Tuesday, February 12, 2013
Institute for Quantum Information Seminar
Exponential decay of correlations implies area law
Fernando Brandao, ETH Zurich, Institute for Theoretical Physics
Quantum states of many particles are fundamental to our understanding of many-body physics. Yet they are extremely daunting objects, requiring in the worst case an exponential number of parameters in the number of subsystems to be even approximately described. How then can multi-particle states be useful for giving predictions to physical observables? The intuitive explanation is that physically relevant quantum states, defined as the ones appearing in nature, are usually much simpler than generic quantum states.
In this talk I will discuss a very recent theorem that gives further justification to this intuition.
The theorem states that exponential decay of correlations, a physically motivated restriction on the set of multi-particle quantum states, implies an area law for the entanglement entropy of systems defined on a line, and thus also an efficient classical description for such systems. The result can be seen as a rigorous justification to the intuition that states with exponential decay of correlations, usually associated with non-critical phases of matter, are simple to describe.
I will outline the main steps in the proof, that relies on several previous tools from quantum information theory and that can also be seen as providing a limitation to the phenomenon of data hiding in quantum states. Based on joint work with Michal Horodecki.