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Maximally Nonprojective Measurements Are Not Always Symmetric Informationally Complete

Cobucci, Gabriele LU orcid ; Brinster, Raphael ; Khandelwal, Shishir LU ; Kampermann, Hermann ; Bruß, Dagmar ; Wyderka, Nikolai and Tavakoli, Armin LU (2026) In Physical Review Letters 136(6).
Abstract

Standard quantum measurements are projective. However, the full scope of quantum measurements is represented by positive operator-valued measures (POVMs) and many of these break the limitations of projective measurements as resources in quantum information. It is therefore natural to consider how accurately an experimenter with access only to projective measurements and classical processing can simulate POVMs. The most well-known class of nonprojective measurements is called symmetric informationally complete (SIC). Such measurements are both ubiquitous in the broader scope of quantum information theory and known to be the most strongly nonprojective measurements in qubit systems. Here, we show that beyond qubit systems, the SIC... (More)

Standard quantum measurements are projective. However, the full scope of quantum measurements is represented by positive operator-valued measures (POVMs) and many of these break the limitations of projective measurements as resources in quantum information. It is therefore natural to consider how accurately an experimenter with access only to projective measurements and classical processing can simulate POVMs. The most well-known class of nonprojective measurements is called symmetric informationally complete (SIC). Such measurements are both ubiquitous in the broader scope of quantum information theory and known to be the most strongly nonprojective measurements in qubit systems. Here, we show that beyond qubit systems, the SIC property is in general not associated with the most nonprojective measurement. For this, we put forward a semidefinite programming criterion for detecting genuinely nonprojective measurements. This method allows us to determine quantitative simulability thresholds for generic POVMs and to put forward a conjecture on which qutrit and ququart measurements are most strongly nonprojective.

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author
; ; ; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review Letters
volume
136
issue
6
article number
060201
publisher
American Physical Society
external identifiers
  • scopus:105029984875
  • pmid:41765825
ISSN
0031-9007
DOI
10.1103/slt1-gfv6
language
English
LU publication?
yes
id
1d75170a-1185-4907-af05-cf2f4c21c39e
date added to LUP
2026-04-17 12:11:57
date last changed
2026-09-06 16:59:26
@article{1d75170a-1185-4907-af05-cf2f4c21c39e,
  abstract     = {{<p>Standard quantum measurements are projective. However, the full scope of quantum measurements is represented by positive operator-valued measures (POVMs) and many of these break the limitations of projective measurements as resources in quantum information. It is therefore natural to consider how accurately an experimenter with access only to projective measurements and classical processing can simulate POVMs. The most well-known class of nonprojective measurements is called symmetric informationally complete (SIC). Such measurements are both ubiquitous in the broader scope of quantum information theory and known to be the most strongly nonprojective measurements in qubit systems. Here, we show that beyond qubit systems, the SIC property is in general not associated with the most nonprojective measurement. For this, we put forward a semidefinite programming criterion for detecting genuinely nonprojective measurements. This method allows us to determine quantitative simulability thresholds for generic POVMs and to put forward a conjecture on which qutrit and ququart measurements are most strongly nonprojective.</p>}},
  author       = {{Cobucci, Gabriele and Brinster, Raphael and Khandelwal, Shishir and Kampermann, Hermann and Bruß, Dagmar and Wyderka, Nikolai and Tavakoli, Armin}},
  issn         = {{0031-9007}},
  language     = {{eng}},
  number       = {{6}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review Letters}},
  title        = {{Maximally Nonprojective Measurements Are Not Always Symmetric Informationally Complete}},
  url          = {{http://dx.doi.org/10.1103/slt1-gfv6}},
  doi          = {{10.1103/slt1-gfv6}},
  volume       = {{136}},
  year         = {{2026}},
}