RT Journal Article
T1 Purifications of multipartite states: limitations and constructive methods
A1 Cuevas, Gemma de las
A1 Schuch, Norbert
A1 Pérez García, David
A1 Cirac, J.I.
AB We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two such descriptions: (i) as a matrix product density operator of bond dimension D; and (ii) as a purification that is written as a matrix product state of bond dimension D'. We show that these descriptions are inequivalent in the sense that D' cannot be upper bounded by D only. Then we provide two constructive methods to obtain (ii) out of (i). The sum of squares (sos) polynomial method scales exponentially in the number of different eigenvalues, and its approximate version is formulated as a semidefinite program, which gives efficient approximate purifications whose D' only depends on D. The eigenbasis method scales quadratically in the number of eigenvalues, and its approximate version is very efficient for rapidly decaying distributions of eigenvalues. Our results imply that a description of mixed states which is both efficient and locally positive semidefinite does not exist, but that good approximations do.
PB IOP Publishing
SN 1367-2630
YR 2013
FD 2013-12-10
LK https://hdl.handle.net/20.500.14352/33484
UL https://hdl.handle.net/20.500.14352/33484
LA eng
NO Comunidad de Madrid
NO European CHIST-ERA
NO Alexander von Humboldt foundation
DS Docta Complutense
RD 19 abr 2025