Search for: All records

Modeling open quantum systems is a difficult task for many experiments. A standard method for modeling open system evolution uses an environment that is initially uncorrelated with the system in question, evolves the two unitarily, and then traces over the bath degrees of freedom to find an effective evolution of the system. This model can be insufficient for physical systems that have initial correlations. Specifically, there are evolutions ρS=trE(ρSE)→ρ′S=trE(UρSEU†) which cannot be modeled as ρS=trE(ρSE)→ρ′S=trE(UρS⊗ρEU†). An example of this is ρSE=|Φ+⟩⟨Φ+| and USE=CNOT with control on the environment. Unfortunately, there is no known method of modeling an open quantum system which is completely general. We first present some restrictions on the availability of completely positive (CP) maps via the standard prescription. We then discuss some implications a more general treatment would have for quantum control methods. In particular, we provide a theorem that restricts the reversibility of a map that is not completely positive (NCP). Let Φ be NCP and Φ~ be the corresponding CP map given by taking the absolute value of the coefficients in Φ. The theorem shows that the CP reversibility conditions for Φ~ do not provide reversibility conditions for Φ unless Φ is positive on the domain of the code space.