arXiv subjects

Marijn Waaijer

Publications and source records attributed to Marijn Waaijer.

4 recordsLinked to original sources

arXiv2025

Holevo classicalisation and context integration: Global versus protocolwise integration

Suppose that a family of commutative measurement contexts is given, together with the corresponding classical probability laws. We study the problem under what conditions these contextwise descriptions can be combined into a single classical representation. We distinguish two ways in which this can be done. In {\em global integration}, the prescribed observable algebras are required to fit into a single commutative context and the corresponding probability laws to arise as marginals of one joint law. In {\em protocolwise integration}, by contrast, the context label is retained as part of the description, and the contextwise laws appear as conditional distributions within a single model of the measurement protocol. We show that global integration involves two distinct notions of compatibility: operator-algebraic compatibility of the underlying observables and probabilistic compatibility of their classicalised laws. The former implies the latter, but the converse fails; under the topological hypotheses stated below, probabilistic compatibility is characterised by a Kellerer-type marginal criterion. Protocolwise integration, on the other hand, always exists and is represented operator-algebraically by a direct-sum construction. When global integration exists, the two constructions arise as reductions of a common commutative refinement. We illustrate the distinction in the Bell--CHSH experiment, where Fine's theorem relates global probabilistic integration to Bell locality and the CHSH inequalities. This shows that the obstruction revealed by Bell--CHSH concerns not classical representation as such, but classical representation preserving specified cross-context identifications.

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arXiv2025

Indiscernibility of quantum states

This paper provides a systematic study of the operational idea that a quantum ``state'' is only defined up to what can be distinguished by a chosen family of observables. Concretely, any von Neumann algebra of observables $\mathscr{M}$ induces an equivalence relation on pure and mixed states by declaring two preparations indiscernible when they give identical statistics for every observable in $\mathscr{M}$. The corresponding quotient, the \emph{Holevo space} associated with $\mathscr{M}$, is the effective (relational) state space of the experiment, explicitly dependent on the observer's available measurements. We analyse the resulting geometry and topology of these quotients, and prove a context-complete classical representation theorem: for every von Neumann algebra $\mathscr{M}$ there is a canonical lift $a\mapsto \widehat a$ to bounded continuous functions on the Holevo space, reproducing expectation values pointwise. In the commutative case this reduces to ordinary probability theory on the joint spectrum. The framework is illustrated in explicit examples, including position measurements of a free particle and polarisation measurements in the qubit, EPR, and Bell settings. In particular, in the EPR scenario, Charlie's joint observable defines a simplex of joint outcome distributions, whereas the Alice/Bob marginal viewpoint collapses the effective description to a lower-dimensional space by ``forgetting'' the correlation parameter. We show that by varying the polariser settings, the indiscernibility classes become conjugated (and generically reshuffled), and different settings are typically incompatible at the level of observable algebras.

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arXiv2024

Delayed choice experiments: An analysis in forward time

In this article, we present a detailed analysis of two famous delayed choice experiments: Wheeler's classic gedanken-experiment and the delayed quantum eraser. Our analysis shows that the outcomes of both experiments can be fully explained on the basis of the information collected during the experiments using textbook quantum mechanics only. At no point in the argument, information from the future is needed to explain what happens next. In fact, more is true: for both experiments, we show, in a strictly mathematical way, that a modified version in which the time-ordering of the steps is changed to avoid the delayed choice leads to exactly the same final state. In this operational sense, the scenarios are completely equivalent in terms of conclusions that can be drawn from their outcomes.

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arXiv2021

Relational analysis of the Frauchiger--Renner paradox and interaction-free detection of records from the past

We present an analysis of the Frauchiger-Renner Gedankenexperiment from the point of view of the relational interpretation of quantum mechanics. Our analysis shows that the paradox obtained by Frauchiger and Renner disappears if one rejects promoting one agent's certainty to another agent's certainty when it cannot be validated by records from the past. A by-product of our analysis is an interaction-free detection scheme for the existence of such records.

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