QuantAlpsAn ecosystem for quantum science & technologies :
From the philosopher to the industrial

Nathan Claudet (Inria Mocqua and Université de Lorraine, CNRS, LORIA)
2 PM
Title: Recognizing graph states with the same entanglement by looking at the underlying graphs
Abstract: Graph states form a ubiquitous family of quantum states that are in one-to-one correspondence with mathematical graphs. Graph states are used in many applications, such as measurement-based quantum computation, as multipartite entangled resources. It is thus crucial to understand when two such states have the same entanglement, i.e. when they can be transformed into each other using only local operations. In this case, we say that the graph states are LU-equivalent (local unitary). If the local operations are restricted to the Clifford group, we say that the graph states are LC-equivalent (local Clifford). Interestingly, a simple graph rule called local complementation fully captures LC-equivalence, in the sense that two graph states are LC-equivalent if and only if the underlying graphs are related by a sequence of local complementations. While it was once conjectured that two LU-equivalent graph states are always LC-equivalent, counterexamples do exist and local complementation fails to fully capture the entanglement of graph states. We introduce a generalization of local complementation that does fully capture LU-equivalence. Using this characterization, we prove the existence of an infinite strict hierarchy of local equivalences between LC- and LU-equivalence. This also leads to the design of a quasi-polynomial algorithm for deciding whether two graph states are LU-equivalent, and to a proof that two LU-equivalent graph states are LC-equivalent if they are defined on at most 19 qubits.

Philip Verduyn Lunel (Sorbonne Université - LIP6)
3 PM
Title: Quantum Position Verification and Orthogonality Broadcasting
Abstract: The no-cloning theorem leads to information-theoretic security in various quantum cryptographic protocols. However, this security typically derives from a possibly weaker property that classical information encoded in certain quantum states cannot be broadcast. Inspired by the analysis of the security of QPV protocols, in this talk, we introduce the study of "orthogonality broadcasting." When attempting to broadcast the orthogonality of two different qubit bases, we establish that the power of classical and quantum communication is equivalent. However, quantum communication is shown to be strictly more powerful for broadcasting orthogonality in higher dimensions. We then relate orthogonality broadcasting to quantum position verification (QPV) and provide a new method for establishing error bounds in the no pre-shared entanglement model that can address protocols previous methods could not. Our key technical contribution is an uncertainty relation that uses the geometric relation of the states that undergo broadcasting rather than the non-commutative aspect of the final measurements.
This talk is based on joint work with Ian George, Rene Allerstorfer, and Eric Chitambar