Decoherence and the Classes of Maximally Entangled States

Self-interactions and interaction with the environment inevitably push quantum systems towards highly mixed states, which is the definition of decoherence. However, if decoherence is completely suppressed, then any quantum system evolves unitarily through pure states towards maximally entangled configurations. We argue that these maximally entangled states of the systems fall into the well-defined classes that can be uniquely described by the values of certain entanglement invariants. After discussing these ideas, we present examples of maximally entangled states for a number of generic systems, construct compact states in the most entangled classes for tripartite systems, and suggest how they may be constructed for other Formula: see text-partite systems. We study random walks through the space of entanglement classes to see how unitary evolution along paths to the maximally entangled states, i.e. entanglement growth, works in practice.