Sat, 2014-03-22 16:48 - admin

F. G.S.L. Brandao and M. Horodecki

Nature Physics 9, 721-726 (2013)

Many-particle quantum systems in principle need an exponential number of parameters (relative to the

number of particles) to describe. Intuitively, one expects that physically relevant systems, such as those

appearing in nature, need far fewer parameters to be described, and are thus far simpler than the generic case.

However, given a system at low temperature, one would like to know if it is indeed possible to find such a

simple description of the state. One property that many physical systems have is a so called 'exponential

decay of correlations' - correlations between observables on distant parts of the system should decay

exponentially fast in the distance.

In their work, Brandao and Horodecki show that 1D systems that display an exponential decay of

correlations, also show an 'area law' for entanglement, meaning that the entanglement of the system is

proportional to the size of its boundary, as opposed to its size (i.e. volume), as is the case for generic

quantum systems. They then show that this further implies the existence of an efficient classical description

of such states, in terms of so called 'matrix product states', used extensively in numerical simulations of

quantum systems. In total this thus finally provides a rigorous justification of the physical intuition that many

physical systems are simple to describe.