent articulation links this principle explicitly to irreducible randomness: "the irreducible randomness of quantum events arises because an elementary system carries only one bit of information" (Svozil, 9 Dec 2025).

2. Formal Consequences and Hilbert Space Structure

Zeilinger and collaborators map the information content assigned to a system directly onto the structure of its Hilbert space (Laurent et al., 2022):

• For a system with $I$ bits, the dimension of its Hilbert space $H$ satisfies $\dim H = 2^I$. An elementary system ($I=1$) thus corresponds to a qubit with $\dim H=2$.
• For $N$ elementary systems, the total information capacity is $N$ bits and $\dim H_{\text{total}} = 2^N$.
• In the entangled state $\ket{\psi^-}$ of two spin-1/2 particles, the two bits of total information are "exhausted" by the joint properties, with individual constituents left "completely undefined." Consequently, local probabilities are maximally random: $P(+)_ {\vec{n}} = P(-)_{\vec{n}} = 1/2$ (Svozil, 9 Dec 2025).
• The conservation of information in isolated processes is mapped to the unitary structure of quantum dynamics. The Born rule, $p_j = \mathrm{Tr}(\rho \Pi_j)$, then fixes the objective quantum probabilities, with the "information invariance" principle ensuring that any complete set of complementary measurements on an elementary system distributes exactly one bit across their outcomes (Laurent et al., 2022).

3. Illustrative Examples and Experimental Implications

Zeilinger’s principle predicts both structural and operational features of quantum systems. For single qubit measurements—such as sequential Stern–Gerlach measurements—the state can answer only one yes/no question per system.

Entanglement sharply illustrates informational exhaustion. In a spin singlet $\ket{\psi^-}$, the two available bits are fully "used up" to specify joint properties (e.g., "spins are opposite along $z$"), so local measurements yield irreducibly random results (Svozil, 9 Dec 2025). The operational protocol for quantum clocks provides a concrete scenario: each local outcome is a "tick" ($+1$ detection), and the maximal frequency of coincident ticks measured across varying angles exceeds the classical benchmark by up to 13.6% due to this quantum informational constraint and contextuality. However, this nonclassical behavior only emerges when correlations at multiple settings are compared, as a classical model can mimic the quantum rate at any single angle (Svozil, 9 Dec 2025).

The table below summarizes the core information-theoretic implications for quantum and classical models:

Scenario	Quantum (Zeilinger Principle)	Classical (Peres' Model)
Local Randomness	$P(+)=P(-)=1/2$	Deterministic for given $\vec{J}$
Entanglement Information Distribution	All bits exhausted by joint prop.	Bits/values assigned locally
Coincidence Rate at angle $\theta$	$R_{QM}(\theta)=\frac{1}{2}\sin^2(\theta/2)$	$R_{cl}(\theta)=\frac{\theta}{2\pi}$

4. Critiques and the Contextuality-Based Alternative

A principal critique targets the "idealism" inherent in treating information as ontologically primary. Laurent & Pris and others argue that the assertion "an elementary system carries one bit" conflates epistemic knowledge (information about a system) with ontic status (the physical reality of the system) (Laurent et al., 2022, Pris, 2021). The critique identifies internal inconsistencies: Zeilinger refers both to systems as bearers of information (ontic) and to information as accessible only via observation (epistemic).

The contextuality principle is proposed as a replacement: "Quantum systems and their properties are identifiable only with reference to the specific means of observation—i.e., the context—in which they are measured" (Laurent et al., 2022). Properties arise only within a measurement context, so it is meaningless to attribute bits or propositions to a system in a context-independent fashion. The mathematical analogue is that a system answers a single yes/no question, identified only in the experimental context, aligning with assignment of a rank-1 projector $\Pi$.

This contextual realist stance interprets the features Zeilinger attributes to information-carrying—quantization, irreducible randomness, complementarity, and joint entanglement correlations—as consequences of the inseparability of properties and context, not as a result of information being a physical substrate (Pris, 2021).

5. Quantum Causality, Nonlocality, and Correlations

Zeilinger's information principle implies that the lack of local information in entangled systems mandates "irreducible non-locality." The absence of pre-defined local properties (due to informational exhaustion) is interpreted as non-local transfer or sharing of information during measurement. Opponents counter that quantum causality, as encoded in the entangled wavefunction and actualized only within a specific context, suffices to account for observed correlations without invoking nonlocal information transfer (Laurent et al., 2022). "Unperformed experiments have no results" (Peres’ dictum) is cited to stress that it is meaningless to attribute outcomes to counterfactual measurements, as quantum systems need not satisfy constraints across all angles simultaneously—an unavoidable nonclassical feature demonstrable via Bell-type inequalities (Svozil, 9 Dec 2025).

6. Synthesis, Limitations, and Foundational Significance

Zeilinger's Foundational Principle offers a prescriptive route for reconstructing quantum theory: the minimal unit of information (one bit) prescribes a two-dimensional Hilbert space, enforces complementarity, and constrains quantum probabilities. It catalyzed a major turn towards information-theoretic and operational formulations in the quantum foundations community (Laurent et al., 2022).

However, several limitations persist:

• The reification of information provokes category error critiques and philosophical unease.
• The principle requires nonlocality to explain correlations, whereas contextuality-based interpretations attribute non-classicality to the contextual emergence of properties.
• The contextuality principle, while more ontologically parsimonious, is less prescriptive regarding Hilbert space dimension and formalism, emphasizing instead a Wittgensteinian, rule-based realism (Pris, 2021).

In summary, Zeilinger's Foundational Principle links quantum structure directly to bounded informational content. Its significance is both technical and philosophical: it has reshaped discussions on what quantum mechanics fundamentally describes and how best to represent the emergence of physical phenomena from formal constraints grounded in information or in context (Laurent et al., 2022, Pris, 2021, Svozil, 9 Dec 2025).