On Multipartite Entanglement and its Use

Entanglement is a unique feature of quantum mechanics. Over the years, we have understood bipartite entanglement a lot more, while our understanding of multipartite entanglement has lagged. In this work, we aim to fill some gaps in this knowledge. Firstly, we provide a quantum algorithm to test whether a given multipartite state is multipartite entangled or multipartite separable. To develop this separability test, we start with a separability test for the bipartite scenario using the quantum steering effect. Our separability test consists of a distributed quantum computation involving two parties: a computationally limited verifier, who prepares a purification of the state of interest, and a computationally unbounded prover. We then modified the separability test to get a variational quantum steering algorithm (VQSA), implementable on quantum computers that are available today. We then simulate our VQSA on noisy quantum simulators and find favorable convergence properties on the examples tested. We extend our separability test to the multipartite scenario by using the appropriate definitions.

We expect that multipartite entanglement will find use in quantum network scenarios. Quantum networks consist of various quantum technologies, spread across vast distances, and involve various users at the same time. Certifying the functioning and efficiency of the individual components is a task that is well studied and widely used. However, the power of quantum networks can only be realized by integrating all the required quantum technologies and platforms across numerous users. In this work, we demonstrate how to certify the distillable entanglement available in multipartite states produced by quantum networks, without relying on the physical realization of its constituent components. We do so by using the paradigm of device independence.

Finally, we introduce multipartite intrinsic non-locality as a method for quantifying resources in the multipartite scenario of device-independent (DI) conference key agreement. We prove that multipartite intrinsic non-locality is additive, convex, and monotone under a class of free operations called local operations and common randomness. As one of our technical contributions, we establish a chain rule for two variants of multipartite mutual information, which we then use to prove that multipartite intrinsic non-locality is additive. This chain rule may be of independent interest in other contexts. All of these properties of multipartite intrinsic non-locality are helpful in establishing that: multipartite intrinsic non-locality is an upper bound on secret key rate in the general multipartite scenario of DI conference key agreement.