Quantum Physics

In quantum systems with infinitely many degrees of freedom, states can be infinitely entangled across a pair of subsystems. But are there different forms of infinite entanglement? In the first part of my talk, I will present a von Neumann algebraic framework for studying information-theoretic properties of infinite systems. Using this framework, we find operational tasks that distinguish different forms of infinite entanglement, and, by analysing these tasks, we show that the type classification of von Neumann algebras (types I, II, III, and their respective subtypes) is in 1-to-1 correspondence with operational entanglement properties. Our findings promote the type classification from mere algebraic bookkeeping to a classification of infinite quantum systems based on their operational entanglement properties. In the second part, I will discuss what is known about the type classification of the von Neumann algebras arising in quantum many-body systems. Together with our results, this identifies new operational properties, e.g., embezzlement of entanglement, of well-known physical models, e.g., the critical transverse-field Ising chain or suitable Levin-Wen models. Joint work with: Alexander Stottmeister, Reinhard F. Werner, and Henrik Wilming

The entropy accumulation theorem (EAT) allows us to lower bound the min-entropy of a state that can be generated by a chain of quantum channels satisfying a Markov chain condition, and can be used to prove the security of QKD protocols, including device-independent ones. However, one of its drawbacks is that it only applies to states with a fairly rigid structure; in particular, the Markov chain condition must be satisfied exactly. What happens when we relax this assumption by allowing the required structure to be satisfies only approximately? Does doing so lead to interesting applications? We answer both questions by the affirmative: we present two flavours of approximate EAT, and show that it can be used to prove the security of parallel device-independent QKD, and to analyze QKD protocols under source correlations. Along the way, we will introduce the concept of "approximation chain" which underpins the new results.   This is joint work with Ashutosh Marwah; the talk will cover material from 2412.06723, 2402.12346, and 2308.11736.

This talk will consist of two parts. In the former I discuss published work [LD, Ligthart, Gross, PRA, 2024], and in the latter some new related results. Part 1 -- Although there exist theories with "stronger bipartite entanglement" than quantum mechanics (QM), in sense that they have a larger CHSH value than Tsirelson's bound for QM, all such theories known tend to come at a cost, namely, they have strictly weaker bipartite measurements. Thus it has been conjectured that if one looks at scenarios where the correlations depend both on bipartite states and bipartite measurements, e.g. entanglement swapping, such theories cannot beat QM. However, in our recent work [LD, Ligthart, Gross, PRA, 2024], we constructed a General Probabilistic Theory (GPT) -- Oblate Stabilizer Theory (OST) -- that can both achieve a CHSH value of 4 (the mathematical maximum), and maintain this CHSH value after arbitrarily many rounds of entanglement swapping, effectively ruling out this conjecture. Part 2 -- One particularly non-intuitive feature of OST (for those in the know) is the presence of a "spurious extra dimension" in the local theory: Even though the CHSH violation involves only a two-dimensional section of local state space, we failed to make the entanglement swapping property work without going to three dimensions. In ongoing work, we managed to identify the mechanism behind this phenomenon. To this end, we have introduced a notion of self-testing for GPTs, and, using this we have established a GPT version of the "no-pancake" theorem that says that there is no completely positive map that maps the Bloch sphere to a two-dimensional section. Further, under reasonable assumptions, we have also managed to establish the uniqueness of OST, and provide a prescription for the construction of GPTs capable of stable iterated entanglement swapping.

Abstract: The experimental realization of increasingly complex quantum states in quantum devices underscores the pressing need for new methods of state learning and verification. Among the various classes of quantum states, fermionic systems hold particular significance due to their crucial roles in physics. Despite their importance, research on learning quantum states of fermionic systems remains surprisingly limited. In our work, we aim to present a comprehensive rigorous study on learning and testing states of fermionic systems. We begin by analyzing arguably the simplest important class of fermionic states—free-fermionic states—and subsequently extend our analysis to more complex fermionic states. We meticulously delineate scenarios in which efficient algorithms are feasible, providing experimentally practical algorithms for these cases, while also identifying situations where any algorithm for solving these problems must be inherently inefficient. At the same time, we present novel fundamental results of independent interest on fermionic systems, with additional applications beyond learning and characterizing quantum devices, such as many-body physics, resource theory of non-Gaussianity, and circuit compilation strategies. (Talk based on https://arxiv.org/pdf/2409.17953 , https://arxiv.org/pdf/2402.18665)