Talks

Quantum systems bring unprecedented advantages to the realization of classical cryptographic tasks. A remarkable example is quantum key distribution, which allows two parties, Alice and Bob, to establish a secret key that can be used for unconditionally secure communication. Furthermore, the strong correlations exhibited by quantum systems can be explored to construct cryptographic protocols that are secure even when the parties are completely ignorant about the internal working of their devices. This is the device-independent paradigm. In this talk I will introduce the device-independent scenario and review recent results on device-independent quantum key distribution. Then I will move to the case of many parties and discuss extensions to multipartite cryptographic tasks. Finally, I will present new results where we introduce the paradigm of self-testing with dishonest parties and design a protocol for device-independent certification of the quantum state distributed in a network when some of the nodes may collude and act dishonestly. 

The notorious exponential complexity of quantum problems can be avoided for systems with limited correlations. For example, states of one-dimensional systems with bounded entanglement are approximable by matrix product states. We consider fermionic systems, where correlations can be defined as deviations from Gaussian states. Heuristically, one expects a link between compact non-Gaussian ansatzes and bounded fermionic correlations. This connection, however, has not been rigorously demonstrated. Our work resolves this conceptual gap.

We focus on pure states with a fixed number of fermions. Generalizing the so-called Plücker relations, we introduce k-particle correlation measures ω_k. The vanishing of ω_k at a constant k defines a class H_k of states with limited correlations. These sets H_k are nested, ranging from Gaussian for k=1 to the full n-fermion Hilbert space H for k=n+1. States in H_{k=O(1)} can be represented using a non-Gaussian ansatz of polynomial size. Classes H_k have physical meaning, containing all truncated perturbation series around Gaussian states. We also identify non-perturbative examples of states in H_{k=O(1)}, by a numerical study of excited states in the 1D Hubbard model. Finally, we discuss the information-theoretic implications of our results for the widely used coupled-cluster ansatz.

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