Density matrix in quantum computation and quantum statistical mechanics What is the difference between the density matrix for quantum statistical mechanics and density matrix for quantum information theory?
 A: Conceptually they are same. The only difference between them is the number of particles. In quantum information theory, we deal with single particles (Let's call this particle $m$). In this case, the density matrix ($\rho_m$) encodes probabilities, coherence, and decoherence for that single particle. Quantum statistical mechanics deals with many particles (lets say $N$ particles) so the density matrix ($\rho_t$) is taken to be average of the density matrices of each particle, $\rho_t = \frac{1}{N}\sum_{m=1}^N \rho_m$. However, they are same ($\rho_t = \rho_m$) if all the particles are identical, have same probabilities, coherence and we are only looking at the density matrix of the internal states of the particles. Importantly, you will get the same results if you isolate a particle and perform your measurement, and perform your measurement on all particles at once. 
Additionally, as quantum mechanics is probabilistic in nature, it becomes very difficult to distinguish the two cases mathematically and it makes sense to keep the same mathematical structure for both cases. Single isolated particle states can also be described by pure wavefunctions but in order to incorporate the randomness of decoherence, we need to use the density matrix which is statistical in its formulation.  
EDIT  -  The particles are assumed to be uncorrelated. The dimensionality of the density matrix for the ensemble of particles and for a single particle is same in my explanation. If you add entanglement then you need a density matrix for the whole system. This density matrix will have a dimension which is much higher than the individual particle density matrix.  
