Playlist: 23 videos

### Quantum Physics and Statistical Causal Models

0:45:40

Elie Wolfe (Perimeter Institute for Theoretical Physics)

https://simons.berkeley.edu/talks/applications-inflation-technique-causal-inference

Quantum Physics and Statistical Causal Models

We will review the inflation technique for causal inference. Inflation is a technique for outer-approximating the statistical causal models of marginalized DAGs through a convergent hierarchy of convex relaxations. We will stress how inflation can be adjusted to explore either the (conventional) paradigm of classical latent variables or the more exotic paradigm of nonclassical physical theories such as quantum physics. We will showcase some recent insights obtained though inflation, focusing primarily on results not found in the original publications. Special for this workshop, we will reveal a fundamental connection between do-conditional identifiability and the optimal application of inflation to multilayer DAGs.

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https://simons.berkeley.edu/talks/applications-inflation-technique-causal-inference

Quantum Physics and Statistical Causal Models

We will review the inflation technique for causal inference. Inflation is a technique for outer-approximating the statistical causal models of marginalized DAGs through a convergent hierarchy of convex relaxations. We will stress how inflation can be adjusted to explore either the (conventional) paradigm of classical latent variables or the more exotic paradigm of nonclassical physical theories such as quantum physics. We will showcase some recent insights obtained though inflation, focusing primarily on results not found in the original publications. Special for this workshop, we will reveal a fundamental connection between do-conditional identifiability and the optimal application of inflation to multilayer DAGs.

0:41:10

Mirjam Weilenmann (IQOQI Vienna)

https://simons.berkeley.edu/talks/self-tests-physical-theories-networks-and-their-implications-foundations-quantum-theory

Quantum Physics and Statistical Causal Models

Self-testing usually refers to the task of taking a given set of observed correlations that are assumed to arise via a process that is accurately described by quantum theory, and trying to infer the quantum state and measurements from this. In other words, it is concerned with the question of whether we can tell what quantum black-box devices are doing by looking only at their input-output statistics and is known to be possible in several cases. In this talk, I will introduce a more general question: is it possible to self-test a theory, and, in particular, quantum theory? More precisely, I will ask whether within a particular network there are tasks that can only be performed in theories that have the same correlations as quantum mechanics. I will introduce two candidate tasks, both adaptations of the usual CHSH-Bell-test in a larger network and will show how they can be used to rule out theories. The first one can be used to rule out a variety of theories including the theory of box-world, which is based on a state space that includes PR-boxes. The second one recently allowed us to rule out quantum theory over real Hilbert spaces as incompatible with our experimental observations. Our work goes beyond previous approaches that usually compare different theories according to their properties, often by imposing postulates to recover them. By finding self-tests we design more objective, experimentally verifiable procedures to rule out other theories.

Visit talk page
https://simons.berkeley.edu/talks/self-tests-physical-theories-networks-and-their-implications-foundations-quantum-theory

Quantum Physics and Statistical Causal Models

Self-testing usually refers to the task of taking a given set of observed correlations that are assumed to arise via a process that is accurately described by quantum theory, and trying to infer the quantum state and measurements from this. In other words, it is concerned with the question of whether we can tell what quantum black-box devices are doing by looking only at their input-output statistics and is known to be possible in several cases. In this talk, I will introduce a more general question: is it possible to self-test a theory, and, in particular, quantum theory? More precisely, I will ask whether within a particular network there are tasks that can only be performed in theories that have the same correlations as quantum mechanics. I will introduce two candidate tasks, both adaptations of the usual CHSH-Bell-test in a larger network and will show how they can be used to rule out theories. The first one can be used to rule out a variety of theories including the theory of box-world, which is based on a state space that includes PR-boxes. The second one recently allowed us to rule out quantum theory over real Hilbert spaces as incompatible with our experimental observations. Our work goes beyond previous approaches that usually compare different theories according to their properties, often by imposing postulates to recover them. By finding self-tests we design more objective, experimentally verifiable procedures to rule out other theories.

0:51:5

Giulia Rubino (University of Bristol)

https://simons.berkeley.edu/talks/experimental-entanglement-temporal-order

Quantum Physics and Statistical Causal Models

The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. In this talk, I will present the first demonstration of indefinite temporal order outside of quantum formalism. I will show experimental outcomes that are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, I will introduce physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. I will then show experimental data that invalidate these theories by violating the inequality using entangled temporal order. This will provide experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.

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https://simons.berkeley.edu/talks/experimental-entanglement-temporal-order

Quantum Physics and Statistical Causal Models

The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. In this talk, I will present the first demonstration of indefinite temporal order outside of quantum formalism. I will show experimental outcomes that are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, I will introduce physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. I will then show experimental data that invalidate these theories by violating the inequality using entangled temporal order. This will provide experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.

0:42:0

Marc-Olivier Renou (ICFO Barcelona)

https://simons.berkeley.edu/talks/most-general-causal-theory-correlations-restricted-bounded-multipartite-nonlocal-resources

Quantum Physics and Statistical Causal Models

Quantum correlations are obtained when multiple parties perform independent measurements on a shared quantum state. Bell’s seminal theorem proves that certain correlations predicted by quantum theory resist explanation in terms of any local theory based on shared randomness. But what about alternative explanations for quantum correlations, in terms of an exotic theory involving bipartite causal sources generalising bipartite entanglement (such as the PR box, or more generally any bipartite resource GPT) and shared randomness? I will first prove that no such exotic theory can account for quantum correlations, proposing a concrete test generalising Bell experiments, based on the GHZ state. It certifies that No Bipartite-Nonlocal Causal Theory Can Explain Nature's Quantum Correlations. I will generalise this result to more general causal theory based on k-partite (and not only bipartite) systems and shared randomness. Then, I will propose a fully general definition for the ´most general causal theory of correlations in causal structures´ generalising quantum theory. On a more practical aspect, I will question the standard notion of genuine multipartite nonlocality introduced by Svetlichny and propose a stricter redefinition of it, not subject to the incoherencies of all precedent notions of multipartite nonlocal genuiness and compatible with the notion of no-signalling. Talk based on 10.1103/PhysRevLett.127.200401, 10.1103/PhysRevA.104.052207 and unpublished work.

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https://simons.berkeley.edu/talks/most-general-causal-theory-correlations-restricted-bounded-multipartite-nonlocal-resources

Quantum Physics and Statistical Causal Models

Quantum correlations are obtained when multiple parties perform independent measurements on a shared quantum state. Bell’s seminal theorem proves that certain correlations predicted by quantum theory resist explanation in terms of any local theory based on shared randomness. But what about alternative explanations for quantum correlations, in terms of an exotic theory involving bipartite causal sources generalising bipartite entanglement (such as the PR box, or more generally any bipartite resource GPT) and shared randomness? I will first prove that no such exotic theory can account for quantum correlations, proposing a concrete test generalising Bell experiments, based on the GHZ state. It certifies that No Bipartite-Nonlocal Causal Theory Can Explain Nature's Quantum Correlations. I will generalise this result to more general causal theory based on k-partite (and not only bipartite) systems and shared randomness. Then, I will propose a fully general definition for the ´most general causal theory of correlations in causal structures´ generalising quantum theory. On a more practical aspect, I will question the standard notion of genuine multipartite nonlocality introduced by Svetlichny and propose a stricter redefinition of it, not subject to the incoherencies of all precedent notions of multipartite nonlocal genuiness and compatible with the notion of no-signalling. Talk based on 10.1103/PhysRevLett.127.200401, 10.1103/PhysRevA.104.052207 and unpublished work.

0:36:16

Miguel Navascues (Austrian Academy of Sciences)

https://simons.berkeley.edu/talks/sequential-models

Quantum Physics and Statistical Causal Models

A sequential model is a type of causal network that describes the (discrete) time evolution of a system’s external output, as well as its internal state, and can be regarded as a generalization of a Markov decision process. At each time-step, the system transitions from one internal state to the next through a known equation of motion, which depends on the current state of the system and: (a) unobserved evolution parameters, the same for all times; (b) a number of uncontrolled (and unobserved) variables at each time; and (c) optionally, the (observed) input or policy of an agent interacting with the system. The (observed) output of the system, which can be regarded as a penalty, depends in a known way on all the afore-mentioned variables, the systems’ current internal state and the time. In this talk, I will argue that many tasks in quantum information, but also in other fields, such as mathematical epidemiology, can be formulated as the maximization of the cumulative penalty of a sequential model over variables of type (a) and (b). Next I will introduce general mathematical tools to upper bound this quantity. We will use these tools to bound the maximum probability that a probabilistic finite-state automata generates a specific (finite) sequence of bits and to devise new protocols for entanglement detection in many-body systems. Finally, I will introduce a heuristic to minimize upper bounds on the penalty over all allowed policies. Given any sequential model, the heuristic will generate policies with an acceptable proven worst-case performance with a computational cost comparable to that of establishing the upper bound.

Visit talk page
https://simons.berkeley.edu/talks/sequential-models

Quantum Physics and Statistical Causal Models

A sequential model is a type of causal network that describes the (discrete) time evolution of a system’s external output, as well as its internal state, and can be regarded as a generalization of a Markov decision process. At each time-step, the system transitions from one internal state to the next through a known equation of motion, which depends on the current state of the system and: (a) unobserved evolution parameters, the same for all times; (b) a number of uncontrolled (and unobserved) variables at each time; and (c) optionally, the (observed) input or policy of an agent interacting with the system. The (observed) output of the system, which can be regarded as a penalty, depends in a known way on all the afore-mentioned variables, the systems’ current internal state and the time. In this talk, I will argue that many tasks in quantum information, but also in other fields, such as mathematical epidemiology, can be formulated as the maximization of the cumulative penalty of a sequential model over variables of type (a) and (b). Next I will introduce general mathematical tools to upper bound this quantity. We will use these tools to bound the maximum probability that a probabilistic finite-state automata generates a specific (finite) sequence of bits and to devise new protocols for entanglement detection in many-body systems. Finally, I will introduce a heuristic to minimize upper bounds on the penalty over all allowed policies. Given any sequential model, the heuristic will generate policies with an acceptable proven worst-case performance with a computational cost comparable to that of establishing the upper bound.

0:45:5

Ismael Mourifie (U of Toronto)

https://simons.berkeley.edu/talks/generalized-instrumental-inequalities-complexity-sharpness-robustness

Quantum Physics and Statistical Causal Models

I will discuss a general class of testable implications for the instrumental variable models when the treatment is discrete, but the outcome and instruments are unrestricted: generalized instrumental inequalities (GIV). This class generalized the Pearl instrumental inequalities. I will discuss the complexity of proving the sharpness of the GIV when the support of the outcome is large. Discuss the importance of sharpness results for a correct interpretation of the bounds on the average causal effect under the IV model.

Visit talk page
https://simons.berkeley.edu/talks/generalized-instrumental-inequalities-complexity-sharpness-robustness

Quantum Physics and Statistical Causal Models

I will discuss a general class of testable implications for the instrumental variable models when the treatment is discrete, but the outcome and instruments are unrestricted: generalized instrumental inequalities (GIV). This class generalized the Pearl instrumental inequalities. I will discuss the complexity of proving the sharpness of the GIV when the support of the outcome is large. Discuss the importance of sharpness results for a correct interpretation of the bounds on the average causal effect under the IV model.

0:45:21

Richard Guo (Cambridge)

https://simons.berkeley.edu/talks/latent-variable-justifies-stronger-iv-bounds

Quantum Physics and Statistical Causal Models

For binary instrumental variable models, there seems to be a long-standing gap between two set of bounds on the average treatment effect: the stronger Balke–Pearl ("sharp") bounds versus the weaker Robins-Manski ("natural") bounds. In the literature, the Balke–Pearl bounds are typically derived under stronger assumptions, i.e., either individual exclusion or joint exogeneity, which are untestable cross-world statements, while the natural bounds only require testable assumptions. In this talk, I show that the stronger bounds are in fact justified by the existence of a latent confounder. In fact, the Balke-Pearl bounds are sharp under latent confounding and stochastic exclusion. The "secret sauce" that closes this gap is a set of CHSH-type inequalities that generalized Bell's (1964) inequality.

Visit talk page
https://simons.berkeley.edu/talks/latent-variable-justifies-stronger-iv-bounds

Quantum Physics and Statistical Causal Models

For binary instrumental variable models, there seems to be a long-standing gap between two set of bounds on the average treatment effect: the stronger Balke–Pearl ("sharp") bounds versus the weaker Robins-Manski ("natural") bounds. In the literature, the Balke–Pearl bounds are typically derived under stronger assumptions, i.e., either individual exclusion or joint exogeneity, which are untestable cross-world statements, while the natural bounds only require testable assumptions. In this talk, I show that the stronger bounds are in fact justified by the existence of a latent confounder. In fact, the Balke-Pearl bounds are sharp under latent confounding and stochastic exclusion. The "secret sauce" that closes this gap is a set of CHSH-type inequalities that generalized Bell's (1964) inequality.

0:42:1

Noam Finkelstein (Weill Cornell Medicine)

https://simons.berkeley.edu/talks/tbd-367

Quantum Physics and Statistical Causal Models

Latent variables in directed graphical models can be assumed to have finite cardinality without restricting the marginal model, if all observed variables are discrete. In this talk, we improve on existing non-restrictive cardinality bounds for latent variables by characterizing the dimension of the marginal model to which each latent variable is relevant. We observe that non-restrictive latent variable cardinality bounds depend on whether, and which, counterfactual random variables are being modeled. The improved cardinality bounds facilitate use of the polynomial system characterization to answer causal compatibility and inference questions by reducing the number of unidentified model parameters. Towards the same end, we suggest a 'hybrid' parameterization for latent variable models that yields fewer parameters than existing parameterizations.

Visit talk page
https://simons.berkeley.edu/talks/tbd-367

Quantum Physics and Statistical Causal Models

Latent variables in directed graphical models can be assumed to have finite cardinality without restricting the marginal model, if all observed variables are discrete. In this talk, we improve on existing non-restrictive cardinality bounds for latent variables by characterizing the dimension of the marginal model to which each latent variable is relevant. We observe that non-restrictive latent variable cardinality bounds depend on whether, and which, counterfactual random variables are being modeled. The improved cardinality bounds facilitate use of the polynomial system characterization to answer causal compatibility and inference questions by reducing the number of unidentified model parameters. Towards the same end, we suggest a 'hybrid' parameterization for latent variable models that yields fewer parameters than existing parameterizations.

0:48:45

Eric Cavalcanti (Griffith University)

https://simons.berkeley.edu/talks/semantics-counterfactuals-quantum-causal-models

Quantum Physics and Statistical Causal Models

The classical causal model framework of Pearl addresses a hierarchy of causal reasoning tasks --- predictions, interventions and counterfactuals --- of increasing complexity. Despite its wide range of applicability, the classical causal model formalism fails to accommodate quantum correlations while maintaining faithfulness to relativistic causality. A series of recent works in quantum causal models have produced formalisms that generalise various aspects of the classical framework, while allowing for a faithful description of quantum correlations. However, so far these have been restricted to addressing the first two rungs of Pearl's causal ladder. In this talk I will introduce a formalism for counterfactual reasoning in quantum causal models, completing the quantum generalisation of Pearl's causal hierarchy.

Visit talk page
https://simons.berkeley.edu/talks/semantics-counterfactuals-quantum-causal-models

Quantum Physics and Statistical Causal Models

The classical causal model framework of Pearl addresses a hierarchy of causal reasoning tasks --- predictions, interventions and counterfactuals --- of increasing complexity. Despite its wide range of applicability, the classical causal model formalism fails to accommodate quantum correlations while maintaining faithfulness to relativistic causality. A series of recent works in quantum causal models have produced formalisms that generalise various aspects of the classical framework, while allowing for a faithful description of quantum correlations. However, so far these have been restricted to addressing the first two rungs of Pearl's causal ladder. In this talk I will introduce a formalism for counterfactual reasoning in quantum causal models, completing the quantum generalisation of Pearl's causal hierarchy.

0:42:55

Beata Zjawin (ICTQT)

https://simons.berkeley.edu/talks/graphical-criteria-inequality-constraints-directed-acyclic-graphs-hidden-variables

Quantum Physics and Statistical Causal Models

When some variables in a directed acyclic graph (DAG) are hidden, a notoriously complicated set of constraints on the distribution of observed variables is implied. In this talk, we present inequality constraints implied by graphical criteria in hidden variable DAGs. For DAGs that exhibit e-separation relations, we present entropic inequality constraints and we show how they can be used to learn about the true causal model from an observed data distribution (arXiv:2107.07087). For DAGs that exhibit d-separation relations and with a promise that unobserved variables have known cardinalities, we present inequality constraints that resemble constraints present in models that involve quantum systems (arXiv:2109.05656).

Visit talk page
https://simons.berkeley.edu/talks/graphical-criteria-inequality-constraints-directed-acyclic-graphs-hidden-variables

Quantum Physics and Statistical Causal Models

When some variables in a directed acyclic graph (DAG) are hidden, a notoriously complicated set of constraints on the distribution of observed variables is implied. In this talk, we present inequality constraints implied by graphical criteria in hidden variable DAGs. For DAGs that exhibit e-separation relations, we present entropic inequality constraints and we show how they can be used to learn about the true causal model from an observed data distribution (arXiv:2107.07087). For DAGs that exhibit d-separation relations and with a promise that unobserved variables have known cardinalities, we present inequality constraints that resemble constraints present in models that involve quantum systems (arXiv:2109.05656).