However, it still is possible to associate a density matrix.

In general, a quantum state is described by a density matrix.

This means that is essentially the density matrix put into normal order.

The density matrix operator may also be realized in phase space.

However, usually one casts these equations into a density matrix form.

It is possible to carry out the fitting of a physical density matrix on the measured data even for large systems.

Next, the density matrix approach is presented for perspective.

So is formed by the most significant eigenstates of the reduce density matrix.

The role which was originally reserved for the quantities is thus taken over by the density matrix of the system S.

It has been shown that the density matrix for any state of light can be written as:

The density matrix can be shown to transform to the interaction picture in the same way as any other operator.

Assume the system is prepared in the state described by the density matrix ρ.

Quantum logic also provides a satisfactory understanding of density matrices.

One of these is the use of the density matrix, and its associated master equation.

In this case the full density matrix is factorable for all times as .

Now suppose is the density matrix for a tripartite system .

Let be the set of density matrices defined previously for Eq.

Mathematically, a density matrix has to satisfy the following conditions:

The density matrix is also a crucial tool in quantum decoherence theory.

In quantum mechanics, a pure density matrix is one of the form .

This can be seen by examining the density matrix averaged over all values of :

Physically, the density matrix is a way to represent pure states and mixed states.

This uses the Schrödinger picture, where evolution of the state (represented by its density matrix) is considered.

A mixed state of the composite system is described by a density matrix acting on .

Thus the density matrix describing ρ is diagonal in the energy representation.