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What is density matrix notation?

We will now formally introduce the density matrix notation by looking at the how it is used to represent both pure and mixed states. 1. Pure States Pure states are those for which we can precisely define their quantum state at every point in time.

What is the state purity of a density matrix?

State Purity A very useful property of the density matrix is that when taking the trace Tr of its square ρ2, we obtain a scalar value γ that is good measure of the purity of the state the matrix represents. For normalized states, this value is always less than or equal to 1, with the equality occurring for the case of a pure state:

What is the density matrix of a quantum state?

Density matrix. Describing a quantum state by its density matrix is a fully general alternative formalism to describing a quantum state by its ket (state vector) or by its statistical ensemble of kets. However, in practice, it is often most convenient to use density matrices for calculations involving mixed states,...

Why do we need density matrix for mixed states?

Since a mixed state can consist of a myriad of pure states, it can be difficult to track how the whole ensemble evolves when, for example, gates are applied to it. It is here that we turn to the density matrix representation.

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