Quantum teleportation and quantum state discrimination

Quantum teleportation is a fundamental task in quantum information theory wherein two parties Alice and Bob use a shared entangled quantum state and classical communication to teleport an unknown quantum state. This task is mathematically equivalent to a certain quantum state discrimination problem, where the goal is to perform a measurement that optimally distinguishes among a given set of quantum states. This problem in turn has a useful description in terms of a class of optimization problems called semidefinite programs (SDP). These SDPs are a generalization of linear programs with a nice duality theory and efficient solvers available in programming environments such as python and MATLAB.

In this project we will study various quantum teleportation protocols using the SDP formulation of the corresponding state discrimination problem. In particular, we aim to determine how the quality of teleportation protocols is affected in the following scenarios:
* when Alice and Bob only have a noisy version of the shared entanglement at their disposal (noisy resources);
* when the measurement involved in the teleportation protocol is restricted due to physical limitations (locality constraints).

Both settings model realistic laboratory conditions that need to be taken into account when implementing quantum teleportation in an experiment, and hence it is an important goal to gain a better theoretical understanding of the resulting limitations.