| Correlations between different parts of a physical system are ubiquitous in nature. Their characterization is crucial for the study of complex systems, but also interesting from the viewpoint of quantum information theory. To quantify such correlations, measures based on the notion of exponential families have been studied [T. Kahle et al., Phys. Rev. E 79, 026201 (2009)]. The basic element of this approach is to use the distance of a probability distribution to the thermal states of k-particle Hamiltonians as a measure of the correlations in the distribution. For the case of classical probability distributions, we show that such measures are lacking some desirable properties of correlation measures. However, we propose a modified definition which can be used to overcome this problem [T. Galla et al., arXiv:1107.1180]. In the quantum case, the probability distribution is replaced by a density matrix, but still the same type of correlation measures can be defined. We present an algorithm to compute such measures efficiently for quantum states. We also demonstrate that this approach can be used to show that certain relevant quantum states (such as the cluster states) cannot be approximated by ground states of two-body Hamiltonians. |
|