Eigenvalue distributions of reduced density matrices. (English) Zbl 1304.81051
In this work the authors provide a method based on symplectic geometry to answer the question: What is the probability distribution of the eigenvalues of the one-body reduced density matrices of a pure many-particle quantum state drawn at random from the unitarily invariant distribution? As explained in the text, the eigenvalue distributions that are computed are Duistermaat-Heckman measures, which are defined using the push-forward of the Liouville measure on a symplectic manifold along the moment map. In the second part of the work, the authors study the representation theory connected to the one-body quantum marginal problem, and ”the relevant multiplicities include the Kronecker coefficients, which play a major role in the representation theory of the unitary and symmetric groups”.
Reviewer: Carlos F. Lardizabal (Porto Alegre)
MSC:
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
| 81S10 | Geometry and quantization, symplectic methods |
| 81P16 | Quantum state spaces, operational and probabilistic concepts |
Keywords:
Density matrices; Quantum marginal problem; Weyl group; Weyl chamber; Duistermaat-Heckman measures; Kronecker coefficientsReferences:
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