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Hello.
I need some help to prove the first property of the density matrix for a pure state.
According to this property, the density matrix is definite positive (or semi-definite positive). I've been trying to prove it mathematically, but I can't.
I need to prove that |a|^2 x |c|^2 + |b|^2 x |d|^2 + ab*c*d + a*bcd* >= 0,
where a, b, c, and d are complex numbers, and * means the complex conjugate.
My Density Matrix M (2x2) has the following elements:
m11 = |a|^2, m12 = ab*, m21 = a*b, m22 = |b|^2
And (c; d) is just a ket in the C2 space.
I hope you can help me. Thanks you!
I need some help to prove the first property of the density matrix for a pure state.
According to this property, the density matrix is definite positive (or semi-definite positive). I've been trying to prove it mathematically, but I can't.
I need to prove that |a|^2 x |c|^2 + |b|^2 x |d|^2 + ab*c*d + a*bcd* >= 0,
where a, b, c, and d are complex numbers, and * means the complex conjugate.
My Density Matrix M (2x2) has the following elements:
m11 = |a|^2, m12 = ab*, m21 = a*b, m22 = |b|^2
And (c; d) is just a ket in the C2 space.
I hope you can help me. Thanks you!