Contextuality from Single-State Ontological Models: An Information-Theoretic Obstruction

Song-Ju Kim

arxiv: 2602.16716 · v3 · submitted 2026-02-03 · 💻 cs.AI · cs.IT· math.IT· quant-ph

Contextuality from Single-State Ontological Models: An Information-Theoretic Obstruction

Song-Ju Kim This is my paper

Pith reviewed 2026-05-16 07:39 UTC · model grok-4.3

classification 💻 cs.AI cs.ITmath.ITquant-ph

keywords contextualityontological modelsconditional mutual informationquantum foundationsinformation theorysingle-state modelsauxiliary register

0 comments

The pith

Classical single-state ontological models must store at least I(C;O|λ) bits of contextual information in an auxiliary register to reproduce operational statistics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies classical ontological models that keep a fixed ontic state for a subsystem while routing all contextual distinctions through a separate auxiliary register. It establishes an information-theoretic lower bound: the contextual information carried by that register cannot be smaller than the conditional mutual information between the chosen intervention and the observed outcome, given the ontic state. This bound follows from elementary properties of mutual information once the same subsystem state is reused across different interventions. A reader following the argument sees that contextuality in such models is not a failure of the subsystem description itself but a necessary overhead when the state is forced to remain unchanged. The result therefore reframes the appearance of contextuality as a representational constraint rather than an intrinsic feature of the underlying reality.

Core claim

Whenever a classical single-state model reproduces operational statistics using an auxiliary contextual register, the required contextual information is lower-bounded by the conditional mutual information I(C;O∣λ) between intervention C and outcome O conditioned on the subsystem ontic state λ. The mathematical inequality is elementary, yet its structural meaning is that contextual distinctions need not be fully internalized within the subsystem ontic state alone when state reuse is enforced.

What carries the argument

The conditional mutual information I(C;O|λ) that lower-bounds the amount of contextual data an auxiliary register must carry when a single fixed ontic state is reused across interventions.

If this is right

Contextual distinctions can be offloaded to an auxiliary register without embedding them inside the reused subsystem ontic state.
The obstruction is a quantitative limit on information flow rather than an absolute prohibition on classical description.
The same bound applies to any model family that enforces fixed subsystem states across changing interventions.
A constructive example demonstrates that the bound is tight for certain operational statistics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The bound supplies a concrete figure of merit for the minimal classical overhead needed to simulate a given contextual behavior under state reuse.
One could test whether any quantum contextual experiment admits a classical simulation whose auxiliary register falls below the computed I(C;O|λ) value; such a finding would falsify the bound.
The perspective may extend to resource theories that quantify contextuality by the size of the minimal auxiliary system required under fixed-state constraints.
Similar information bounds could be derived for multi-partite settings in which several subsystems share a common ontic state description.

Load-bearing premise

The model reuses a fixed subsystem-level ontic state space across multiple interventions, with contextual distinctions handled only via an auxiliary register.

What would settle it

A concrete classical single-state model that reproduces the given operational statistics yet stores strictly less contextual information in its auxiliary register than the value of I(C;O|λ) for the relevant intervention-outcome pair.

Figures

Figures reproduced from arXiv: 2602.16716 by Song-Ju Kim.

read the original abstract

Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a fixed subsystem-level ontic state space is reused across multiple interventions. Our main result is an information-theoretic obstruction: whenever a classical single-state model reproduces operational statistics using an auxiliary contextual register, the required contextual information is lower-bounded by the conditional mutual information $I(C;O\mid \lambda)$ between intervention $C$ and outcome $O$ conditioned on the subsystem ontic state $\lambda$. The mathematical inequality itself is elementary, but its interpretive significance is structural: under shared-state reuse, contextual distinctions need not be fully internalized within the subsystem ontic state alone. We provide a constructive illustration of this point and clarify how the issue should be understood as a limitation of subsystem-level classical representation, rather than as a dualism about physical reality. We further discuss how this perspective relates to ontological models and to contextuality in quantum foundations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives an elementary lower bound on contextual information in single-state ontological models via I(C;O|λ), mainly valuable for interpretive framing of subsystem limits rather than technical novelty.

read the letter

This paper's main takeaway is that classical single-state ontological models, which fix the subsystem ontic state λ across interventions, must use an auxiliary register for context, and that register needs to hold at least I(C;O|λ) information. The bound comes straight from the chain rule once λ is independent of the intervention C. What stands out as new is the way this is cast as an information-theoretic obstruction specific to models with shared ontic states at the subsystem level. The authors apply standard identities and note that the math is elementary, which is accurate based on the description. They do well to include a constructive illustration that shows how the auxiliary register can manage the distinctions without putting everything into λ. This supports their point that the issue is a limitation of subsystem-level classical representation, not a claim about physical reality itself. The discussion ties it back to ontological models in quantum foundations without overcomplicating things. The soft spots are limited. Since the core inequality is basic, the contribution rests more on the framing and interpretation than on a difficult derivation. The abstract is clear on the model assumptions, but the full paper would need to show how this compares to earlier results on contextuality to confirm the novelty. No circularity or unsupported steps appear in the stated result. This work is aimed at specialists in quantum foundations who study contextuality through information or resource lenses. A reader already engaged with ontological models would get value from the precise bound and the example. It deserves a serious referee because it adds a concrete constraint that could guide further analysis in the area. I recommend sending it for peer review.

Referee Report

1 major / 2 minor

Summary. The paper claims that classical single-state ontological models reusing a fixed subsystem ontic state λ across interventions require an auxiliary contextual register whose information content is lower-bounded by the conditional mutual information I(C;O|λ). This bound is derived from elementary information-theoretic identities (chain rule or data-processing inequality) once the outcome O is generated from λ, C, and the auxiliary register, and is illustrated constructively to show that contextual distinctions need not be internalized entirely within the subsystem ontic state.

Significance. If the central inequality holds under the stated model assumptions, the result supplies a precise, elementary information-theoretic measure of the contextual cost incurred by restricting to single-state subsystem representations. This framing usefully separates the limitation of the representational scheme from any claim about physical reality itself and connects directly to existing work on ontological models and contextuality. The emphasis on an elementary derivation is a strength, as it shifts attention to interpretive consequences rather than technical complexity.

major comments (1)

[Main result] Main result (around the statement of the inequality): the abstract asserts the bound follows directly from standard identities, yet the manuscript does not display the explicit chain-rule expansion or the precise definition of the auxiliary-register entropy term. Without these steps, it is impossible to confirm that no hidden restrictions on the model class (e.g., independence of λ from C) are tacitly required for the inequality to be tight.

minor comments (2)

[Notation and model definition] The notation for the auxiliary contextual register is introduced only informally; an explicit equation or diagram showing its functional dependence on C and its independence from λ would improve readability.
[Constructive illustration] In the constructive illustration, the numerical value of I(C;O|λ) should be computed explicitly for the example so that readers can verify that the bound is achieved or approached.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment and recommendation for minor revision. We address the single major comment below.

read point-by-point responses

Referee: Main result (around the statement of the inequality): the abstract asserts the bound follows directly from standard identities, yet the manuscript does not display the explicit chain-rule expansion or the precise definition of the auxiliary-register entropy term. Without these steps, it is impossible to confirm that no hidden restrictions on the model class (e.g., independence of λ from C) are tacitly required for the inequality to be tight.

Authors: We agree that an explicit derivation will improve clarity and confirm the assumptions. In the revised manuscript we will insert, immediately after the statement of the main inequality, a short paragraph that (i) recalls the model definition (outcome O generated conditionally on the triple (λ, C, R) with λ the fixed subsystem ontic state), (ii) applies the chain rule to obtain I(C;O|λ) = H(O|λ) − H(O|C,λ), and (iii) invokes the data-processing inequality on the Markov chain C → R → O given λ to conclude that the entropy of the auxiliary register satisfies H(R) ≥ I(C;O|λ). The paragraph will also state the precise definition of the auxiliary-register entropy term. This expansion uses only the single-state reuse assumption already stated in the paper; λ is independent of C by construction of the model class, with no further restrictions imposed. revision: yes

Circularity Check

0 steps flagged

No significant circularity; elementary inequality from model definition

full rationale

The central result states that contextual information is lower-bounded by I(C;O|λ) under the model's fixed subsystem ontic state λ and auxiliary register. This follows directly from the chain rule or data-processing inequality once outcomes O are generated conditionally on λ, C, and the register; the bound is an identity applied to the stated assumptions rather than a self-referential fit, redefinition, or self-citation chain. No load-bearing step reduces to its own inputs by construction, and the paper treats the inequality as elementary while emphasizing its interpretive consequences for subsystem representations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The result rests on standard information theory and the definition of single-state ontological models; no free parameters or new entities are introduced in the abstract.

axioms (1)

standard math Standard chain rule and non-negativity properties of conditional mutual information
The lower bound is asserted to follow directly from these properties applied to the model.

pith-pipeline@v0.9.0 · 5475 in / 1135 out tokens · 31671 ms · 2026-05-16T07:39:21.395190+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

whenever a classical single-state model reproduces operational statistics using an auxiliary contextual register, the required contextual information is lower-bounded by the conditional mutual information I(C;O∣λ)
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

H(M)≥I(C;O|λ)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Contextual Control without Memory Growth in a Context-Switching Task
cs.AI 2026-04 unverdicted novelty 7.0

Intervention on a fixed-size recurrent state enables contextual control in sequential decisions without memory growth or direct context input.
Contextual Chain: Single-State Ledger Design for Mobile/IoT Networks with Frequent Partitions
cs.DC 2026-04 unverdicted novelty 6.0

Simulation at N=20 across 500 seeds finds that adaptive synchronization, not quarantine, primarily drives final agreement and recovery-time improvement after partitions in noisy regimes.

Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages · cited by 2 Pith papers

[1]

An ontic state space Λ, whose elementsλ∈Λ rep- resent underlying physical states

work page
[2]

Preparation distributionsµ(λ|P) over ontic states for each preparation procedureP

work page
[3]

Response functionsξ(o|M, λ) giving the condi- tional probability of outcomeogiven measurement Mand ontic stateλ. Observable statistics are reproduced as p(o|P, M) = Z Λ µ(λ|P)ξ(o|M, λ)dλ.(1) All randomness in the model arises from classical prob- ability distributions over ontic states and response func- tions. B. Single-State Ontological Models and Inter...

work page
[4]

The ontic state space Λ is fixed and reused across all interventions or measurement contexts

work page
[5]

The ontic state space Λ is not indexed, duplicated, or refined according to the interventionC

work page
[6]

All observable statistics are generated from a single underlying classical probability space over Λ. Under these conditions, all contextual dependence must be mediated through the response functionsξ(o| C, λ) acting on a common ontic state space, rather than through context-dependent enlargement or branching of Λ. Definition 3(Interventions).Acontextis mo...

work page
[7]

A preparation distributionµ(λ) over ontic states

work page
[8]

Response functionsξ(o|C, λ) giving outcome probabilities conditioned on the ontic state and in- tervention. Observable statistics are given by p(o|C) = Z Λ µ(λ)ξ(o|C, λ)dλ.(2) To represent operational distinctions not internalized in the subsystem ontic stateλ, an auxiliary contextual variableMmay be introduced. The role ofMis not to postulate a second on...

work page
[9]

a fixed subsystem ontic state spaceΛis reused across interventions; 2.Λis not indexed or refined according toC; and

work page
[10]

The proposition isolates a simple but useful obstruc- tion

operational statistics are reproduced using an aux- iliary contextual variableMsuch that p(o|λ, M, C) =p(o|λ, M).(3) Then H(M)≥I(C;O|λ).(4) In particular, wheneverI(C;O|λ)>0, any such model requiresH(M)>0. The proposition isolates a simple but useful obstruc- tion. The quantityI(C;O|λ) measures how much the interventionCremains informative about the out- ...

work page
[11]

This toy example is not intended as a full contextuality construction of the pairwise-marginal type suggested in Fig

= 1/2. This toy example is not intended as a full contextuality construction of the pairwise-marginal type suggested in Fig. 1; its narrower role is to exhibit a case in which intervention-dependent information remains rel- evant even after conditioning on the reused subsystem ontic state. Let the outcome be given by O=λ⊕f(C), wheref(C)∈ {0,1}is an interv...

work page
[12]

The ontic state is represented by a ran- dom variableλ∈Λ, distributed according to a prepara- tion distributionµ(λ)

Setup We consider a classical ontological model with a fixed ontic state space Λ, satisfying the single-state conditions of Definition 2. The ontic state is represented by a ran- dom variableλ∈Λ, distributed according to a prepara- tion distributionµ(λ). LetCdenote the set of interventions (measurement contexts), withC∈ Ca random variable specifying the 7...

work page
[13]

Auxiliary Contextual Bookkeeping Under the single-state constraint, the ontic state space Λ is fixed and cannot be refined or indexed by the inter- vention. If one chooses to absorb intervention-dependent distinctions into an auxiliary bookkeeping variableM rather than into a refinement of the reused subsystem state space Λ, then the model takes the form ...

work page
[14]

Information-Theoretic Bound We now derive the lower bound on the contextual in- formation required. From the channel structure C→(λ, M)→O,(A6) the data-processing inequality implies I(C;O|λ)≤I(C;M|λ).(A7) This inequality expresses that, within the chosen book- keeping representation, any residual dependence ofOon the interventionCbeyond the reused ontic s...

work page
[15]

An illustrative example is given in Sec

On Saturation The lower bound can be saturated in simple construc- tions where the auxiliary contextual variableMcarries precisely the intervention-dependent bookkeeping needed to reproduce the operational distinctions at issue, with- out introducing additional correlations. An illustrative example is given in Sec. IV, whereM may be taken as a determinist...

work page
[16]

Independence from Ontic State Capacity and Dynamics Importantly, the bound is not about the size of the ontic state space Λ by itself. Rather, it concerns a modeling choice: Λ is reused across interventions with- out intervention-indexed refinement, while intervention- dependent distinctions are tracked by auxiliary book- keeping. In that setting, increas...

work page
[17]

In regimes whereI(C;O|λ)>0, this further yieldsH(M)>0

Conclusion of the Proof We have shown that whenever a classical single-state ontological description is represented with an auxiliary contextual variableMsatisfying the Markov condition p(o|λ, M, C) =p(o|λ, M), the information-theoretic bound H(M)≥I(C;O|λ) (A13) follows immediately. In regimes whereI(C;O|λ)>0, this further yieldsH(M)>0. This proves Propos...

work page
[18]

John S. Bell. On the problem of hidden variables in quan- tum mechanics.Reviews of Modern Physics, 38:447–452, 1966

work page 1966
[19]

The problem of hidden variables in quantum mechanics.Journal of Mathematics and Mechanics, 17:59–87, 1967

Simon Kochen and Ernst Specker. The problem of hidden variables in quantum mechanics.Journal of Mathematics and Mechanics, 17:59–87, 1967

work page 1967
[20]

Hidden variables, joint probability, and the bell inequalities.Physical Review Letters, 48:291–295, 1982

Arthur Fine. Hidden variables, joint probability, and the bell inequalities.Physical Review Letters, 48:291–295, 1982

work page 1982
[21]

Spekkens

Robert W. Spekkens. Contextuality for preparations, transformations, and unsharp measurements.Physical Review A, 71:052108, 2005

work page 2005
[22]

Spekkens

Nicholas Harrigan and Robert W. Spekkens. Einstein, in- completeness, and the epistemic view of quantum states. Foundations of Physics, 40(2):125–157, 2010

work page 2010
[23]

The sheaf- theoretic structure of non-locality and contextuality.New Journal of Physics, 13:113036, 2011

Samson Abramsky and Adam Brandenburger. The sheaf- theoretic structure of non-locality and contextuality.New Journal of Physics, 13:113036, 2011

work page 2011
[24]

Experimentally testable state- independent quantum contextuality.Physical Review Letters, 101:210401, 2008

Ad´ an Cabello. Experimentally testable state- independent quantum contextuality.Physical Review Letters, 101:210401, 2008

work page 2008
[25]

Claude E. Shannon. A mathematical theory of communi- cation.Bell System Technical Journal, 27:379–423, 623– 656, 1948

work page 1948
[26]

Simon.Models of Bounded Rationality

Herbert A. Simon.Models of Bounded Rationality. MIT Press, 1982

work page 1982
[27]

Anderson.The Adaptive Character of Thought

John R. Anderson.The Adaptive Character of Thought. Lawrence Erlbaum Associates, 1990

work page 1990
[28]

Oxford University Press, 1986

Alan Baddeley.Working Memory. Oxford University Press, 1986

work page 1986
[29]

Cover and Joy A

Thomas M. Cover and Joy A. Thomas.Elements of In- formation Theory. Wiley, 2nd edition, 2006

work page 2006

[1] [1]

An ontic state space Λ, whose elementsλ∈Λ rep- resent underlying physical states

work page

[2] [2]

Preparation distributionsµ(λ|P) over ontic states for each preparation procedureP

work page

[3] [3]

Response functionsξ(o|M, λ) giving the condi- tional probability of outcomeogiven measurement Mand ontic stateλ. Observable statistics are reproduced as p(o|P, M) = Z Λ µ(λ|P)ξ(o|M, λ)dλ.(1) All randomness in the model arises from classical prob- ability distributions over ontic states and response func- tions. B. Single-State Ontological Models and Inter...

work page

[4] [4]

The ontic state space Λ is fixed and reused across all interventions or measurement contexts

work page

[5] [5]

The ontic state space Λ is not indexed, duplicated, or refined according to the interventionC

work page

[6] [6]

All observable statistics are generated from a single underlying classical probability space over Λ. Under these conditions, all contextual dependence must be mediated through the response functionsξ(o| C, λ) acting on a common ontic state space, rather than through context-dependent enlargement or branching of Λ. Definition 3(Interventions).Acontextis mo...

work page

[7] [7]

A preparation distributionµ(λ) over ontic states

work page

[8] [8]

Response functionsξ(o|C, λ) giving outcome probabilities conditioned on the ontic state and in- tervention. Observable statistics are given by p(o|C) = Z Λ µ(λ)ξ(o|C, λ)dλ.(2) To represent operational distinctions not internalized in the subsystem ontic stateλ, an auxiliary contextual variableMmay be introduced. The role ofMis not to postulate a second on...

work page

[9] [9]

a fixed subsystem ontic state spaceΛis reused across interventions; 2.Λis not indexed or refined according toC; and

work page

[10] [10]

The proposition isolates a simple but useful obstruc- tion

operational statistics are reproduced using an aux- iliary contextual variableMsuch that p(o|λ, M, C) =p(o|λ, M).(3) Then H(M)≥I(C;O|λ).(4) In particular, wheneverI(C;O|λ)>0, any such model requiresH(M)>0. The proposition isolates a simple but useful obstruc- tion. The quantityI(C;O|λ) measures how much the interventionCremains informative about the out- ...

work page

[11] [11]

This toy example is not intended as a full contextuality construction of the pairwise-marginal type suggested in Fig

= 1/2. This toy example is not intended as a full contextuality construction of the pairwise-marginal type suggested in Fig. 1; its narrower role is to exhibit a case in which intervention-dependent information remains rel- evant even after conditioning on the reused subsystem ontic state. Let the outcome be given by O=λ⊕f(C), wheref(C)∈ {0,1}is an interv...

work page

[12] [12]

The ontic state is represented by a ran- dom variableλ∈Λ, distributed according to a prepara- tion distributionµ(λ)

Setup We consider a classical ontological model with a fixed ontic state space Λ, satisfying the single-state conditions of Definition 2. The ontic state is represented by a ran- dom variableλ∈Λ, distributed according to a prepara- tion distributionµ(λ). LetCdenote the set of interventions (measurement contexts), withC∈ Ca random variable specifying the 7...

work page

[13] [13]

Auxiliary Contextual Bookkeeping Under the single-state constraint, the ontic state space Λ is fixed and cannot be refined or indexed by the inter- vention. If one chooses to absorb intervention-dependent distinctions into an auxiliary bookkeeping variableM rather than into a refinement of the reused subsystem state space Λ, then the model takes the form ...

work page

[14] [14]

Information-Theoretic Bound We now derive the lower bound on the contextual in- formation required. From the channel structure C→(λ, M)→O,(A6) the data-processing inequality implies I(C;O|λ)≤I(C;M|λ).(A7) This inequality expresses that, within the chosen book- keeping representation, any residual dependence ofOon the interventionCbeyond the reused ontic s...

work page

[15] [15]

An illustrative example is given in Sec

On Saturation The lower bound can be saturated in simple construc- tions where the auxiliary contextual variableMcarries precisely the intervention-dependent bookkeeping needed to reproduce the operational distinctions at issue, with- out introducing additional correlations. An illustrative example is given in Sec. IV, whereM may be taken as a determinist...

work page

[16] [16]

Independence from Ontic State Capacity and Dynamics Importantly, the bound is not about the size of the ontic state space Λ by itself. Rather, it concerns a modeling choice: Λ is reused across interventions with- out intervention-indexed refinement, while intervention- dependent distinctions are tracked by auxiliary book- keeping. In that setting, increas...

work page

[17] [17]

In regimes whereI(C;O|λ)>0, this further yieldsH(M)>0

Conclusion of the Proof We have shown that whenever a classical single-state ontological description is represented with an auxiliary contextual variableMsatisfying the Markov condition p(o|λ, M, C) =p(o|λ, M), the information-theoretic bound H(M)≥I(C;O|λ) (A13) follows immediately. In regimes whereI(C;O|λ)>0, this further yieldsH(M)>0. This proves Propos...

work page

[18] [18]

John S. Bell. On the problem of hidden variables in quan- tum mechanics.Reviews of Modern Physics, 38:447–452, 1966

work page 1966

[19] [19]

The problem of hidden variables in quantum mechanics.Journal of Mathematics and Mechanics, 17:59–87, 1967

Simon Kochen and Ernst Specker. The problem of hidden variables in quantum mechanics.Journal of Mathematics and Mechanics, 17:59–87, 1967

work page 1967

[20] [20]

Hidden variables, joint probability, and the bell inequalities.Physical Review Letters, 48:291–295, 1982

Arthur Fine. Hidden variables, joint probability, and the bell inequalities.Physical Review Letters, 48:291–295, 1982

work page 1982

[21] [21]

Spekkens

Robert W. Spekkens. Contextuality for preparations, transformations, and unsharp measurements.Physical Review A, 71:052108, 2005

work page 2005

[22] [22]

Spekkens

Nicholas Harrigan and Robert W. Spekkens. Einstein, in- completeness, and the epistemic view of quantum states. Foundations of Physics, 40(2):125–157, 2010

work page 2010

[23] [23]

The sheaf- theoretic structure of non-locality and contextuality.New Journal of Physics, 13:113036, 2011

Samson Abramsky and Adam Brandenburger. The sheaf- theoretic structure of non-locality and contextuality.New Journal of Physics, 13:113036, 2011

work page 2011

[24] [24]

Experimentally testable state- independent quantum contextuality.Physical Review Letters, 101:210401, 2008

Ad´ an Cabello. Experimentally testable state- independent quantum contextuality.Physical Review Letters, 101:210401, 2008

work page 2008

[25] [25]

Claude E. Shannon. A mathematical theory of communi- cation.Bell System Technical Journal, 27:379–423, 623– 656, 1948

work page 1948

[26] [26]

Simon.Models of Bounded Rationality

Herbert A. Simon.Models of Bounded Rationality. MIT Press, 1982

work page 1982

[27] [27]

Anderson.The Adaptive Character of Thought

John R. Anderson.The Adaptive Character of Thought. Lawrence Erlbaum Associates, 1990

work page 1990

[28] [28]

Oxford University Press, 1986

Alan Baddeley.Working Memory. Oxford University Press, 1986

work page 1986

[29] [29]

Cover and Joy A

Thomas M. Cover and Joy A. Thomas.Elements of In- formation Theory. Wiley, 2nd edition, 2006

work page 2006