**Caslav Brukner**, University of Vienna

*Timeless formulation of Wigner’s friend scenarios*

At the heart of the quantum measurement problem lies the ambiguity about exactly when to use the unitary evolution of the quantum state and when to use the state-update in dynamics of quantum mechanical systems. In the Wigner’s friend gedankenexperiment, different observers (one of whom is observed by the other) describe one and the same interaction differently. One – the friend – uses the state-update rule and the other – Wigner – chooses unitary evolution. This can lead to paradoxical situations in which Wigner and his friend assign different probabilities to the outcomes of subsequent measurements. In my talk, I will apply the Page-Wootters mechanism (PWM) as a timeless description of the Wigner's friend-like scenario. This description assigns one timeless state to the entire experimental scenario from which it is possible to derive probabilities without the need to involve the evolution of the quantum state during – and in-between – measurements. I will consider several rules for assigning two-time conditional probabilities within the PWM. All of these reduce to standard (“textbook”) rules for non-Wigner’s friend scenarios. However, when applied to the Wigner’s friend setup, they differ. Each rule potentially resolves the probability-assignment paradox in a different way. Moreover, one rule imposes that a joint probability distribution for the measurement outcomes of Wigner and his friend is well-defined only when Wigner’s measurement does not disturb the friend’s memory, in agreement with the recent “no-go theorem for observer-independent facts”.

(with Veronika Baumann, Flavio Del Santo, Alexander R. H. Smith, Flaminia Giacomini, and Esteban Castro-Ruiz)

**Esteban Castro-Ruiz**, University of Vienna

*Time reference frames and gravitating quantum clocks*

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.

**Giulio Chiribella**, University of Hong Kong & University of Oxford

*10 years of the quantum SWITCH: state of the art and new perspectives*

The quantum SWITCH is the simplest example of indefinite causal structure. Technically, it is a higher-order transformation that takes two physical processes A and B in input and combines them in a coherent superposition of two alternative orders, AB and BA. In the past decade, the quantum SWITCH has been the object of active research, both theoretically and experimentally. In this talk, I will review the state of the art, and outline two new applications to quantum Shannon theory and quantum metrology.

**John Donoghue,** University of Massachusetts

*Dueling Arrows of Causality, Causal Uncertainty and Quadratic Gravity*

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.

**Andrzej Dragan**, University of Warsaw & National University of Singapore

*Quantum principle of relativity*

**Doreen Fraser,** University of Waterloo

*Lessons from the role of non-relativistic causal models in the history of QFT?*

There are a number of cases in the history of particle physics in which analogies to non-relativistic condensed matter physics models guided the development of new relativistic particle physics models. This heuristic strategy for model construction depended for its success on the causal structure of the non-relativistic models and the fact that this causal structure is not preserved in the relativistic models. Focusing on the case of spontaneous symmetry breaking, the heuristic role of representations of causal structure and time in the non-relativistic models will be examined. I will reflect on whether the use of non-relativistic causal models to construct relativistic quantum field theory models offers methodological lessons for the shift from definite causal structures in pre-general relativistic quantum theories to indefinite causal structures in quantum gravity.

**Flaminia Giacomini,** Perimeter Institute

*Quantum mechanics and the covariance of physical laws in quantum reference frames*

In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? Here, we introduce a general method to quantise reference frame transformations, which generalises the usual reference frame transformation to a “superposition of coordinate transformations”. We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entanglement and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, to an extension of the weak equivalence principle, and to the possibility of defining the rest frame of a quantum system.

**Gavin Morley**, University of Warwick

*Levitating microdiamonds towards testing the macroscopic limits of the quantum superposition principle*

We are building an experiment in which a levitated 1 µm diamond containing a nitrogen vacancy (NV) centre would be put into a spatial quantum superposition [1-3]. This would be able to test theories of spontaneous wavefunction collapse [4]. We have helped theory collaborators to propose how to do this experiment [5-9], as well as a much more experimentally ambitious extension which would test if gravity permits a quantum superposition [10]. There are related proposals from other groups [11-13].

[1] A. T. M. A. Rahman, A. C. Frangeskou, M. S. Kim, S. Bose, G. W. Morley & P. F. Barker, Sci. Rep. 6, 21633 (2016).

[2] A. T. M. A. Rahman, A. C. Frangeskou, P. F. Barker & G. W. Morley, Rev. Sci. Instrum. 89, 023109 (2018).

[3] A. C. Frangeskou, A. T. M. A. Rahman, L. Gines, S. Mandal, O. A. Williams, P. F. Barker & G. W. Morley, NJP 20, 043016 (2018).

[4] A. Bassi, K. Lochan, S. Satin, T. P. Singh & H. Ulbricht, Rev. Mod. Phys. 85, 471 (2013).

[5] S. Bose & G. W. Morley, arXiv:1810.07045 (2018).

[6] M. Scala, M. S. Kim, G. W. Morley, P. F. Barker & S. Bose, PRL 111, 180403 (2013).

[7] C. Wan, M. Scala, G. W. Morley, A. T. M. A. Rahman, H. Ulbricht, J. Bateman, P. F. Barker, S. Bose & M. S. Kim, PRL 117, 143003 (2016).

[8] R. J. Marshman, A. Mazumdar, G. W. Morley, P. F. Barker, H. Steven & S. Bose, arXiv:1807.10830 (2018).

[9] J. S. Pedernales, G. W. Morley & M. B. Plenio, arXiv:1906.00835 (2019).

[10] S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroš, M. Paternostro, A. A. Geraci, P. F. Barker, M. S. Kim & G. Milburn, PRL 119, 240401 (2017).

[11] Z.-q. Yin, T. Li, X. Zhang & L. M. Duan, PRA 88, 033614 (2013).

[12] A. Albrecht, A. Retzker & M. B. Plenio, PRA 90, 033834 (2014).

[13] C. Marletto & V. Vedral, PRL 119, 240402 (2017).

**Aleks Kissinger**, University of Oxford

*Composing causal orderings*

When studying (definite or indefinite) causal orderings of processes, it is often useful to consider higher-order processes, i.e. processes which take other processes as their input. However, as a recent no-go result of Guerin et al indicates, our naive first-order notions of "composition" of processes become ill-defined at higher-order. Unlike state spaces, there are multiple non-equivalent notions of "joint system" for process spaces and many different ways one might attempt to plug processes together, with only some giving well-defined (i.e. normalised) processes as outputs. While this starts to look a bit like the Wild West, I'll show in this talk that we can get quite a bit of mileage from considering just two kinds of joint systems: a "non-signalling" tensor product, and a (de Morgan dual) "signalling" product. The interaction between these two products has in fact been well-understood by logicians since the 1980s in a very different disguise: multiplicative linear logic. Using this connection, I'll show how a set of "contractibility" criteria due to Danos and Regnier give a relatively simple, dimension-independent technique for determining whether an arbitrary plugging of higher-order processes is well-defined.

**Ognyan Oreshkov**, Universite Libre de Bruxelles

*Cyclic quantum causal models and violations of causal inequalities*

I will present an extension of the recent theory of quantum causal models to cyclic causal structures. This offers a novel causal perspective on processes beyond those corresponding to standard circuits, such as processes with dynamical causal order and causally nonseparable processes, including processes violating causal inequalities. As an application, I will use the algebraic structure of process operators that is induced by the causal structure to prove that all unitarily extendible bipartite processes are causally separable, i.e., their unitary extensions are variations of the quantum SWITCH. Remarkably, the latter implies that all unitarily extendible tripartite quantum processes have realizations on time-delocalized systems within standard quantum mechanics. This includes, in particular, classical processes violating causal inequalities, which admit simple implementations! I will explain what the violation of causal inequalities implies for the variables of interest in these implementations. The answer is given again by the theory of cyclic causal models.

Based on joint works with Jonathan Barrett, Cyril Branciard, Robin Lorenz, and Julian Wechs.

**Jacques Pienaar,** University of Massachusetts

*Causality in Qbism*

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'.

**Tim Ralph**, University of Queensland

*Quantum Models of CTCs and a space-based experiment*

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.

**Katja Ried**, University of Innsbruck

*Indefinite causal order without post-selection*

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.

**David Schmid, **Perimeter Institute

*Unscrambling the Omelette of Causation and Inference in Operational and Ontological Theories*

I will discuss how the standard frameworks for operational theories involve a scrambling of causal and inferential concepts. I will then present a new framework for operational theories which separates out the inferential and the causal aspects of a given physical theory. Generalized probabilistic theories and operational probabilistic theories are recovered within our framework when one ignores some of these distinctions. We then make similar refinements to the traditional notion of ontological theories, and discuss how our framework revises the standard notions of ontological representations and of generalized noncontextuality.

**Alexander Smith**, Dartmouth College

*What happens when we quantize time?*

The lesson of general relativity is background independence: a physical theory should not be formulated in terms of external structures. This motivates a relational approach to quantum dynamics, which is necessary for a quantum theory of gravity. Using a covariant POVM to define a time observable, I will introduce the so-called trinity of relational quantum dynamics comprised of three distinct formulations of the same relational quantum theory: evolving constants of motion, the Page-Wootters formalism, and a symmetry reduction procedure. The equivalence between these formulations yields a temporal frame change map that transforms between the dynamics seen by different clocks. This map will be used to illustrate a temporal nonlocality effect that results in a superposition of time evolutions from the perspective of a clock indicating a superposition of different times. Then, a time-nonlocal modification to the Schrödinger equation will be shown to manifest when a system is coupled to the clock that is tracking its evolution. Such clock-system interactions should be expected at some scale when the gravitational interaction between them is taken into account. Finally, I will examine relativistic particles with internal degrees of freedom that constitute a clock that tracks their proper time. By evaluating the conditional probability associated with two such clocks reading different proper times, I will show that these clocks exhibit a novel quantum time dilation effect when moving in a superposition of different momenta.

**Lee Smolin**, Perimeter Institute

*Two views of relative locality*

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.