Density matrix

Matrix describing a quantum system in a pure or mixed state

In quantum mechanics, a density matrix is a matrix that describes an ensemble of physical systems as quantum states. It allows for the calculation of the probabilities of the outcomes of any measurements performed upon the systems of the ensemble using the Born rule. It is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed ensembles. Mixed ensembles arise in quantum mechanics in two different situations:when the preparation of the systems lead to numerous pure states in the ensemble, and thus one must deal with the statistics of possible preparations, and when one wants to describe a physical system that is entangled with another, without describing their combined state; this case is typical for a system interacting with some environment. In this case, the density matrix of an entangled system differs from that of an ensemble of pure states that, combined, would give the same statistical results upon measurement.

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