Quantum state purification

Abstract

Quantum state purification is a process in which decoherence is partially reversed by using multiple copies of the input states that have been subject to the same decoherence effect. This thesis focuses on purifying the decoherence caused by the depolarizing channel. In the first half of the thesis, the purification problem is formally introduced and one efficient purification procedure featuring the swap-test is presented and analyzed. The rest of the thesis formulates the optimal purification problem as an optimization problem and applies it to qubit and qutrit purification.