Solves quantum purity amplification for arbitrary n, m, eigenstates, and dimension d, with asymptotic input scaling O(m/(ε D_min²)) independent of d and non-asymptotic bounds from generalized Young diagrams.
Schur positivity and Schur log-concavity
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abstract
We prove Okounkov's conjecture, a conjecture of Fomin-Fulton-Li-Poon, and a special case of Lascoux-Leclerc-Thibon's conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. An alternative proof of this result is provided. We also give an intriguing log-concavity property of Schur functions.
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quant-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs
Solves quantum purity amplification for arbitrary n, m, eigenstates, and dimension d, with asymptotic input scaling O(m/(ε D_min²)) independent of d and non-asymptotic bounds from generalized Young diagrams.