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I am referring to the http://arxiv.org/abs/quant-ph/0609163" [Broken] discussed at length in other threads with a purely technical question to help me understand more of the paper.

On page 12, formula 26 defines the norm of a vector as

[tex]\langle\psi|\psi\rangle = \psi_1^*\psi_1 + \psi_2^*\psi_2 .[/tex]

My question is: isn't there a square root missing to get a norm. When I look up my lecture notes on functional analysis, a norm on a Hilbert space is defined by

[tex]||f|| = \sqrt{(f,f)}[/tex]

where [itex](\cdot,\cdot)[/itex] is the scalar product. If the above formula 26 would nevertheless be correct, I would end up with a scalar product with a square in, which is not linear and therefore not a scalar product.

What am I confusing here?

Thanks,

Harald.

On page 12, formula 26 defines the norm of a vector as

[tex]\langle\psi|\psi\rangle = \psi_1^*\psi_1 + \psi_2^*\psi_2 .[/tex]

My question is: isn't there a square root missing to get a norm. When I look up my lecture notes on functional analysis, a norm on a Hilbert space is defined by

[tex]||f|| = \sqrt{(f,f)}[/tex]

where [itex](\cdot,\cdot)[/itex] is the scalar product. If the above formula 26 would nevertheless be correct, I would end up with a scalar product with a square in, which is not linear and therefore not a scalar product.

What am I confusing here?

Thanks,

Harald.

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