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Qmechanic ♦
Qmechanic ♦
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How to prove that $\mathrm{tr}(\rho^2)=1$ if and only whenif the state is pure?

How can I prove that $\mathrm{tr}(\rho^2) $ = 1 if and only if the state is pure?

How can I prove that $\mathrm{tr}(\rho^2) $ = 1 if and only if the state is pure?

My idea: I know how to show that $\mathrm{tr}(\rho^2) \leq 1$ and from there I am trying to show by contradiction that $\mathrm{tr}(\rho^2) = 1$ can only but true for pure state, but I am kind of stuck.

I just need a hint on how to prove this.

How to prove that $\mathrm{tr}(\rho^2)=1$ only when the state is pure?

How can I prove that $\mathrm{tr}(\rho^2) $ = 1 if and only if the state is pure?

My idea: I know how to show that $\mathrm{tr}(\rho^2) \leq 1$ and from there I am trying to show by contradiction that $\mathrm{tr}(\rho^2) = 1$ can only but true for pure state, but I am kind of stuck.

I just need a hint on how to prove this.

How to prove that $\mathrm{tr}(\rho^2)=1$ if and only if the state is pure?

How can I prove that $\mathrm{tr}(\rho^2) $ = 1 if and only if the state is pure?

My idea: I know how to show that $\mathrm{tr}(\rho^2) \leq 1$ and from there I am trying to show by contradiction that $\mathrm{tr}(\rho^2) = 1$ can only but true for pure state, but I am kind of stuck.

I just need a hint on how to prove this.

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Emilio Pisanty
Emilio Pisanty
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How to proofprove that tr$\mathrm{tr}(p^2\rho^2)=1=1$ only when the state is pure?

How can I prove that tr($\rho^2) $$\mathrm{tr}(\rho^2) $ = 1 onlyif and only whenif the state is pure  ?

My idea: I know how to show that tr($\rho^2) \leq$ 1$\mathrm{tr}(\rho^2) \leq 1$ and from there I am trying to show by contradiction that tr($\rho^2) $ = 1$\mathrm{tr}(\rho^2) = 1$ can only but true for pure states butstate, but I am kind of stuck.

I just need a hint on how to prove this.

How to proof that tr(p^2)=1 only when the state is pure?

How can I prove that tr($\rho^2) $ = 1 only and only when the state is pure  ?

My idea: I know how to show that tr($\rho^2) \leq$ 1 and from there I am trying to show by contradiction that tr($\rho^2) $ = 1 can only but true for pure states but I am kind of stuck.

I just need a hint on how to prove this.

How to prove that $\mathrm{tr}(\rho^2)=1$ only when the state is pure?

How can I prove that $\mathrm{tr}(\rho^2) $ = 1 if and only if the state is pure?

My idea: I know how to show that $\mathrm{tr}(\rho^2) \leq 1$ and from there I am trying to show by contradiction that $\mathrm{tr}(\rho^2) = 1$ can only but true for pure state, but I am kind of stuck.

I just need a hint on how to prove this.

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George Farah
George Farah
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How to proof that tr(p^2)=1 only when the state is pure?

How can I prove that tr($\rho^2) $ = 1 only and only when the state is pure ?

My idea: I know how to show that tr($\rho^2) \leq$ 1 and from there I am trying to show by contradiction that tr($\rho^2) $ = 1 can only but true for pure states but I am kind of stuck.

I just need a hint on how to prove this.