Indefinite Causal Structure

The approach to quantum theory known as QBism notoriously asserts that the quantum state is not even a partial representation of reality, but instead quantifies an agent's subjective degrees of belief about future experiences. Despite its counter-intuitive premise, QBists argue that this interpretation has the potential to illuminate and demystify certain aspects of quantum theory. In this talk I will discuss how `causality' might be interpreted by a QBist, and whether doing so might help us understand the bizarre hypothetical phenomenon of `indefinite causality'.

The possibility of indefinite causal order has garnered considerable interest in recent years, both for its promise as a resource, e.g. for communication, and for its role in exploring the fundamental physical constraints on causal structure. In order to gain a better understanding of the phenomenon, one approach is to design experiments that implement – or at least simulate – scenarios with indefinite causal order. While post-selection is one way to simulate exotic causal structures, this approach may not provide the desired insights. Instead, I will discuss how one might go about implementing indefinite causal order without post-selection.

The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and it is expected to become indefinite when matter behaves quantum mechanically. Here we explore the problem of operationally defining events and their localisation in the presence of gravitating quantum systems. We develop a framework for "time reference frames," in which events are defined in terms of quantum operations with respect to a quantum clock. We find that, when clocks and quantum systems interact gravitationally, the temporal localisability of events becomes relative, depending on the time reference frame. We argue that the impossibility to find a reference frame in which all events are localised is a signature of an indefinite metric, which might yield an indefinite causal order of events. Even if the metric is indefinite, for any event we can find a time reference frame with respect to which the event is localised in time, while other events may remain delocalised. In this frame, time evolution takes its standard (Schrödinger) form, including the unitary dilation of the quantum operation defining the event. In addition, this form is preserved when moving from the frame localising one event to the frame localising another one, thereby implementing a form of covariance with respect to quantum reference frame transformations.

I will discuss various models of how quantum systems might interact with Closed Time-like Curves and some of the curious effects that can arise. I will then use this to motivate a speculative gravitational decoherence model and describe a recent space-based experiment which made the first test of such models.

Relative locality is a quantum gravity phenomenon in which whether an event is local or not-and the degree of non-locality-is dependent on the position and motion of the observer, as well as on the energy of the observer’s probes. It was first discovered and studied, beginning in 2010, in a limit in which h and G both go to zero, with their ratio, which is the Planck energy-squared, and c held fixed (arXiv:1101.0931, arXiv:1103.5626). Relative locality was also found in a different, non-relativistic limit, involving quantum reference frames, in which c is taken to infinity while h and G are held fixed. I describe some of what we learned in the first studies, in the hope it might be useful to people developing the quantum reference frame approach.

Quadratic gravity is a renormalizeable theory of quantum gravity which is unitary, but which violates causality by amounts proportional to the inverse Planck scale. To understand this, I will first discuss the arrow of causality in quantum field theory (with a detour concerning the arrow of time), and then discuss theories with dueling arrows of causality. But the causality violation might be better described by causality uncertainty. This is discussed both in quadratic gravity and in the effective field theory of general relativity.