Alladi Ramakrishnan Hall

Some Problems in Quantum State Discrimination

Tanmay Singal

IMSc

I cover four problems in Quantum State Discrimination in this thesis. The first two are in
Local Distinguishability of Orthogonal Bipartite Quantum states and the remaining two in
Minimum Error Discrimination (MED) of linearly independent (LI) states. In the first
problem, I propose a framework for studying the one-way LOCC distinguishability of
pairwise orthogonal bipartite quantum states. I show how some significant known results
emerge out of this framework and add a few interesting results to the list. In the second
problem I develop a necessary condition for the local distinguishability of n maximally
entangled states in nxn systems; these conditions go beyond the known orthogonality
preserving conditions and are also shown to be sufficient for an important class of maximally
entangled states known as Generalized Bell states when n=4. In the problem of MED for LI
states, I first show how the structure of the problem for pure states can be used to arrive at the
solution, and later on I generalize the known structure to LI mixed states, for which this
structure can be similarly used to obtain the optimal POVM. The algorithms employed are as
efficient as standard semidefinite programming algorithms to solve the problem.