Correspondence between entangled states and entangled bases under local transformations

Autor(en)

Florian Pimpel, Martin J. Renner, Armin Tavakoli

Abstrakt

We investigate whether pure entangled states can be associated to a measurement basis in which all vectors are local unitary transformations of the original state. We prove that for bipartite states with a local dimension that is either 2, 4, or 8, every state corresponds to a basis. Via numerics, we strongly evidence the same conclusion for two qutrits and three qubits also. However, for some states of four qubits, we are unable to find a basis, leading us to conjecture that not all quantum states admit a corresponding measurement. Furthermore, we investigate whether there can exist a set of local unitaries that transform any state into a basis. While we show that such a state-independent construction cannot exist for general quantum states, we prove that it does exist for real-valued n-qubit states if and only if n=2,3, and that such constructions are impossible for any multipartite system of an odd local dimension. Our results suggest a rich relationship between entangled states and iso-entangled measurements with a strong dependence on both particle numbers and dimension.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Technische Universität Wien, Österreichische Akademie der Wissenschaften (ÖAW), Lund University

Journal

Physical Review A

Band

108

Anzahl der Seiten

9

ISSN

2469-9926

DOI

https://doi.org/10.48550/arXiv.2301.13285

Publikationsdatum

08-2023

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik, 103026 Quantenoptik

ASJC Scopus Sachgebiete

Atomic and Molecular Physics, and Optics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/ed7ab723-e558-4514-bf68-5630fc1c2b08