Details
| Original language | English |
|---|---|
| Article number | 105301 |
| Number of pages | 34 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 57 |
| Issue number | 10 |
| Publication status | Published - 26 Feb 2024 |
Abstract
We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian associated with the representation and a left-invariant metric distance on the group. Our method works for any connected Lie group, and the metric is independent of the chosen representation. The approach also applies to projective representations and allows us to provide bounds on the energy-constrained diamond norm distance of any suitably continuous channel representation of the group.
Keywords
- energy constrained, error bounds, Lie groups, projective representation, unitary representations
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
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In: Journal of Physics A: Mathematical and Theoretical, Vol. 57, No. 10, 105301, 26.02.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Error bounds for Lie group representations in quantum mechanics
AU - van Luijk, Lauritz
AU - Galke, Niklas
AU - Hahn, Alexander
AU - Burgarth, Daniel
N1 - Funding Information: L v L acknowledges support by the Quantum Valley Lower Saxony. NG acknowledges financial support from the Spanish Agencia Estatal de Investigación, Project PID2019-107609GB-I00 and Spanish Plan de Recuperación, Transformación y Resiliencia financed by the European Union-NextGenerationEU. A H was supported by the Sydney Quantum Academy. D B acknowledges funding by the Australian Research Council (Project Numbers FT190100106, DP210101367, CE170100009).
PY - 2024/2/26
Y1 - 2024/2/26
N2 - We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian associated with the representation and a left-invariant metric distance on the group. Our method works for any connected Lie group, and the metric is independent of the chosen representation. The approach also applies to projective representations and allows us to provide bounds on the energy-constrained diamond norm distance of any suitably continuous channel representation of the group.
AB - We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian associated with the representation and a left-invariant metric distance on the group. Our method works for any connected Lie group, and the metric is independent of the chosen representation. The approach also applies to projective representations and allows us to provide bounds on the energy-constrained diamond norm distance of any suitably continuous channel representation of the group.
KW - energy constrained
KW - error bounds
KW - Lie groups
KW - projective representation
KW - unitary representations
UR - http://www.scopus.com/inward/record.url?scp=85187887866&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2211.08582
DO - 10.48550/arXiv.2211.08582
M3 - Article
AN - SCOPUS:85187887866
VL - 57
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 10
M1 - 105301
ER -