Quantum state purification

In quantum information theory, quantum state purification refers to the process of representing a mixed state as a pure quantum state of higher-dimensional Hilbert space. The purification allows the original mixed state to be recovered by taking the partial trace over the additional degrees of freedom. The purification is not unique, the different purifications that can lead to the same mixed states are limited by the Schrödinger–HJW theorem.

Purification is used in algorithms such as entanglement distillation, magic state distillation and algorithmic cooling.