QUROPE Quantum Information Processing and Communication in Europe

Absolutely maximally entangled (AME) states are those multipartite quantum states that carry absolute maximum entanglement in all possible bipartitions. AME states are known to play a relevant role in multipartite teleportation, in quantum secret sharing, and they provide the basis novel tensor networks related to holography.

We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1/2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction 1/q, which are non-Abelian Fractional Quantum Hall states in 2D.

We provide a method for constructing finite temperature states of one-dimensional spin chains displaying quantum criticality. These models are constructed using correlators of products of quantum fields and have an analytical purification.

We propose 1D and 2D lattice wave functions constructed from the SU(n)1 Wess-Zumino-Witten (WZW) model and derive their parent Hamiltonians. When all spins in the lattice transform under SU(n) fundamental representations, we obtain a two-body Hamiltonian in 1D, including the SU(n) Haldane-Shastry model as a special case.

The Kalmeyer-Laughlin state, which is a lattice version of the bosonic Laughlin state at filling factor one half, has attracted much attention due to its topological and chiral spin liquid properties. Here we show that the Kalmeyer-Laughlin state on the torus can be expressed in terms of a correlator of conformal fields from the SU(2)1 Wess-Zumino-Witten model. This reveals an interesting underlying mathematical structure and provides a natural way to generalize the Kalmeyer-Laughlin state to arbitrary lattices on the torus.

We exploit a natural Projected Entangled-Pair State (PEPS) representation for the resonating AKLT-loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional (2D) lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power-law. On kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid.

We introduce a two-parameter family of strongly-correlated wave functions for bosons and fermions in lattices. One parameter, q, is connected to the filling fraction. The other one, eta, allows us to interpolate between the lattice limit (eta=1) and the continuum limit (eta-->0^+) of families of states appearing in the context of the fractional quantum Hall effect or the Calogero-Sutherland model. We give evidence that the main physical properties along the interpolation remain the same.

We propose to use a permutation symmetric sample of multi-level atoms to simulate the properties of topologically ordered states. The Rydberg blockade interaction is used to prepare states of the sample which are equivalent to resonating valence bond states, Laughlin states, and string-net condensates and to create and study the properties of their quasi-particle-like fundamental excitations.

Quantum mechanics offers new possibilities to process and transmit information. In recent years, algorithms and cryptographic protocols exploiting the superposition principle and the existence of entangled states have been designed. They should allow us to realize communication and computational tasks that outperform any classical strategy. Here we show that quantum mechanics also provides fresh perspectives in the field of random networks.