Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 040203 |
| Fachzeitschrift | Physical review letters |
| Jahrgang | 136 |
| Ausgabenummer | 4 |
| Publikationsstatus | Veröffentlicht - 30 Jan. 2026 |
Abstract
The uniqueness of purifications of quantum states on a system A up to local unitary transformations on a purifying system B is central to quantum information theory. We show that, if the two systems are modeled by commuting von Neumann algebras MA and MB on a Hilbert space H, then uniqueness of purifications is equivalent to Haag duality MA=MB′. In particular, the uniqueness of purifications can fail in systems with infinitely many degrees of freedom—even when MA and MB are commuting factors that jointly generate B(H) and hence allow for local tomography of all density matrices on H. We present a simple argument showing that the uniqueness of purifications, and, hence, Haag duality, fail in ground state sectors of topologically ordered models at renormalization group fixed points on infinite two-dimensional lattices, partitioned into the union of two spatially separated cones and its complement.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
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in: Physical review letters, Jahrgang 136, Nr. 4, 040203, 30.01.2026.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Uniqueness of Purifications Is Equivalent to Haag Duality
AU - Van Luijk, Lauritz
AU - Stottmeister, Alexander
AU - Wilming, Henrik
N1 - Publisher Copyright: © 2026 authors. Published by the American Physical Society.
PY - 2026/1/30
Y1 - 2026/1/30
N2 - The uniqueness of purifications of quantum states on a system A up to local unitary transformations on a purifying system B is central to quantum information theory. We show that, if the two systems are modeled by commuting von Neumann algebras MA and MB on a Hilbert space H, then uniqueness of purifications is equivalent to Haag duality MA=MB′. In particular, the uniqueness of purifications can fail in systems with infinitely many degrees of freedom—even when MA and MB are commuting factors that jointly generate B(H) and hence allow for local tomography of all density matrices on H. We present a simple argument showing that the uniqueness of purifications, and, hence, Haag duality, fail in ground state sectors of topologically ordered models at renormalization group fixed points on infinite two-dimensional lattices, partitioned into the union of two spatially separated cones and its complement.
AB - The uniqueness of purifications of quantum states on a system A up to local unitary transformations on a purifying system B is central to quantum information theory. We show that, if the two systems are modeled by commuting von Neumann algebras MA and MB on a Hilbert space H, then uniqueness of purifications is equivalent to Haag duality MA=MB′. In particular, the uniqueness of purifications can fail in systems with infinitely many degrees of freedom—even when MA and MB are commuting factors that jointly generate B(H) and hence allow for local tomography of all density matrices on H. We present a simple argument showing that the uniqueness of purifications, and, hence, Haag duality, fail in ground state sectors of topologically ordered models at renormalization group fixed points on infinite two-dimensional lattices, partitioned into the union of two spatially separated cones and its complement.
UR - http://www.scopus.com/inward/record.url?scp=105029373044&partnerID=8YFLogxK
U2 - 10.1103/d7nm-gx37
DO - 10.1103/d7nm-gx37
M3 - Article
C2 - 41698079
AN - SCOPUS:105029373044
VL - 136
JO - Physical review letters
JF - Physical review letters
SN - 0031-9007
IS - 4
M1 - 040203
ER -