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Landau and Streeter proved that a set of Kraus operators, Ai, is extremal if and only if the set

$\{A_{k}^{\dagger}A_{l}\}_{k,l \ldots N}$

are linearly independent. I have seen very convincing arguments both for and against. You can even see two PDFs of Mathematica notebooks "proving" both answers here: http://quantummoxie.wordpress.com/2010/01/28/a-quirky-mathematical-problem-in-need-of-explanation/

What is missing from these proofs?

Landau and Streater proved that a set of Kraus operators, Ai, is extremal if and only if the set

$\{A_{k}^{\dagger}A_{l}\}_{k,l \ldots N}$

are linearly independent. I have seen very convincing arguments both for and against. You can even see two PDFs of Mathematica notebooks "proving" both answers here: http://quantummoxie.wordpress.com/2010/01/28/a-quirky-mathematical-problem-in-need-of-explanation/

What is missing from these proofs?

Landau and Streeter proved that a set of Kraus operators, Ai, is extremal if and only if the set

{A_{k}^{\dag}A_{l}}_{k,l \ldots N} <- sorry the LaTeX here doesn't like this

are linearly independent. I have seen very convincing arguments both for and against. You can even see two PDFs of Mathematica notebooks "proving" both answers here: http://quantummoxie.wordpress.com/2010/01/28/a-quirky-mathematical-problem-in-need-of-explanation/

What is missing from these proofs?

Landau and Streeter proved that a set of Kraus operators, Ai, is extremal if and only if the set

$\{A_{k}^{\dagger}A_{l}\}_{k,l \ldots N}$

are linearly independent. I have seen very convincing arguments both for and against. You can even see two PDFs of Mathematica notebooks "proving" both answers here: http://quantummoxie.wordpress.com/2010/01/28/a-quirky-mathematical-problem-in-need-of-explanation/

What is missing from these proofs?