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Absolute Dimensionality of Quantum Ensembles

Bernal, Alexander ; Cobucci, Gabriele LU orcid ; Renner, Martin J. LU and Tavakoli, Armin LU (2024) In Physical Review Letters 133(24).
Abstract

The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis. We propose an absolute, i.e., basis-independent, notion of dimensionality for ensembles of quantum states. It is based on whether a quantum ensemble can be simulated with states confined to arbitrary lower-dimensional subspaces and classical postprocessing. In order to determine the absolute dimension of quantum ensembles, we develop both analytical witness criteria and a semidefinite programming criterion based on the ensemble's information capacity. Furthermore, we construct explicit simulation models for arbitrary ensembles of pure quantum states subject to white noise, and in natural cases we prove their... (More)

The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis. We propose an absolute, i.e., basis-independent, notion of dimensionality for ensembles of quantum states. It is based on whether a quantum ensemble can be simulated with states confined to arbitrary lower-dimensional subspaces and classical postprocessing. In order to determine the absolute dimension of quantum ensembles, we develop both analytical witness criteria and a semidefinite programming criterion based on the ensemble's information capacity. Furthermore, we construct explicit simulation models for arbitrary ensembles of pure quantum states subject to white noise, and in natural cases we prove their optimality. Also, efficient numerical methods are provided for simulating generic ensembles. Finally, we discuss the role of absolute dimensionality in high-dimensional quantum information processing.

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Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review Letters
volume
133
issue
24
article number
240203
publisher
American Physical Society
external identifiers
  • scopus:85212439246
  • pmid:39750369
ISSN
0031-9007
DOI
10.1103/PhysRevLett.133.240203
language
English
LU publication?
yes
id
ac1f6f86-5f5b-4f7a-96d8-d902c6758f32
date added to LUP
2025-01-17 12:09:25
date last changed
2025-07-05 02:26:26
@article{ac1f6f86-5f5b-4f7a-96d8-d902c6758f32,
  abstract     = {{<p>The dimension of a quantum state is traditionally seen as the number of superposed distinguishable states in a given basis. We propose an absolute, i.e., basis-independent, notion of dimensionality for ensembles of quantum states. It is based on whether a quantum ensemble can be simulated with states confined to arbitrary lower-dimensional subspaces and classical postprocessing. In order to determine the absolute dimension of quantum ensembles, we develop both analytical witness criteria and a semidefinite programming criterion based on the ensemble's information capacity. Furthermore, we construct explicit simulation models for arbitrary ensembles of pure quantum states subject to white noise, and in natural cases we prove their optimality. Also, efficient numerical methods are provided for simulating generic ensembles. Finally, we discuss the role of absolute dimensionality in high-dimensional quantum information processing.</p>}},
  author       = {{Bernal, Alexander and Cobucci, Gabriele and Renner, Martin J. and Tavakoli, Armin}},
  issn         = {{0031-9007}},
  language     = {{eng}},
  number       = {{24}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review Letters}},
  title        = {{Absolute Dimensionality of Quantum Ensembles}},
  url          = {{http://dx.doi.org/10.1103/PhysRevLett.133.240203}},
  doi          = {{10.1103/PhysRevLett.133.240203}},
  volume       = {{133}},
  year         = {{2024}},
}