Universality classes for purification in nonunitary quantum processes

Understand

We consider universal aspects of two problems: (i) the slow purification of a large number of qubits by repeated quantum measurements, and (ii) the singular value structure of a product ${m_t m_{t-1}\ldots m_1}$ of many large random matrices.

• Each kind of process is associated with the decay of natural measures of entropy as a function of time or of the number of matrices in the product.
• We argue that, for a broad class of models, each process is described by universal scaling forms for purification, and that (i) and (ii) represent distinct ``universality classes'' with distinct scaling functions.
• Using the replica trick, these universality classes correspond to one-dimensional effective statistical mechanics models for a gas of ``kinks'', representing domain walls between elements of the permutation group.