Monogamy of entanglement, no-cloning, and dissipative quantum state preparation
Monogamy of entanglement limits the distribution of quantum correlations in a many-body system. The no-cloning theorem states that quantum information cannot be copied. From quantum cryptography to quantum chemistry simulations, these principles govern our approach to quantum information processing and distinguish it from classical information processing. For the most part, mathematical investigations of the monogamy of entanglement and "no-cloning" have been independent. We make an in-depth comparison of these two principles, demonstrating their common origin and gaining insight from simple examples. Through this pursuit, we come upon an intriguing "parity difference" between causal and acausal quantum correlations (i.e. between quantum channels and states), which is not present in classical statistical mechanics. We then connect this investigation of quantum part-whole relationships to the task of dissipatively preparing a many-body entangled state using (quasi-)local resources. We determine conditions under which a target state is able to be the unique steady state of frustration-free quasi-local Liouvillian dynamics and discuss some illuminating examples.
References: JPA 48, 035307 (2015) and QIC 16, 0657 (2016)