Using interventions to discover quantum causal structure

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.iii 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.iv Declaration by authorThis thesis is composed of my original wor...

Optimal quantum networks and one-shot entropies

“…having used equation (31) with λ replaced by its inverse l = w 1 . In words, the problem is to find the maximum weight for which one can squeeze the tester operator T yes under some dual comb Γ.…”