Correspondence between entangled states and entangled bases under local transformations
(2023) In Physical Review A 108(2).- Abstract
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... (More)
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.
(Less)
- author
- Pimpel, Florian ; Renner, Martin J. and Tavakoli, Armin LU
- organization
- publishing date
- 2023-08
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Physical Review A
- volume
- 108
- issue
- 2
- article number
- 022220
- publisher
- American Physical Society
- external identifiers
-
- scopus:85169294397
- ISSN
- 2469-9926
- DOI
- 10.1103/PhysRevA.108.022220
- language
- English
- LU publication?
- yes
- id
- 5562d30b-bce6-43a7-8e94-cae5616073ef
- date added to LUP
- 2023-12-19 16:22:44
- date last changed
- 2023-12-19 16:24:57
@article{5562d30b-bce6-43a7-8e94-cae5616073ef,
abstract = {{<p>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.</p>}},
author = {{Pimpel, Florian and Renner, Martin J. and Tavakoli, Armin}},
issn = {{2469-9926}},
language = {{eng}},
number = {{2}},
publisher = {{American Physical Society}},
series = {{Physical Review A}},
title = {{Correspondence between entangled states and entangled bases under local transformations}},
url = {{http://dx.doi.org/10.1103/PhysRevA.108.022220}},
doi = {{10.1103/PhysRevA.108.022220}},
volume = {{108}},
year = {{2023}},
}