Quantum Causal Networks

Contextuality from Quantum Physics to Psychology, 2015

When individuals have little knowledge about a causal system and must make causal inferences based on vague and imperfect information, their judgments often deviate from the normative prescription of classical probability. Previously, many researchers have dealt with violations of normative rules by elaborating causal Bayesian networks through the inclusion of hidden variables. While these models often provide good accounts of data, the addition of hidden variables is often post hoc, included when a Bayes net fails to capture data. Further, Bayes nets with multiple hidden variables are often difficult to test. Rather than elaborating a Bayes net with hidden variables, we generalize the probabilistic rules of these models. The basic idea is that any classic Bayes net can be generalized to a quantum Bayes net by replacing the probabilities in the classic model with probability amplitudes in the quantum model. We discuss several predictions of quantum Bayes nets for human causal reasoning.

arXiv: Quantum Physics, 2019

It is known that the classical framework of causal models is not general enough to allow for causal reasoning about quantum systems. Efforts have been devoted towards generalization of the classical framework to the quantum case, with the aim of providing a framework in which cause-effect relations between quantum systems, and their connection with empirically observed data, can be rigorously analyzed. Building on the results of Allen et al., Phys. Rev. X 7, 031021 (2017), we present a fully-fledged framework of quantum causal models. The approach situates causal relations in unitary transformations, in analogy with an approach to classical causal models that assumes underlying determinism and situates causal relations in functional dependences between variables. We show that for any quantum causal model, there exists a corresponding unitary circuit, with appropriate causal structure, such that the quantum causal model is returned when marginalising over latent systems, and vice ver...

Frontiers in Psychology, 2012

People can often outperform statistical methods and machine learning algorithms in situations that involve making inferences about the relationship between causes and effects. While people are remarkably good at causal reasoning in many situations, there are several instances where they deviate from expected responses. This paper examines three situations where judgments related to causal inference problems produce unexpected results and describes a quantum inference model based on the axiomatic principles of quantum probability theory that can explain these effects. Two of the three phenomena arise from the comparison of predictive judgments (i.e., the conditional probability of an effect given a cause) with diagnostic judgments (i.e., the conditional probability of a cause given an effect). The third phenomenon is a new finding examining order effects in predictive causal judgments. The quantum inference model uses the notion of incompatibility among different causes to account for all three phenomena. Psychologically, the model assumes that individuals adopt different points of view when thinking about different causes. The model provides good fits to the data and offers a coherent account for all three causal reasoning effects thus proving to be a viable new candidate for modeling human judgment.

PsycEXTRA Dataset

When people make inferences about causal situations with vague and imperfect information, their judgments often deviate from the normative prescription of classical probability. As a result, it is difficult to apply popular models of causal reasoning such as ∆P and causal power, which provide good accounts of behavior in casual learning tasks and tasks where statistical information is provided directly. We propose a unified explanation of human causal reasoning using quantum probability theory that can account for causal reasoning across many different domains. In our approach, we postulate a hierarchy of mental representations, from fully quantum to fully classical, that could be adopted for different situations. We illustrate our approach with new experiments and model comparisons.

The Palgrave Handbook of Quantum Models in Social Science, 2017

How do people reason about causes and effects? If you wake up in the morning with a stomach ache, how do you infer that it was the seafood you had for dinner rather than stress that caused your stomach to hurt? Human causal reasoning has intrigued scholars as far back as Hume and Kant and currently involves researchers from a variety of fields including cognitive science, developmental psychology, and philosophy. Many researchers approach this topic by developing models that can explain the processes by which people reason about causes and effects. In this chapter, we review these modeling approaches and comment on their strengths and weaknesses. We then introduce a new approach based on quantum probability theory. 1 Classical Probability Models of Causal Reasoning Some of the first models of causal reasoning were centered around the idea that people use the covariation between causes and effects as a basis for causal judgments (Jenkins and Ward 1965; Kelley 1973). These approaches trace

Physical Review A, 2013

Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is independent of the causal relation that holds between the conditioned variable and the conditioning variable, in the conventional quantum formalism, there is a significant difference between how one treats experiments involving two systems at a single time and those involving a single system at two times. In this article, we develop the formalism of quantum conditional states, which provides a unified description of these two sorts of experiment. In addition, concepts that are distinct in the conventional formalism become unified: channels, sets of states, and positive operator valued measures are all seen to be instances of conditional states; the action of a channel on a state, ensemble averaging, the Born rule, the composition of channels, and nonselective state-update rules are all seen to be instances of belief propagation. Using a quantum generalization of Bayes' theorem and the associated notion of Bayesian conditioning, we also show that the remote steering of quantum states can be described within our formalism as a mere updating of beliefs about one system given new information about another, and retrodictive inferences can be expressed using the same belief propagation rule as is used for predictive inferences. Finally, we show that previous arguments for interpreting the projection postulate as a quantum generalization of Bayesian conditioning are based on a misleading analogy and that it is best understood as a combination of belief propagation (corresponding to the nonselective state-update map) and conditioning on the measurement outcome.

Cognitive Science, 2015

We develop a quantum probability model that can account for situations where people’s causal judgments violate the properties of causal Bayes nets and demonstrate how the parameters of our model can be interpreted to provide information about underlying cognitive processes. We implement this model within a hierarchical Bayesian inference framework that allows us to systematically identify individual differences and also provide a latent classification of individuals into categories of causal and associative reasoners. Finally, we implement a basic normative causal Bayes net within the same inference framework that allows us to directly compare quantum and classical probability models using Bayes factors.

We analyse a quantum-like Bayesian Network that puts together cause/effect relationships and semantic similarities between events. These semantic similarities constitute acausal connections according to the Synchronicity principle and provide new relationships to quantum like probabilistic graphical models. As a consequence, beliefs (or any other event) can be represented in vector spaces, in which quantum parameters are determined by the similarities that these vectors share between them. Events attached by a semantic meaning do not need to have an explanation in terms of cause and effect.

Nature Physics, 2015

The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both, unless one can implement a randomized intervention. We here consider the problem of causal inference for quantum variables. We introduce causal tomography, which unifies and generalizes conventional quantum tomography schemes to provide a complete solution to the causal inference problem using a quantum analogue of a randomized trial. We furthermore show that, in contrast to the classical case, observed quantum correlations alone can sometimes provide a solution. We implement a quantum-optical experiment that allows us to control the causal relation between two optical modes, and two measurement schemes-one with and one without randomizationthat extract this relation from the observed correlations. Our results show that entanglement and coherence, known to be central to quantum information processing, also provide a quantum advantage for causal inference.

Journal of Quantum Information Science, 2014

A survey on agents, causality and intelligence is presented and an equilibrium-based computing paradigm of quantum agents and quantum intelligence (QAQI) is proposed. In the survey, Aristotle's causality principle and its historical extensions by , and the causal set initiative are reviewed; bipolar dynamic logic (BDL) is introduced as a causal logic for bipolar inductive and deductive reasoning; bipolar quantum linear algebra (BQLA) is introduced as a causal algebra for quantum agent interaction and formation. Despite the widely held view that causality is undefinable with regularity, it is shown that equilibrium-based bipolar causality is logically definable using BDL and BQLA for causal inference in physical, social, biological, mental, and philosophical terms. This finding leads to the paradigm of QAQI where agents are modeled as quantum ensembles; intelligence is revealed as quantum intelligence. It is shown that the ensembles formation, mutation and interaction of agents can be described as direct or indirect results of quantum causality. Some fundamental laws of causation are presented for quantum agent entanglement and quantum intelligence. Applicability is illustrated; major challenges are identified in equilibrium based causal inference and quantum data mining. 229 or animals. Despite the tremendous research efforts on agents, we still don't know how a biological brain works exactly, how large the largest agent-the universe is, and how small the smallest agent-the most fundamental subatomic (quantum) particle-is. Without logically definable causality, we still haven't found a unifying mathematical definition for the word "agent" that is fundamental for all beings and their interactions ([9], Ch 6). Even though string theory was considered "theory of everything", it is criticized as not observable, not experimentally testable, and failed to provide falsifiable predictions [10] . Therefore, we don't know whether strings really exist or whether there is actually any smallest fundamental agent at all.