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The diagonal components of a density matrix represent the probability to find a particle in the corresponding state of the matrix; so in a spin +/- 1/2 (+ for up, - for down) system it's the probability to find a particle in either spin +1/2 or spin -1/2 state.

If the state of the system is pure up, then the density matrix is (1,0;0;0). If the state of the system is pure down then the density matrix is (0,0;0,1).

What do the non-diagonal components represent? can you please explain with examples of states in a system, and how the non diagonal components would change with different system situations? I heard it has something to do with correlation. But I can't get the idea.

Thank you for any efforts :)

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# Density matrix's non-diagonal components

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