Many of the advantages that the flourishing fields of quantum technologies and quantum information theory achieve over their classical counterparts rely on quantum correlations. Such correlations represent a valuable resource and their characterization and quantification is a key theoretical task.We study the quantum correlations for systems which are symmetric under the exchange of any two particles for two main reasons. Firstly, exchange symmetry constrains the set of possible states for the system and reduces the degrees of freedom required to describe them, simplifying the characterization of quantum correlations. Furthermore,systems that exhibit exchange symmetry have notable physical properties that make them well-suited for quantum information tasks and quantum simulation. In this thesis we investigate how exchange symmetry affects the mathematical description, as well as the physical realization and measurement, of quantum correlations. To begin with, we address the open problem of quantifying identical-particle entanglement. We introduce a novel entanglement measure accounting for the wavefunction (anti)symmetrization in the first quantised picture of systems of fermions and bosons. This measure, which may be evaluated by means of semidefinite programming, is sensitive to quantum correlations originating from interactions and other entanglement generating dynamical processes, rather than the kinematic effect of (anti)symmetrization. We apply our novel measure to estimate entanglement based on measurements of a system of two ultracold fermionic atoms in an optical trap. Exchange symmetry is not only a property of identical-particle states, but can pertain also to distinguishable subsystems. Based on the properties of subspaces of states which are symmetric or antisymmetric under particle exchange, we introduce a novel class of exchange-symmetric bound entangled states. We provide a simple parametrization that makes it possible to obtain states which are bound entangled in terms of a convex combination of well-studied exchange-symmetric states. Finally, we study the quantum correlations of a family of states with exchange symmetry in the multipartite device-independent scenario. We evaluate the noise robustness of the task of entanglement certification for varying numbers of uncharacterised measurement devices for the states of the family. The resulting structure enables us to establish a hierarchy of quantum correlations in the tripartite case.
|Date of Award||24 Sep 2019|
- University Of Strathclyde
|Sponsors||University of Strathclyde|
|Supervisor||Marco Piani (Supervisor) & Andrew Daley (Supervisor)|