Papers New

We present an exhaustive classification of the 2644 causally complete spaces of input histories on 3 events with binary inputs, together with the algorithm used to find them. This paper forms the supplementary material for a trilogy of works: spaces of input histories, our dynamical generalisation of causal orders, are introduced in “The Combinatorics of Causality”; the sheaf-theoretic treatment of causal distributions is detailed in “The Topology of Causality”; the polytopes formed by the associated empirical models are studied in “The Geometry of Causality”.

We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. We define causaltopes, our chosen portmanteau of “causal polytopes”, for arbitrary spaces of input histories and arbitrary choices of input contexts. We show that causaltopes are obtained by slicing simpler polytopes of conditional probability distributions with a set of causality equations, which we fully characterise. We provide efficient linear programs to compute the maximal component of an empirical model supported by any given sub-causaltope, as well as the associated causal fraction. We introduce a notion of causal separability relative to arbitrary causal constraints. We provide efficient linear programs to compute the maximal causally separable component of an empirical model, and hence its causally separable fraction, as the component jointly supported by certain sub-causaltopes. We study causal fractions and causal separability for several novel examples, including a selection of quantum switches with entangled or contextual control. In the process, we demonstrate the existence of “causal contextuality”, a phenomenon where causal inseparability is clearly correlated to, or even directly implied by, non-locality and contextuality.

We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality by Abramsky and Brandenburger, which it extends to include arbitrary causal orders (be they definite, dynamical or indefinite). We define a notion of causal function for arbitrary spaces of input histories, and we show that the explicit imposition of causal constraints on joint outputs is equivalent to the free assignment of local outputs to the tip events of input histories. We prove factorisation results for causal functions over parallel, sequential, and conditional sequential compositions of the underlying spaces. We prove that causality is equivalent to continuity with respect to the lowerset topology on the underlying spaces, and we show that partial causal functions defined on open sub-spaces can be bundled into a presheaf. In a striking departure from the Abramsky-Brandenburger setting, however, we show that causal functions fail, under certain circumstances, to form a sheaf. We define empirical models as compatible families in the presheaf of probability distributions on causal functions, for arbitrary open covers of the underlying space of input histories. We show the existence of causally-induced contextuality, a phenomenon arising when the causal constraints themselves become context-dependent, and we prove a no-go result for non-locality on total orders, both static and dynamical.

We give a conceptual exposition of aspects of gravitational radiation, especially in relation to energy. Our motive for doing so is that the strong analogies with electromagnetic radiation seem not to be widely enough appreciated. In particular, we reply to some recent papers in the philosophy of physics literature that seem to deny that gravitational waves carry energy. Our argument is based on two points: (i) that for both electromagnetism and gravity, in the presence of material sources, radiation is an effective concept, unambiguously emerging only in certain regimes or solutions of the theory; and (ii) similarly, energy conservation is only unambiguous in certain regimes or solutions of general relativity. Crucially, the domain of (i), in which radiation is meaningful, has a significant overlap with the domain of (ii), in which energy conservation is meaningful. Conceptually, the overlap of regimes is no coincidence: the long-standing question about the existence of gravitational waves was settled precisely by finding a consistent way to articulate their energy and momentum.

In this essay, we present a new understanding of the cosmological constant problem, built upon the realization that the vacuum energy density can be expressed in terms of a phase space volume. We introduce a UV-IR regularization which implies a relationship between the vacuum energy and entropy. Combining this insight with the holographic bound on entropy then yields a bound on the cosmological constant consistent with observations. It follows that the universe is large, and the cosmological constant is naturally small, because the universe is filled with a large number of degrees of freedom.

The precision of quantum metrology is widely believed to be restricted by the Heisenberg limit, corresponding to a root mean square error that is inversely proportional to the number of independent processes probed in an experiment, N. In the past, some proposals have challenged this belief, for example using non-linear interactions among the probes. However, these proposals turned out to still obey the Heisenberg limit with respect to other relevant resources, such as the total energy of the probes. Here, we present a photonic implementation of a quantum metrology protocol surpassing the Heisenberg limit by probing two groups of independent processes in a superposition of two alternative causal orders. Each process creates a phase space displacement, and our setup is able to estimate a geometric phase associated to two sets of N displacements with an error that falls quadratically with N. Our results only require a single-photon probe with an initial energy that is independent of N. Using a superposition of causal orders outperforms every setup where the displacements are probed in a definite order. Our experiment features the demonstration of indefinite causal order in a continuous-variable system, and opens up the experimental investigation of quantum metrology setups boosted by indefinite causal order.

A promising route to testing quantum gravity in the laboratory is to look for gravitationally-induced entanglement (GIE) between two or more quantum matter systems. Principally, proposals for such tests have used microsolid systems, with highly non-classical states, such as N00N states or highly-squeezed states. Here, we consider, for the first time, GIE between two cold atomic gasses as a test of quantum gravity. We propose placing two atom interferometers next to each other in parallel and looking for correlations in the number of atoms at the output ports as evidence of GIE and quantum gravity. There are no challenging macroscopic superposition states, such as N00N or Schr”odinger cat states, instead classical-like `coherent’ states of atoms. This requires the total mass of the atom interferometers to be on the Planck mass scale, and long integration times. With current state-of-the-art quantum squeezing in cold atoms, however, we argue that the mass scale can be reduced to approachable levels and outline how such a mass scale can be achieved in the near future.

I discuss some general information-theoretic properties of quantum mechanical probes in semiclassical gravity: their purview, i.e. what they can see and act on (in terms of a generalised entanglement wedge), their spontaneous evaporation into a cloud of highly entropic particles when one tries to make them see too much (perhaps a parable on the dangers of straining one’s eyes), and the subsequent resolution of an apparent information paradox.

Counting the solutions to Boolean formulae defines the problem #SAT, which is complete for the complexity class #P. We use the ZH-calculus, a universal and complete graphical language for linear maps which naturally encodes counting problems in terms of diagrams, to give graphical reductions from #SAT to several related counting problems. Some of these graphical reductions, like to #2SAT, are substantially simpler than known reductions via the matrix permanent. Additionally, our approach allows us to consider the case of counting solutions modulo an integer on equal footing. Finally, since the ZH-calculus was originally introduced to reason about quantum computing, we show that the problem of evaluating ZH-diagrams in the fragment corresponding to the Clifford+T gateset, is in $FP^{#P}$. Our results show that graphical calculi represent an intuitive and useful framework for reasoning about counting problems.

Active states, from which work can be extracted by time-dependent perturbations, are an important resource for quantum thermodynamics in the absence of heat baths. Here we characterize this resource, establishing a resource theory that captures the operational scenario where an experimenter manipulates a quantum system by means of energy-preserving operations and resets to non-active states. Our resource theory comes with simple conditions for state convertibility and an experimentally accessible resource quantifier that determines the maximum advantage of active states in the task of producing approximations of the maximally coherent state by means of energy-preserving quantum operations.