arXiv subjects

Gábor Hofer-Szabó

Publications and source records attributed to Gábor Hofer-Szabó.

14 recordsLinked to original sources

arXiv2026

Trajectory of Probabilities, Probability on Trajectories, and the Stochastic-Quantum Correspondence

The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which assigns probabilities to possible histories. A lack of a clear distinction between these two probabilistic descriptions has given rise to a number of conceptual difficulties, particularly in recent analyses of stochastic-quantum correspondence. This paper provides a systematic account of their relationship. We define probability dynamics and stochastic process families together with a precise notion of implementation that connects the two descriptions. We show that implementations are generically non-unique, that every probability dynamics admits a Markovian implementation, and characterize when non-Markovian implementations are possible. We expose fallacies in common arguments for the linearity of probability dynamics based on the law of total probability and clarify the proper interpretation of ``transition matrices'' by distinguishing dynamics-level maps from the conditional probability matrices of implementing processes. We further introduce decomposability as the appropriate general notion of stepwise evolution for (possibly nonlinear) probability dynamics, relate it to divisibility in the linear case -- showing that the two can come apart -- and disentangle both notions from Markovianity and time-homogeneity. Finally, we connect these results to what we call statistical dynamics, in which linearity is indeed physically motivated, and contrast the framework with quantum mechanics.

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arXiv2025

Operational equivalence and causal structure

In operational quantum mechanics two measurements are called operationally equivalent if they yield the same distribution of outcomes in every quantum state and hence are represented by the same operator. In this paper, I will show that the ontological models for quantum mechanics and, more generally, for any operational theory sensitively depend on which measurement we choose from the class of operationally equivalent measurements, or more precisely, which of the chosen measurements can be performed simultaneously. To this goal, I will take first three examples -- a classical theory, the EPR-Bell scenario and the Popescu-Rochlich box; then realize each example by two operationally equivalent but different operational theories -- one with a trivial and another with a non-trivial compatibility structure; and finally show that the ontological models for the different theories will be different with respect to their causal structure, contextuality, and fine-tuning.

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arXiv2024

Noncommuting common causes revisited

In this paper, we revisit the concept of noncommuting common causes; refute two objections raised against them, the triviality objection and the lack of causal explanatory force; and explore how their existence modifies the EPR argument. More specifically, we show that 1) product states screening off all quantum correlations do not compromise noncommuting common causal explanations; 2) noncommuting common causes can satisfy the law of total probability; 3) perfect correlations can have indeterministic noncommuting common causes; and, as a combination of the above claims, 4) perfect correlations can have noncommuting common causes which are both nontrivial and satisfy the law of total probability.

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arXiv2023

Sequential measurements and the Kochen-Specker arguments

It will be shown that the Peres-Mermin square admits value-definite noncontextual hidden-variable models if the observables associated with the operators can be measured only sequentially but not simultaneously. Namely, sequential measurements allow for noncontextual models in which hidden states update between consecutive measurements. Two recent experiments realizing the Peres-Mermin square by sequential measurements will also be analyzed along with other hidden-variable models accounting for these experiments.

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arXiv2022

Two concepts of noncontextuality in quantum mechanics

There are two different and logically independent concepts of noncontextuality in quantum mechanics. First, an ontological (hidden variable) model for quantum mechanics is called noncontextual if every ontic (hidden) state determines the probability of the outcomes of every measurement independently of what other measurements are simultaneously performed. Second, an ontological model is noncontextual if any two measurements which are represented by the same self-adjoint operator or, equivalently, which have the same probability distribution of outcomes in every quantum state also have the same probability distribution of outcomes in every ontic state. I will call the first concept simultaneous noncontextuality, the second measurement noncontextuality. In the paper I will overview and critically analyze some of the most significant accounts of contextuality in the literature and subsume them under these two categories.

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arXiv2020

Three noncontextual hidden variable models for the Peres-Mermin square

I will argue that the Peres-Mermin square does not necessarily rule out a value-definite (deterministic) noncontextual hidden variable model if the operators are not given a physical interpretation satisfying the following two requirements: (i) each operator is uniquely realized by a single physical measurement; (ii) commuting operators are realized by simultaneous measurements. To underpin this claim, I will construct three hidden variable models for three different physical realizations of the Peres-Mermin square: one violating (i), another violating (ii), and a third one violating both (i) and (ii).

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arXiv2020

Commutativity, comeasurability, and contextuality in the Kochen-Specker arguments

If noncontextuality is defined as the robustness of a system's response to a measurement against other simultaneous measurements, then the Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality. Namely, for the argument to be effective, (i) each operator must be uniquely associated with a measurement and (ii) commuting operators must represent simultaneous measurements. However, in all Kochen-Specker arguments discussed in the literature either (i) or (ii) is not met. Arguments meeting (i) contain at least one subset of mutually commuting operators which do not represent simultaneous measurements and hence fail to physically justify the functional composition principle. Arguments meeting (ii) associate some operators with more than one measurement and hence need to invoke an extra assumption different from noncontextuality.

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arXiv2020

On the three types of Bell's inequalities

Bell's inequalities can be understood in three different ways depending on whether the numbers featuring in the inequalities are interpreted as classical probabilities, classical conditional probabilities, or quantum probabilities. In the paper I will argue that the violation of Bell's inequalities has different meanings in the three cases. In the first case it rules out the interpretation of certain numbers as probabilities of events. In the second case it rules out a common causal explanation of conditional correlations of certain events (measurement outcomes) conditioned on other events (measurement settings). Finally, in the third case the violation of Bell's inequalities neither rules out the interpretation of these numbers as probabilities of events nor a common causal explanation of the correlations between these events---provided both the events and the common causes are interpreted non-classically.

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arXiv2019

Quantum mechanics as a noncommutative representation of classical conditional probabilities

The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical representation of classical conditional probabilities is situated within the broader frame of noncommutative representations. To this goal, we adopt some parts of the quantum formalism and ask whether empirical data can constrain the rest of the representation to conform to quantum mechanics. We will show that as the set of empirical data grows conventional elements in the representation gradually shrink and the noncommutative representations narrow down to the unique quantum mechanical representation.

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arXiv2019

Bell's local causality is a d-separation criterion

This paper aims to motivate Bell's notion of local causality by means of Bayesian networks. In a locally causal theory any superluminal correlation should be screened off by atomic events localized in any so-called \textit{shielder-off region} in the past of one of the correlating events. In a Bayesian network any correlation between non-descendant random variables are screened off by any so-called \textit{d-separating set} of variables. We will argue that the shielder-off regions in the definition of local causality conform in a well defined sense to the d-separating sets in Bayesian networks.

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arXiv2012

Bell inequality and common causal explanation in algebraic quantum field theory

Bell inequalities, understood as constraints between classical conditional probabilities, can be derived from a set of assumptions representing a common causal explanation of classical correlations. A similar derivation, however, is not known for Bell inequalities in algebraic quantum field theories establishing constraints for the expectation of specific linear combinations of projections in a quantum state. In the paper we address the question as to whether a 'common causal justification' of these non-classical Bell inequalities is possible. We will show that although the classical notion of common causal explanation can readily be generalized for the non-classical case, the Bell inequalities used in quantum theories cannot be derived from these non-classical common causes. Just the opposite is true: for a set of correlations there can be given a non-classical common causal explanation even if they violate the Bell inequalities. This shows that the range of common causal explanations in the non-classical case is wider than that restricted by the Bell inequalities.

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arXiv2012

Noncommuting local common causes for correlations violating the Clauser-Horne inequality

In the paper the EPR-Bohm scenario will be reproduced in an algebraic quantum field theoretical setting with locally finite degrees of freedom. It will be shown that for a set of spatially separated correlating events (projections) maximally violating the Clauser-Horne inequality there can be given a common causal explanation if commutativity is abandoned between the common cause and the correlating events. Moreover, the noncommuting common cause will be local and supported in the common past of the correlating events.

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arXiv2012

Noncommutative Common Cause Principles in Algebraic Quantum Field Theory

States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set {C, non-C} screens off the correlation between A and B.

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arXiv2011

Reichenbach's Common Cause Principle in Algebraic Quantum Field Theory with Locally Finite Degrees of Freedom

In the paper it will be shown that Reichenbach's Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A and B supported in spacelike separated double cones O(a) and O(b), respectively, a correlating state can be given for which there is no nontrivial common cause (system) located in the union of the backward light cones of O(a) and O(b) and commuting with the both A and B. Since noncommuting common cause solutions are presented in these states the abandonment of commutativity can modulate this result: noncommutative Common Cause Principles might survive in these models.

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