Eigenvalue Distributions of Reduced Density Matrices

Matthias Christandl; Brent Doran; Stavros  Kousidis; Michael Walter

doi:10.1007/s00220-014-2144-4

Eigenvalue Distributions of Reduced Density Matrices

Matthias Christandl, Brent Doran, Stavros Kousidis, Michael Walter

Institut for Matematiske Fag

24 Citationer (Scopus)

Abstract

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.

Originalsprog	Engelsk
Tidsskrift	Communications in Mathematical Physics
Vol/bind	332
Sider (fra-til)	1-52
ISSN	0010-3616
DOI	https://doi.org/10.1007/s00220-014-2144-4
Status	Udgivet - nov. 2014

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10.1007/s00220-014-2144-4

Citationsformater

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title = "Eigenvalue Distributions of Reduced Density Matrices",

abstract = "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{\textquoteright}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.",

author = "Matthias Christandl and Brent Doran and Stavros Kousidis and Michael Walter",

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T1 - Eigenvalue Distributions of Reduced Density Matrices

AU - Christandl, Matthias

AU - Doran, Brent

AU - Kousidis, Stavros

AU - Walter, Michael

PY - 2014/11

Y1 - 2014/11

N2 - 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.

AB - 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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DO - 10.1007/s00220-014-2144-4

M3 - Journal article

SN - 0010-3616

VL - 332

SP - 1

EP - 52

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

ER -

Eigenvalue Distributions of Reduced Density Matrices

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