GERARDO ADESSO 'Accessible Quantification of Multiparticle Entanglement'

Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology, and life sciences. For arbitrary multiparticle systems, entanglement quantification typically involves nontrivial optimisation problems, and may require demanding tomographical techniques. Here we develop an experimentally feasible approach to the evaluation of geometric measures of multiparticle entanglement. Our approach provides analytical results for particular classes of mixed states of N qubits, and computable lower bounds to global, partial, or genuine multiparticle entanglement of any general state. For global and partial entanglement, useful bounds are obtained with minimum effort, requiring local measurements in just three settings for any N. For genuine entanglement, a number of measurements scaling linearly with N is required. We demonstrate the power of our approach to estimate and quantify different types of multiparticle entanglement in a variety of N-qubit states useful for quantum information processing and recently engineered in laboratories with quantum optics and trapped ion setups.


MIGUEL NAVASCUÉS 'The structure of Matrix Product States'

For the past twenty years, Matrix Product States (MPS) have been widely used in solid state physics to approximate the ground state of one-dimensional spin chains. In this Letter, exploiting an unnoticed connection with the theory of matrix algebras, we derive two structural properties of MPS, namely: a) there exist local operators which are invisible for all MPS of a given bond dimension; and b) there exist local operators which, when applied over any MPS of a given bond dimension, decouple the particles where they act from the spin chain while at the same time glue the two loose ends back again into a MPS. Exploiting property a), we show how to construct instances of local Hamiltonians for which standard MPS-based variational methods will return arbitrarily bad estimations of the ground state energy. Also building on a), we propose an exponentially more efficient implementation of the semidefinite programming hierarchies described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of finite-dimensional quantum correlations. Combining properties a) and b), we derive a family of local operators whose average values are non-negative for all MPS. We use this family to devise convex relaxations for linear optimization over MPS. Finally, we generalize some of our results to the ansatz of Projected Entangled Pairs States (PEPS).


Seminar, November 4, 2015, 15:00. Seminar Room

Hosted by Prof. Antonio Acín