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Density Matrix - Alternative to State Vector

 

 

As you know, in quantum mechanics we operate with state vectors. However, it is very convenient to use the alternative notation to solve some problems. This alternative representation is expressed by the density matrix.

A density matrix does not violate quantum postulates like state vectors and even postulates have equivalents just like state vectors.

It is represented by the density matrix or density operator rho (ρ).

The mathematical representation is as follows:,

Let's take the density matrix as an example:


As you can see, the density matrix is very practical and very easy to calculate. In particular, it is a pretty good alternative for computations in quantum mechanical systems that make up multiple qubits. You may have noticed another similarity right away. Yes, the trace of the density matrix is equal to 1. This means that we know that the state vector must be normalized. It means the same with the sum of all probabilities is equal to 1.


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