For all our familiarity with mental processes, their nature remains elusive, and the lessons offered so far by artificial intelligence seem at best incomplete. This reaffirms the need for a conceptually different approach. Recent developments in quantum mechanics, involving nothing larger (or smaller) than tabletop setups, shed light on the issue by showing that events do not always follow a fixed causal order, and that processes exist that are causally non-separable. While experiments have so far preceded theory, fueling debate about the physical interpretation of key results, this mirrors an earlier controversy where results at odds with prevailing paradigms were subsequently vindicated, giving rise to a quantum formalism that is now canonical. In this instance, validation would yield a precise definition of causal agency as an intent-bearing process, the behavior of which is nonrandom, not determined by preceding events, and not derivable from sequential events within the process itself. By focusing on causality rather than on freedom and its interpretive pitfalls, this definition allows to make headway in an old metaphysical discussion.
For all our familiarity with mental processes, their nature remains elusive, and the lessons offered so far by artificial intelligence seem at best incomplete. This reaffirms the need for a conceptually different approach. Recent developments in quantum mechanics, involving nothing larger (or smaller) than tabletop setups, shed light on the issue by showing that events do not always follow a fixed causal order, and that processes exist that are causally non-separable. While experiments have so far preceded theory, fueling debate about the physical interpretation of key results, this mirrors an earlier controversy where results at odds with prevailing paradigms were subsequently vindicated, giving rise to a quantum formalism that is now canonical. In this instance, validation would yield a precise definition of causal agency as an intent-bearing process, the behavior of which is nonrandom, not determined by preceding events, and not derivable from sequential events within the process itself. By focusing on causality rather than on freedom and its interpretive pitfalls, this definition allows to make headway in an old metaphysical discussion.
The idea that events are equipped with a partial causal order is central to our understanding of physics in the tested regimes: given two pointlike events A and B , either A is in the causal past of B , B is in the causal past of A , or A and B are space-like separated. Operationally, the meaning of these order relations corresponds to constraints on the possible correlations between experiments performed in the vicinities of the respective events: if A is in the causal past of B , an experimenter at A could signal to an experimenter at B but not the other way around, while if A and B are space-like separated, no signaling is possible in either direction. In the context of a concrete physical theory, the correlations compatible with a given causal configuration may obey further constraints. For instance, space-like correlations in quantum mechanics arise from local measurements on joint quantum states, while time-like correlations are established via quantum channels. Similarly to other variables, however, the causal order of a set of events could be random, and little is understood about the constraints that causality implies in this case. A main difficulty concerns the fact that the order of events can now generally depend on the operations performed at the locations of these events, since, for instance, an operation at A could influence the order in which B and C occur in A ’s future. So far, no formal theory of causality compatible with such dynamical causal order has been developed. Apart from being of fundamental interest in the context of inferring causal relations, such a theory is imperative for understanding recent suggestions that the causal order of events in quantum mechanics can be indefinite. Here, we develop such a theory in the general multipartite case. Starting from a background-independent definition of causality, we derive an iteratively formulated canonical decomposition of multipartite causal correlations. For a fixed number of settings and outcomes for each party, these correlations form a polytope whose facets define causal inequalities. The case of quantum correlations in this paradigm is captured by the process matrix formalism. We investigate the link between causality and the closely related notion of causal separability of quantum processes, which we here define rigorously in analogy with the link between Bell locality and separability of quantum states. We show that causality and causal separability are not equivalent in general by giving an example of a physically admissible tripartite quantum process that is causal but not causally separable. We also show that there are causally separable quantum processes that become non-causal if extended by supplying the parties with entangled ancillas. This motivates the concepts of extensibly causal and extensibly causally separable (ECS) processes, for which the respective property remains invariant under extension. We characterize the class of ECS quantum processes in the tripartite case via simple conditions on the form of the process matrix. We show that the processes realizable by classically controlled quantum circuits are ECS and conjecture that the reverse also holds.
Summary form only given. A causal order describes the order in which events occur, and how these different events can effect each other. Recently, a description of quantum mechanics making no assumption about the order of events was developed [1]. In this formalism, events are treated in terms of the ability to exchange information between each other. Applying this new formalism to quantum mechanics has shown that processes without a defined causal order can exist. Information can nonetheless be transferred through these processes. Extraordinarily, these processes can accomplish tasks which are not otherwise possible [2-4]. In our group, we have been studying methods to create and characterize one such process: the “quantum SWITCH” [5, 6]. We have shown that, using this process, one can obtain computational advantages [5]. We have also performed a specific sequence of measurements, which we used to determine just how “non-causal” our constructed process is [6].
The concept of causal nonseparability has been recently introduced, in opposition to that of causal separability, to qualify physical processes that locally abide by the laws of quantum theory, but cannot be embedded in a well-defined global causal structure. While the definition is unambiguous in the bipartite case, its generalisation to the multipartite case is not so straightforward. Two seemingly different generalisations have been proposed, one for a restricted tripartite scenario and one for the general multipartite case. Here we compare the two, showing that they are in fact inequivalent. We propose our own definition of causal (non)separability for the general case, which—although a priori subtly different—turns out to be equivalent to the concept of ‘extensible causal (non)separability’ introduced before, and which we argue is a more natural definition for general multipartite scenarios. We then derive necessary, as well as sufficient conditions to characterise causally (non)separable processes in practice. These allow one to devise practical tests, by generalising the tool of witnesses of causal nonseparability.
Abstract Quantum mechanics is our most successful and versatile account of the basic constituents of matter, of their interaction and of their compounds. We introduce the theory via a sketch of its history and lay out its mathematical structure in some detail. Before this background we address the important and controversial question of how to interpret that structure. We contextualise our own position, which is linked to our account of ontological emergence as detailed in Chap. 2 , and which is mathematically best expressed in the Heisenberg picture of quantum dynamics. Indeterminism and irreversible processes are fundamental for our approach. We discuss the dialectics of the deterministic challenge to our position and argue that indeterminism in the form of quantum randomness has turned from a philosophical riddle to a technological resource. This claim is supported by a discussion of quantum information science, including some of its basic protocols. Towards the end of the chapter we argue that agency and quantum mechanics come as a package deal. For one, quantum mechanics describes the world as offering open possibilities for the future at a fundamental physical level, which is needed for real higher-order organisation, including agency. Of course, this does not in any way show that the actual existence of agents in our world is guaranteed. But it does show that general agency scepticism has no basis in physics. Second, we show that quantum mechanics is best understood as a theory that describes our agential interactions with nature, and not as a theory that represents nature from the point of view of an inert, detached observer.
Two mysteries -loosely connected?The Authors who have suggested a deep connection between the solution of the mind-body problem and the understanding of quantum mechanics are too numerous to list.But what exactly would be the alleged structural fit between these two deeply puzzling theoretical issues?Can a genuine philosophical issue -which by its very nature is conceptual in nature -ultimately be resolved by advances in the empirical sciences?The connection is all too often asserted to lie in the subjects confounding natures, but the mere fact that two problems are of equal impenetrability to the human mind does not imply that there is a profound interdependence between the two.There is however an obvious way in which quantum mechanics might have a bearing on the philosophical mind-body problem: if quantum mechanics implies that for some physical events there is no physical cause, then at least the very strong variants of the so-called "principle of causal closure" of the physical realm lose much of their corroborative underpinning in physics as practiced by real physicists as such, and are thus constrained to the speculative physicalism advanced by metaphysicians.However, unless one assumes a strong version of the principle of sufficient reason, which would exclude chance events in principle, even events supposedly not caused by some physical cause are not immediately thereby caused by some nonphysical cause.Moreover the fact is that not all of the interpretations of quantum mechanics imply indeterministic 'choices' of events: neither the many-worlds interpretation nor a Bohmian hidden variable interpretation assume indeterminism.Even in the most obvious theoretical nexus
The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? Here, we address these questions from the standpoint of quantum mechanics in a new framework for multipartite correlations that does not assume a pre-defined global causal structure but only the validity of quantum mechanics locally. All known situations that respect causal order, including space-like and time-like separated experiments, are captured by this framework in a unified way. Surprisingly, we find correlations that cannot be understood in terms of definite causal order. These correlations violate a 'causal inequality' that is satisfied by all space-like and time-like correlations. We further show that in a classical limit causal order always arises, which suggests that space-time may emerge from a more fundamental structure in a quantum-to-classical transition. Causal order is a concept that is engrained in the standard understanding of time, both in classical and quantum mechanics. Oreshkovet al.generalize the standard formalism of quantum theory to a framework with no pre-existing causal order, and find a new class of correlations that have no analogue in the classical world.