Maximal lexicographic spectra and ranks for states with fixed uniform margins

2018/01/03 by Xin Li, Li, Xin
Mathematics · Physics and Astronomy · #FOS: Mathematics #Graph theory and applications #Mathematical functions and polynomials #Primary 20C30 #Quantum chaos and dynamical systems #Representation Theory (math.RT) #Secondary 15A18

paper · pdf · doi:10.48550/arxiv.1801.00986

openalex publication_date 2018/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We find the spectrum in maximal lexicographic order for quantum states ρ_AB\inH_A⊗ H_B with margins ρ_A=(1)/(n)I_n and ρ_B=(1)/(m)I_m and discuss the construction of ρ_AB. By nonzero rectangular Kronecker coefficients, we give counterexamples for Klyachko's conjecture which says that a quantum state with maximal lexicographical spectrum has minimal rank among all states with given margins. Moreover, we show that quantum states with the maximal lexicographical spectrum are extreme points.

Citations

• Quantum marginal problem and representations of the symmetric group
• Quantum state transformations and the Schubert calculus

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