Centennial Workshop on Quantum Probability, Causality, and Information

25 Sept 2026, 13:00 → 27 Sept 2026, 18:00 US/Eastern

Lehman Hall (Harvard University)

Xiao-li Meng (Harvard University), Pavel Nadolsky (Michigan State University)

We are pleased to announce The Centennial Workshop on Quantum Causality, Probability, and Information, to be held at Harvard University in Cambridge, Massachusetts, from September 25–27, 2026.

In the year when we celebrate the 100th anniversary of the publication of Schrödinger equation and Born’s rule, this interdisciplinary workshop will bring together leading researchers from physics, statistics, philosophy, and data science to examine foundational questions at the intersection of causality, probability, and information in modern science. Hosted in collaboration with the Harvard Data Science Initiative and Harvard Data Science Review, the meeting aims to foster deep dialogue across disciplines at a time when advances in quantum theory, large-scale data, and artificial intelligence are reshaping scientific inference.

Scope and Vision

Causality and probability lie at the core of scientific reasoning, yet their interpretation and application vary significantly across fields. In quantum physics, probability enters in non-classical settings; in statistics and AI, it underpins inference from data and prediction; in philosophy, it raises enduring conceptual questions about explanation and knowledge.

This workshop seeks to clarify these perspectives and explore their connections, with particular emphasis on the role of information as a unifying theme across disciplines.

Key guiding questions include:

• What does causality mean in modern science, particularly in quantum contexts?
• How should probability be interpreted across physical theory, statistics, and machine learning?
• What is the relationship between causal models, probabilistic inference, and information-theoretic frameworks?
• Can quantum phenomena be understood within broader probabilistic or informational paradigms?
• How do advances in AI reshape our understanding of uncertainty, inference, and scientific explanation?

 

Topics of Interest

The program will span a range of interconnected themes, including:

• Foundations of causation and causal modeling
• Interpretations of probability (frequentist, Bayesian, quantum, and beyond)
• Quantum probability and its relation to classical probability theory
• Information-theoretic approaches to physics and inference
• The relationship between correlation, causation, and signaling
• Uncertainty quantification in modern physics and data-driven science
• The role of AI and machine learning in scientific reasoning

 

Expected Outcomes

The workshop aims to generate:

• A curated set of questions identifying key open challenges
• A special issue of the Harvard Data Science Review with workshop’s contributions

 

Practical information

Participation in the workshop requires accepted registration. The registration form and a webpage with information about the venue, lodging, and travel can be accessed through the menu on the left-hand side.

 

Organizers

• Christine Aidala (University of Michigan)
• Jacob Barandes (Harvard University)
• Hanti Lin (University of California, Davis)
• Xiao-Li Meng (Harvard University)
• Pavel Nadolsky (Michigan State University)

Friday 25 September

14:00 → 14:15 Opening remarks

Speakers: Pavel Nadolsky, Xiao-Li Meng

14:15 → 15:30 Talk 1: 'Shut up and calculate': Quantum probability and the practical physicist

In this talk, I present a practical introduction to how probabilities arise in quantum mechanics, from the perspective of a Mermin-Feynman interpretation. The axioms of probability are presented in analogy to requirements on physical states, assuming the Copernican principle, linearity of operators, and general properties of linear algebra. I provide no insight as to why the universe works this way.

Speaker: Andrew Larkoski

15:30 → 16:00 Coffee break

16:00 → 17:15 Talk 2: An Unpopular Interpretation of Causal Bayes Nets and a Step toward a General Framework for Probabilistic Causal Modeling

I want to start from an observation about familiar frameworks for causal modeling, draw a few lessons from it, and then say something more general about probabilistic causal modeling itself.

Causal Bayes nets actually admit two interpretations: types I and II. The more popular, but boring, type I nets are reducible to (nonparametric) structural equation models. The more interesting type II nets are the solution X to this analogy: potential outcomes are to stochastic potential outcomes as structural equation models are to X.

This has an immediate application. Type II causal Bayes nets can serve as surrogates for stochastic potential outcomes, making it quite straightforward to prove a new theorem that generalizes the familiar LATE identification result in causal inference and responds to Dawid’s (2000) challenge.

It also reveals a family of closely related approaches usually studied separately: stochastic potential outcomes (in statistics and econometrics), type II causal Bayes nets (with no obvious disciplinary home or provenance), and generalized imaging (in formal epistemology). A modest axiomatization of their shared structure yields a fairly general framework for probabilistic causal modeling.

This framework has two notable features. First, there need not be a single joint probability distribution over all relevant variables. (Yes, some quantum physicists would be happy.) Second, it motivates, without committing itself to, a new way to reduce causation to counterfactuals. (No, Lewisians would not be happy.)

Speaker: Hanti Lin

17:15 → 18:00 Free discussion time

18:30 → 21:00 Speaker's dinner

Saturday 26 September

09:00 → 10:15 Talk 3: "There is more to uncertainty than probability": Putting probity back into probability, and bringing out the uncertainty in uncertainty quantification

Borrowing the motto of the International Journal of Approximate Reasoning — “there is more to uncertainty than probability” — this talk introduces both basics and some recent results on imprecise probability (Gong and Meng, 2021, 2026) for modeling and uncertainty quantification. I begin with a utilitarian taxonomy that, largely for cross-disciplinary communication, sorts probability into three kinds by the degree to which we control it. At one end, design probability is descriptive: it is created and controlled by us, as in random sampling, clinical trials, Monte Carlo simulations, and differential privacy, so we can simply describe it. At the other end, divine probability is ascriptive: we merely ascribe it, naming and believing in something beyond our control, such as the ontic probability of a nonresponse mechanism we cannot observe, or of a quantum outcome, if one holds its indeterminism to be fundamental. Between these two sits the kind this talk is really about, device probability, which is prescriptive: we postulate a model in order to obtain results, using probability as a device.

Much prescriptive probability is defensible, grounded in evidence, experience, or knowledge. The trouble lies in what I call procedural probability: assumptions we adopt not because we can attach any rationale to them, but because a procedure will not run without them — we simply cannot apply the Bayes rule without a mathematically fully specified prior probability model. No one fully trusts such objects, not even those compelled to use them, yet answers can swing wildly with them. Imprecise probability is designed for exactly this predicament: rather than fabricating a single number we do not have, we work with upper and lower probabilities, restoring some probity, some honesty, to probability. Honesty, however, exacts a price. Where ordinary probability updates by the unique Bayes’ rule, imprecise probability offers no single rule. We examine three — the Dempster rule (optimistic), the Geometric rule (pessimistic), and the Generalized Bayes rule (opportunistic) — each with its own pathology. The Dempster and Geometric rules can incur sure loss, whereas the Generalized Bayes rule cannot, but it is the most prone to dilation. The Geometric and Generalized Bayes rules can never escape a total-ignorance prior, however strong the evidence in the data. And, even more troubling, the Dempster and Geometric rules can move in necessary opposition: as one dilates, the other must contract (Gong and Meng, 2021).

Imprecise probability therefore does not solve the problem so much as shift it. Ordinary uncertainty quantification buries its unverifiable assumptions with procedural probability; imprecise probability instead asks us to declare, openly, an outlook: optimistic, pessimistic, or opportunistic. Whether one should prefer to lodge the unmodelable in a choice of procedural probability or in a choice of updating rule is itself a debate worth having. This talk aims to provoke that debate with a community well acquainted with coarse-graining — the deliberate leaving-out of finer details that, in exchange for tractability, introduces its own unmodelable uncertainty: when we must coarse-grain, which approach is the better, and why?

Speaker: Xiao-Li Meng (Department of Statistics, Harvard University)

10:15 → 10:45 Coffee break

10:45 → 12:00 Talk 4: The Causal Stance

There’s a puzzle of fit between causation and fundamental physics. Causal relations don’t figure directly in our fundamental physical theories. More puzzling, though, is that the nature of the determination relations employed by fundamental physics seems incompatible with the nature of causal relations. Yet causal talk is indispensable in everyday life and, arguably, in much of scientific practice generally. On a broadly physical or naturalistic worldview, this raises a puzzle. If fundamental physics is the ultimate story of reality, how does causation fit in? I propose a novel treatment of this puzzle on analogy with Dennett's view about intentionality (1987), drawing out what I call the causal stance. In effect, causal talk and inquiry is explained as our adopting a 'causal stance' towards our target of inquiry (akin to Dennett's 'intentional stance'). While adopting this stance facilitates prediction and explanation, it doesn't carry any ontological commitment about causation itself. Meanwhile, once we get to the fundamental level and fill in the physical details, the causal stance becomes redundant. On the proposed view, the puzzle of fit doesn’t arise. And yet, it preserves and explains the utility of causal talk. Indeed, causal talk is indispensable where the predictive power of the causal stance outstrips that of physical theorizing.

Speaker: Jenn McDonald

12:00 → 13:30 Working lunch

13:30 → 14:45 Talk 5: What probability do quantum particles live by?

Probabilities are central to the physics of elementary particles. I describe several notions of probability characterizing quantum particles, including objective densities of quantum states and subjective degrees of belief in the epistemology of particle measurements. These probabilities share common mathematical building blocks, such as heterodimensional multilinear maps (functor representations) and functional integration. An intriguing question is why the probabilistic framework of the Standard Model of elementary particles is so successful in providing a quantitative description of the microscopic world across a vast range of energies. To what precision are theoretical parameters of particle interactions universal? These questions will come to the forefront in the coming decades through large-scale research programs at elementary-particle colliders.

Speaker: Pavel Nadolsky

nadolsky_short.pdf

14:45 → 15:15 Coffee break

15:15 → 16:30 Talk 6: The History-Ladenness of Quantum Theory

Does a quantum wave function refer to a physical object that actually propagates in a configuration space of possibly many dimensions? If the probabilities from the Born rule refer only to measurements, then what exactly counts as a measurement, and what is happening when there are no measurements going on?

In this talk, I will present a deflationary account of quantum theory based on stochastic processes that are non-Markovian, or history-laden. As I will explain, a wave function can then be understood merely as a trick for taking this history-ladenness and recasting it in terms of fictitious variables in the present state of the system, giving a so-called hidden Markov model. If we resist this move, then quantum probabilities are demoted to ordinary probabilities of events, wave functions are demoted from having an ontological status, and measurements are demoted to banal stochastic interactions. The dynamical laws of this stochastic theory generically feature indivisibility, meaning a failure to divide into Markovian laws for subintervals of time.

In the final part of my talk, I will show how replacing wave functions in the present state with a direct dependence on the past gives us new explanatory tools, including a new nomological account of causation. I will also explain how requiring this past-dependence to respect light cones provides the first-ever transparent argument for the Tsirelson bound, which is the maximum amount by which quantum theory can violate the Bell inequality.

Speaker: Jacob Barandes

16:30 → 18:00 Special Session: Young Researcher Presentations

Goodness-of-Fit Tests in Particle Physics Phenomenology by Daniel Adamiak

When evaluating the ability of a model to describe the data, one needs a measure known as the goodness-of-fit. The most common goodness-of-fit test is the chi2 measure, but, as I will show in this talk, there is not a 'single' chi2 measure. Each one answers a slightly different question and obeys its own scaling law, and one must be judicious in selecting which one to use. In this talk, I will discuss the various kinds of chi2, which questions they answer, and derive their scaling behaviour.

Quantum-Inspired Compositional Causal Inference by Isaac Friend

Graph-based interventional causal models can be reformulated in process theories, which are special kinds of categories used for modeling composition of input-output processes. In the process-theoretic framework, we can pose new kinds of causal identification problems, in which the data available for inference of causal effects are generated not by perfect passive observations, but by observation procedures that are noisy, coarse-grained, or disturbing. Such observation procedures are mathematically represented by “classical” analogues of quantum instruments, and the associated causal identification techniques are based on mathematical structures and procedures first developed for the quantum setting.

Speakers: Daniel Adamiak, Isaac Friend

18:30 → 21:30 Reception and social dinner

Sunday 27 September

09:00 → 10:15 Talk 7: Ensemble Spaces: A Common Foundation for Probability, Information Theory and Physical Theories

In the first half of this presentation, we will analyze quantum mechanics using techniques from Reverse Physics. This will clarify what each part of the mathematical structure represents physically, and its implicit assumptions. We will see that the notions of ensemble and entropy play foundational roles, that orthogonality is mutual exclusivity, unitary evolutions are deterministic and reversible processes, nonselective projective measurements are equilibration processes and that one type of process can be recovered from the other.

In the second half we will step back and show that scientific reproducibility requires ensembles to be primitive objects. Following the tenets of Physical Mathematics, we will turn core physical requirements into mathematical definitions to create a general theory of ensemble spaces, which gives us general purpose tools that are valid in all physical theories. In this base theory, we can then understand better the relationships between statistical mixtures, entropy and probability. In particular, we will see that classical spaces are exactly those spaces in which all pure ensembles are mutually exclusive, and probability is recovered by and only by statistical mixtures of mutually exclusive ensembles. The overall picture directly ties together concepts from many different fields, giving a more integrated understanding of each element.

Speaker: Gabriele Carcassi (University of Michigan)

10:15 → 10:45 Coffee break

10:45 → 12:00 Talk 8: From Language Models to Quantum Theory: The Universe as a VR Game

A language model evolves a thought vector by a recurrent network or a transformer network. The output layer projects the thought vector onto a discrete vocabulary of words to produce the logit scores of the words, converts the logit scores to probabilities by softmax, samples one word, and re-embeds the sampled word as the updated thought vector. The cycle repeats: evolve, project, sample, re-embed.

This talk proposes that quantum theory has the same architecture, but with a crucial upgrade: the output layer is interactive. The game engine evolves a state vector by linear unitary rotation under the Hamiltonian. The rendering interface is where the observer enters: she defines the vocabulary (chooses an observable, whose eigenvalues are the possible answers), the Born rule projects the state vector to probabilities by a square-softmax, one eigenvalue is sampled, and the Bohr update re-embeds the sampled outcome as the new state vector. The quantum theory is the source code for a VR game. One line of source code for the engine, three lines for the interface.

The discipline of this framework is the strict separation of engine and interface. Neither can be reduced to the other, and the interface cannot be eliminated. The quantum theory is source code, not clockwork. Complementarity, entanglement, and the measurement problem are consequences of the two-layer separation, not anomalies requiring repair. The classical world emerges from degeneracy: when an observable has high degeneracy, the Born distribution is a delta spike. Einstein's clocks and rods are macroscopic composites of the fundamental quantum field, their readings are highly degenerate observables, and the spacetime metric emerges as organizations or interpretations of their readings.

Hawking asked what breathes fire into the equations. Chalmers asked why there is something it is like to experience. We propose an axiom on the first-person OS to relocate and connect these two questions.

The talk is based on the following preprint: https://zenodo.org/records/22682567

Speaker: Yingnian Wu

12:00 → 13:30 Working lunch

13:30 → 14:45 Talk 9

Speaker: Jamie Robbins

14:45 → 15:15 Coffee break

15:15 → 16:30 Talk 10: General Process Theory of Causality

Analyses of causation standardly take the relata of causal relations to be events. We explore the alternative in which the relata are processes, modeling this view with category theory. On this view, a cause is a set of processes a system must undergo to arrive at the effect, given a causal condition. The framework is general in that it accommodates both Salmon–Dowe process causality and counterfactual approaches formulated within structural causal models. Moreover, by representing background conditions and available interventions alike as arrows in a category, it resolves such vexed puzzles as preemption, transitivity, and structural isomorphs without recourse to normative parameters. We close by drawing out what the framework implies for the relationship between causality and probability. This is joint work with Hayato Saigo, Tatsuya Yoshii, and Tomoyuki Hayashi.

Speaker: Jun Otsuka

16:30 → 17:00 Closing remarks and final open discussion