Watching the Clocks: Interpreting the Page-Wootters Formalism and the Internal Quantum Reference Frame Programme

We discuss some difficulties that arise in attempting to interpret the Page-Wootters and Internal Quantum Reference Frames formalisms, then use a ‘final measurement’ approach to demonstrate that there is a workable single-world realist interpretation for these formalisms. We note that it is necessary to adopt some interpretation before we can determine if the ‘reference frames’ invoked in these approaches are operationally meaningful, and we argue that without a clear operational interpretation, such reference frames might not be suitable to define an equivalence principle. We argue that the notion of superposition should take into account the way in which an instantaneous state is embedded in ongoing dynamical evolution, and this leads to a more nuanced way of thinking about the relativity of superposition in these approaches. We conclude that typically the operational content of these approaches appears only in the limit as the size of at least one reference system becomes large, and therefore these formalisms have an important role to play in showing how our macroscopic reference frames can emerge out of wholly relational facts.

Two Roads to Retrocausality

In recent years the quantum foundations community has seen increasing interest in the possibility of using retrocausality as a route to rejecting the conclusions of Bell’s theorem and restoring locality to quantum physics. On the other hand, it has also been argued that accepting nonlocality leads to a form of retrocausality. In this article we seek to elucidate the relationship between retrocausality and locality. We begin by providing a brief schema of the various ways in which violations of Bell’s inequalities might lead us to consider some form of retrocausality. We then consider some possible motivations for using retrocausality to rescue locality, arguing that none of these motivations is adequate and that therefore there is no clear reason why we should prefer local retrocausal models to nonlocal retrocausal models. Next, we examine several different conceptions of retrocausality, concluding that `all-at-once’ retrocausality is more coherent than the alternative dynamical picture. We then argue that since the `all-at-once’ approach requires probabilities to be assigned to entire histories or mosaics, locality is somewhat redundant within this picture. Thus we conclude that using retrocausality as a way to rescue locality may not be the right route to retrocausality. Finally, we demonstrate that accepting the existence of nonlocality and insisting on the nonexistence of preferred reference frames leads naturally to the acceptance of a form of retrocausality, albeit one which is not mediated by physical systems travelling backwards in time. We argue that this is the more natural way to motivate retrocausal models of quantum mechanics.

Entanglement-asymmetry correspondence for internal quantum reference frames

In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for example, evolution of a quantum system S is described by a stationary joint state of S and a quantum clock, where time-dependence of S arises from conditioning on the value of the clock. Here, we consider (possibly imperfect) internal quantum reference frames R for arbitrary compact symmetry groups, and show that there is an exact quantitative correspondence between the amount of entanglement in the invariant state on RS and the amount of asymmetry in the corresponding conditional state on S. Surprisingly, this duality holds exactly regardless of the choice of coherent state system used to condition on the reference frame. Averaging asymmetry over all conditional states, we obtain a simple representation-theoretic expression that admits the study of the quality of imperfect quantum reference frames, quantum speed limits for imperfect clocks, and typicality of asymmetry in a unified way. Our results shed light on the role of entanglement for establishing asymmetry in a fully symmetric quantum world.

Controlling wave-particle duality with quantum entanglement

Wave-particle duality and entanglement are two fundamental characteristics of quantum mechanics. All previous works on experimental investigations in wave{particle properties of single photons (or single particles in general) show that a well-defined interferometer setting determines a well-defined property of single photons. Here we take a conceptual step forward and control the wave-particle property of single photons with quantum entanglement. By doing so, we experimentally test the complementarity principle in a scenario, in which the setting of the interferometer is not defined at any instance of the experiment, not even in principle. To achieve this goal, we send the photon of interest (S) into a quantum Mach-Zehnder interferometer (MZI), in which the output beam splitter of the MZI is controlled by the quantum state of the second photon (C), who is entangled with a third photon (A). Therefore, the individual quantum state of photon C is undefined, which implements the undefined settings of the MZI for photon S. This is realized by using three cascaded phase-stable interferometers for three photons. There is typically no well-defined setting of the MZI, and thus the very formulation of the wave-particle properties becomes internally inconsistent.

Determinism Beyond Time Evolution

Physicists are increasingly beginning to take seriously the possibility of laws outside the traditional time-evolution paradigm; yet our understanding of determinism is still predicated on a forwards time-evolution picture, making it manifestly unsuited to the diverse range of research programmes in modern physics. In this article, we use a constraint-based framework to set out a generalization of determinism which does not presuppose temporal directedness, distinguishing between strong, weak and delocalised holistic determinism. We discuss some interesting consequences of these generalized notions of determinism, and we show that this approach sheds new light on the long-standing debate surrounding the nature of objective chance.

Contextuality in entanglement-assisted one-shot classical communication

We consider the problem of entanglement-assisted one-shot classical communication. In the zero-error regime, entanglement can increase the one-shot zero-error capacity of a family of classical channels following the strategy of Cubitt et al., Phys. Rev. Lett. 104, 230503 (2010). This strategy uses the Kochen-Specker theorem which is applicable only to projective measurements. As such, in the regime of noisy states and/or measurements, this strategy cannot increase the capacity. To accommodate generically noisy situations, we examine the one-shot success probability of sending a fixed number of classical messages. We show that preparation contextuality powers the quantum advantage in this task, increasing the one-shot success probability beyond its classical maximum. Our treatment extends beyond Cubitt et al. and includes, for example, the experimentally implemented protocol of Prevedel et al., Phys. Rev. Lett. 106, 110505 (2011). We then show a mapping between this communication task and a corresponding nonlocal game. This mapping generalizes the connection with pseudotelepathy games previously noted in the zero-error case. Finally, after motivating a constraint we term context-independent guessing, we show that contextuality witnessed by noise-robust noncontextuality inequalities obtained in R. Kunjwal, Quantum 4, 219 (2020), is sufficient for enhancing the one-shot success probability. This provides an operational meaning to these inequalities and the associated hypergraph invariant, the weighted max-predictability, introduced in R. Kunjwal, Quantum 3, 184 (2019). Our results show that the task of entanglement-assisted one-shot classical communication provides a fertile ground to study the interplay of the Kochen-Specker theorem, Spekkens contextuality, and Bell nonlocality.

Discretizing parametrized systems: the magic of Ditt-invariance

Peculiar phenomena appear in the discretization of a system invariant under reparametrization. The structure of the continuum limit is markedly different from the usual one, as in lattice QCD. First, the continuum limit does not require tuning a parameter in the action to a critical value. Rather, there is a regime where the system approaches a sort of asymptotic topological invariance (“Ditt-invariance”). Second, in this regime the expansion in the number of discretization points provides a good approximation to the transition amplitudes. These phenomena are relevant for understanding the continuum limit of quantum gravity. I illustrate them here in the context of a simple system.