Supervisors: David Jennings and Terry Rudolph

Collaborators: Sania Jevtic and Matthew Pusey

Quantum steering ellipsoids

The Bloch sphere is invaluable as a tool for visualising a single qubit state, the most elementary system in quantum information theory. A two-qubit system is of fundamental importance for studying bipartite correlations, but the 15-dimensional state space has a great deal of structure and complexity. Quantum steering ellipsoids naturally extend the Bloch sphere picture to provide a visualisation of two-qubit systems. If Alice and Bob share a correlated state then a local measurement by Bob steers Alice’s qubit inside the Bloch sphere. Given all possible measurements by Bob, the set of states to which Alice can be steered form her steering ellipsoid. This forms the basis for an intuitive and faithful representation of two-qubit states.

steering ellipsoids

The geometric approach of steering ellipsoids offers many new perspectives. For example, a two-qubit state is seen to be separable if and only if its steering ellipsoid fits inside a tetrahedron inside the Bloch sphere. Remarkably, this can be used to provide novel derivations of purely geometric results such as Euler’s triangle inequality. Beyond two-qubit states, the formalism can describe a range of other scenarios, including monogamy of entanglement, higher dimensional quantum systems, and entanglement witnesses.