Enhanced Purification Protocol for Entangled Two-Qubit Systems

Due to the unpredictable and delicate nature of quantum states, quantum systems need processes to remove error and purify corrupted quantum entangled bits. Purification protocols can reduce error and prevent corrupted states from multiplying in such systems.The primary errors come from corruption of the state whether through phase or bit flips. By accounting for the various types of errors, such as X (bit flips), Z (phase-flips), or Y (both) errors, different methods can be used to detect errors and increase the trustworthiness of a system.

By using a bit-flip check to find X and Y errors and a phase-flip check to detect Z and Y errors, we can ascertain if an error has presented itself in the entangled pair. I will show how by using these two methods in tandem, I create a purification protocol that can detect the majority of errors that result in the corruption of a system while minimizing the use of quantum resources.