## Recent papers

#### Approximate Unitary *k*-Designs from Shallow, Low-Communication Circuits

**Nicholas LaRacuente and Felix Leditzky**

arXiv:2407.07876

In this paper we give constructions of approximate unitary designs from shallow, low-communication circuits. A *unitary k-design* is a set of unitaries that approximates the first k moments of the Haar measure, the unique left- and right-invariant measure on the unitary group that can be understood as a uniform distribution on unitaries. Our construction is recursive and uses overlapping Haar twirls on subsystems that are analyzed using von Neumann’s alternating projection method.

#### Multivariate Fidelities

**Theshani Nuradha, Hemant K. Mishra, Felix Leditzky and Mark M. Wilde**

arXiv:2404.16101

The bivariate fidelity between quantum states is an important measure of distance between quantum states that can be used to quantify how well a certain information-theoretic task approximates a target state. In this paper we focus on multivariate fidelities, that is, distance measures for a collection of quantum states. We give various multivariate generalizations of the classical and quantum bivariate fidelity and prove a range of useful properties like the data-processing inequality and symmetry under exchange of arguments, and inequalities relating the different multivariate fidelities to each other. For a particular example, the multivariate log-Euclidean fidelity, we also give an operational interpretation in the context of quantum hypothesis testing.

#### Operational Nonclassicality in Quantum Communication Networks

**Brian Doolittle, Felix Leditzky and Eric Chitambar**

arXiv:2403.02988

In a quantum communication network the senders (or nodes) can send each other quantum or classical information, assisted by shared entanglement, local processing and measurements. A crucial question is whether a communication network is genuinely quantum (or nonclassical), in the sense that its behavior could only be reproduced by a purely classical network if additional resources (such as extra classical communication) are available. In this paper we devise a framework based on linear constraints that characterizes classical communication networks with given constraints on the classical communication between nodes. Violating these classical constraints with quantum resources then certifies the nonclassicality of a given network, much like the violation of a Bell inequality in a bipartite scenario. We achieve these operational certifications of nonclassicality using variational quantum algorithms, which can be implemented on available quantum hardware. The code for this paper is available on GitHub.