Conference

The dynamics of closed quantum systems undergoing unitary processes has been well studied, leading to notions of measures for the expressive power of parameterized quantum circuits, relative to the unique, maximally expressive, average behaviour of ensembles of unitaries. Such unitary expressivity measures have further been linked to concentration phenomena known as barren plateaus. However, existing quantum hardware are not isolated from their noisy environment, and such non-unitary dynamics must therefore be described by more general trace-preserving operations. To account for hardware noise, we propose several, non-unique measures of expressivity for quantum channels and study their properties, highlighting how average non-unitary channels differ from average unitary channels. In the limit of large composite system and environments, average noisy quantum channels are shown to be maximally globally depolarizing, with next-leading-order non-unital perturbative behaviour. Furthermore, we rigorously prove that highly-expressive parameterized quantum channels will suffer from barren plateaus, thus generalizing explanations of noise-induced phenomena. This work is based on forthcoming work with Diego Martin, Zoe Holmes, and Marco Cerezo, in affiliation with Los Alamos National Laboratory.

We present a study of the relationship between energy and entanglement in finite regions of possibly arbitrary shape in QFT. We show how one can quantify the entanglement avoiding divergences by using techniques inspired by the formalism of particle detectors in relativistic quantum information. We also show how the energy cost of entanglement extraction varies with the shape and size of the regions, as well as analyze the energy density of the quantum field after this entanglement has been extracted.

Violations of Bell’s inequality have been studied for spin-1/2 systems in much detail. Turns out that one can show Bell violation for systems that are expressed in terms of continuous variables such as position and momentum. The most ubiquitous examples of such systems are Gaussian states, notably the two-mode squeezed vacuum state. I will talk about how one can quantify violations of local realism in such states. I will discuss the dependence of Bell violation on temperature as well as the result that entanglement is not a monotonic function of Bell's inequality.

What types of differences among causal structures with latent variables are impossible to distinguish by statistical data obtained by probing each visible variable? If the probing scheme is simply passive observation, then it is well-known that many different causal structures can realize the same joint probability distributions. Even for the simplest case of two visible variables, for instance, one cannot distinguish between causal influence of one variable on the other and the two variables sharing a latent common cause. However, it is possible to distinguish between these two causal structures if we have recourse to more powerful probing schemes, such as the possibility of intervening on one of the variables and observing the other. Herein, we address the question of which causal structures remain indistinguishable even given the most informative types of probing schemes on the visible variables. We find that two causal structures remain indistinguishable if and only if they are both associated with the same mDAG structure (as defined by Evans (2016)). We also consider the question of when one causal structure dominates another in the sense that it can realize all of the joint probability distributions that can be realized by the other using a given probing scheme. (Equivalence of causal structures is the special case of mutual dominance.) Finally, we investigate to what extent one can weaken the probing schemes implemented on the visible variables and still have the same discrimination power as a maximally informative probing scheme.