Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 332, Issue 1, Pages 1-52Publisher
SPRINGER
DOI: 10.1007/s00220-014-2144-4
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Funding
- German Science Foundation [CH 843/2-1]
- Swiss National Science Foundation [PP00P2_128455, 20CH21_138799, 200021_138071]
- Swiss National Center of Competence in Research 'Quantum Science and Technology (QSIT)'
- Swiss State Secretariat for Education and Research supporting COST action [MP1006]
- European Research Council under the European Union [337603]
- Excellence Initiative of the German Federal Government through the Junior Research Group Program within the Institutional Strategy [ZUK 43]
- Excellence Initiative of the German State Government through the Junior Research Group Program within the Institutional Strategy [ZUK 43]
- Swiss National Science Foundation (SNF) [200021_138071, 20CH21_138799, PP00P2_128455] Funding Source: Swiss National Science Foundation (SNF)
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Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced density matrices. As a corollary, by taking the distribution's support, which is a convex moment polytope, we recover a complete solution to the one-body quantum marginal problem. We obtain the probability distribution by reducing to the corresponding distribution of diagonal entries (i.e., to the quantitative version of a classical marginal problem), which is then determined algorithmically. This reduction applies more generally to symplectic geometry, relating invariant measures for the coadjoint action of a compact Lie group to their projections onto a Cartan subalgebra, and can also be quantized to provide an efficient algorithm for computing bounded height Kronecker and plethysm coefficients.
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