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Using interventions to discover quantum causal structure

Sally Shrapnel

Published Nov 18, 2016• 2 citations
Publisher

Abstract

Identifying causal relations plays an indispensable role in science, economics, medicine and everyday life. Interventionist causation associates the discovery of such relations with the possibility of manipulation or intervention. A causes B, if manipulating A in the right way can bring about changes in B. The main technical tool, the causal model, can be seen as a device for telling us how and why certain actions are more effective than others. Such models have found application in almost every scientific discipline. However, despite several decades of sophisticated analysis and a wealth of technical results, interventionist causal methods are known to fail in the quantum case. The quantum domain, with its peculiar, counterintuitive features, is widely considered an inhospitable environment in which to apply our usual causal discovery tools. This causal skepticism presents us with a puzzle. Physicists are now able to manipulate and control quantum systems, and the design and construction of quantum technology relies on an ability to identify when one strategy will work and another will fail. From the perspective of interventionist causation, it seems that a formal account of quantum causal modelling ought to be possible. The main contribution of this thesis is to provide an extension of interventionist methodology to the quantum case. In Chapter 1, I introduce interventionist causation from the perspective of two giants of the field: Judea Pearl and James Woodward. The Causal Markov Condition (CMC) and Faithfulness assumptions are presented, and I draw particular attention to the discovery of casual structure. I touch on some of the well-known problems with interventionist causation per se. In Chapter 2, I put this methodology to work in a quantum mechanical context. Following tradition, we examine one of the Bell experiments in order to determine how the classical interventionist framework fails. Noting that the usual response is to demand that one drops either the CMC or Faithfulness, I suggest that neither approach is particularly satisfactory and argue for an alternative. I discuss some reasons why the interventionist is forced to pursue this different path. In Chapter 3, I motivate the possibility of an interventionist account of quantum causation. I first look at how physicists represent quantum technology in order to make interventionist and counterfactual inferences: via the use of quantum circuit diagrams. Using three examples I demonstrate the manner in which these diagrams can be used to facilitate causal inference. In Chapter 4, I examine some recent attempts at characterising quantum causal models due to work from the quantum foundations community. I present three such accounts and explain why I endorse a fourth, the focus of the next chapter. In Chapter 5, I present a new framework that allows for the discovery of interventionist quantum causal structure. I finish the thesis with a summary and some suggestions for further work.

DOI
10.14264/uql.2016.1102

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Identifying causal relations plays an indispensable role in science, economics, medicine and everyday life. Interventionist causation associates the discovery of such relations with the possibility of manipulation or intervention. A causes B, if manipulating A in the right way can bring about changes in B. The main technical tool, the causal model, can be seen as a device for telling us how and why certain actions are more effective than others. Such models have found application in almost every scientific discipline. However, despite several decades of sophisticated analysis and a wealth of technical results, interventionist causal methods are known to fail in the quantum case. The quantum domain, with its peculiar, counterintuitive features, is widely considered an inhospitable environment in which to apply our usual causal discovery tools. This causal skepticism presents us with a puzzle. Physicists are now able to manipulate and control quantum systems, and the design and construction of quantum technology relies on an ability to identify when one strategy will work and another will fail. From the perspective of interventionist causation, it seems that a formal account of quantum causal modelling ought to be possible. The main contribution of this thesis is to provide an extension of interventionist methodology to the quantum case. In Chapter 1, I introduce interventionist causation from the perspective of two giants of the field: Judea Pearl and James Woodward. The Causal Markov Condition (CMC) and Faithfulness assumptions are presented, and I draw particular attention to the discovery of casual structure. I touch on some of the well-known problems with interventionist causation per se. In Chapter 2, I put this methodology to work in a quantum mechanical context. Following tradition, we examine one of the Bell experiments in order to determine how the classical interventionist framework fails. Noting that the usual response is to demand that one drops either the CMC or Faithfulness, I suggest that neither approach is particularly satisfactory and argue for an alternative. I discuss some reasons why the interventionist is forced to pursue this different path. In Chapter 3, I motivate the possibility of an interventionist account of quantum causation. I first look at how physicists represent quantum technology in order to make interventionist and counterfactual inferences: via the use of quantum circuit diagrams. Using three examples I demonstrate the manner in which these diagrams can be used to facilitate causal inference. In Chapter 4, I examine some recent attempts at characterising quantum causal models due to work from the quantum foundations community. I present three such accounts and explain why I endorse a fourth, the focus of the next chapter. In Chapter 5, I present a new framework that allows for the discovery of interventionist quantum causal structure. I finish the thesis with a summary and some suggestions for further work.
Costa and Shrapnel ([2016]) have recently proposed an interventionist theory of quantum causation. The formalism generalizes the classical methods of Pearl ([2000]) and allows for the discovery of quantum causal structure via localized interventions. Classical causal structure is presented as a special case of this more general framework. I introduce the account and consider whether this formalism provides a causal explanation for the Bell correlations. 1 Introduction2 Classical Causal Models3 What’s the (Quantum) Problem?4 Quantum Causal Models: Why Bother?5 Markov Quantum Causal Models6 The Bell Experiment7 Bell’s Objections
Quantum mechanics has achieved unparalleled success as an operational theory, describing a wide range of experiments to remarkable accuracy. However, the physical foundations on which it rests remain as puzzling as they were a century ago, and a concise statement of the physical principles that underlie quantum mechanics is still outstanding. One promising approach holds that these principles should be formulated in terms of information, since many of the counter-intuitive effects in quantum theory concern questions such as what one can know about a quantum system and how the information encoded therein can be processed and distributed between parties. Another challenging feature of quantum theory is its incompatibility with the other cornerstone of modern physics, general relativity. In order to reconcile the two, one must identify and retain only the essential concepts and principles of each theory, and in the case of general relativity, causality has been identified as such a concept. This raises the question of how our classical understanding of causality must change when quantum theory is taken into account. In order to address these questions about information, knowledge and causality, I turn to the framework of causal models. In classical statistics, causal models explain the relations among a set of variables in terms of causal influences, which makes them a powerful tool for structuring our knowledge about complex systems and developing strategies for interacting with them. More importantly, the framework provides the conceptual underpinnings and mathematical methods for addressing questions about causation, information and knowledge in a rigorous manner. In this thesis, I develop a version of the classical causal models framework that is compatible with quantum theory and explore its physical implications. \n \n \nA first step is to define quantum versions of fundamental elements such as variables, conditionals and belief propagation rules. This allows one to consider the question of what one can come to know about a quantum variable from the point of view of causal modelling. The conditionals relating quantum variables are found to have a richer structure than their classical counterparts, which can be exploited for the task of discerning causal relations given limited data -- a central problem in classical causal modelling. The mathematical properties of quantum conditionals also establish a correspondence between various classes of two-party correlations, such as bound and distillable entanglement, and the types of causal structures that can give rise to them, which may become a useful tool for entanglement theory and quantum information processing. In the context of open quantum systems dynamics, quantum causal models provide a clear physical explanation of not completely positive maps and, more broadly, of non-Markovian quantum dynamics. Finally, I consider the possibility of non-classical effects in the way that different causal mechanisms are combined -- that is, non-classical causal structures. For the simple case of two causally ordered variables, I propose indicators that witness different classes of combinations of causal mechanisms, including a non-classical mixture, and describe an experiment realizing examples of the different classes. \n \n \nAs these results illustrate, the framework of quantum causal models provides both greater conceptual clarity and a comprehensive mathematical formalism for studying a diverse set of problems, ranging from foundational questions to applications in open systems dynamics and the exploration of non-classical causal structures, which are likely to feature in a future theory of quantum gravity. The material presented in this thesis is intended as a foundation and inspiration for further applications of quantum causal models.
Characterising causal structure is an activity that is ubiquitous across the sciences. Causal models are representational devices that can be used as oracles for future interventions, to predict how values of some variables will change in response to interventions on others. Recent work has generalised concepts from this field to situations involving quantum systems, resulting in a new notion of quantum causal structure. A key concept in both the classical and quantum context is that of an intervention. Interventions are the controlled operations required to identify causal structure and ultimately the feature that endows causal models with empirical meaning. Although interventions are a crucial feature of both the classical and quantum causal modelling frameworks, to date there has been no discussion of their physical basis. In this paper, we consider interventions from a physical perspective and show that, in both the classical and quantum case, they are constrained by the thermodynamics of measurement and feedback in open systems. We demonstrate that the perfect “atomic” or “surgical” interventions characterised by Pearl’s famous do-calculus are physically impossible, and this is the case for both classical and quantum systems.
Though the topic of causal inference is typically considered in the context of classical statistical models, recent years have seen great interest in extending causal inference techniques to quantum and generalized theories. Causal identification is a type of causal inference problem concerned with recovering from observational data and qualitative assumptions the causal mechanisms generating the data, and hence the effects of hypothetical interventions. A major obstacle to a theory of causal identification in the quantum setting is the question of what should play the role of "observational data," as any means of extracting data at a certain locus will almost certainly disturb the system. Hence, one might think a priori that quantum measurements are already too much like interventions, so that the problem of causal identification trivializes. This is not the case. Fixing a limited class of quantum instruments (namely the class of all projective measurements) to play the role of "observations," we note that as in the classical setting, there exist scenarios for which causal identification is not possible. We then present sufficient conditions for quantum causal identification, starting with a quantum analogue of the well-known "front-door criterion" and finishing with a broader class of scenarios for which the effect of a single intervention is identifiable. These results emerge from generalizing the process-theoretic account of classical causal inference due to Jacobs, Kissinger, and Zanasi beyond the setting of Markov categories, and thereby treating the classical and quantum problems uniformly.
Causal modelling provides a powerful set of tools for identifying causal structure from observed correlations. It is well known that such techniques fail for quantum systems, unless one introduces 'spooky' hidden mechanisms. Whether one can produce a genuinely quantum framework in order to discover causal structure remains an open question. Here we introduce a new framework for quantum causal modelling that allows for the discovery of causal structure. We define quantum analogues for core features of classical causal modelling techniques, including the causal Markov condition and faithfulness. Based on the process matrix formalism, this framework naturally extends to generalised structures with indefinite causal order.