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Nonprojective Bell-state measurements

Wei, Amanda ; Cobucci, Gabriele LU orcid and Tavakoli, Armin LU (2024) In Physical Review A 110(4).
Abstract

The Bell-state measurement (BSM) is the projection of two qubits onto four orthogonal maximally entangled states. Here we first propose how to appropriately define more general BSMs, which have more than four possible outcomes, and then study whether they exist in quantum theory. We observe that nonprojective BSMs can be defined in a systematic way in terms of equiangular tight frames of maximally entangled states, i.e., a set of maximally entangled states, where every pair is equally, and in a sense maximally, distinguishable. We show that there exists a five-outcome BSM through an explicit construction and find that it admits a simple geometric representation. Then we prove that there exists no larger BSM on two qubits by showing that... (More)

The Bell-state measurement (BSM) is the projection of two qubits onto four orthogonal maximally entangled states. Here we first propose how to appropriately define more general BSMs, which have more than four possible outcomes, and then study whether they exist in quantum theory. We observe that nonprojective BSMs can be defined in a systematic way in terms of equiangular tight frames of maximally entangled states, i.e., a set of maximally entangled states, where every pair is equally, and in a sense maximally, distinguishable. We show that there exists a five-outcome BSM through an explicit construction and find that it admits a simple geometric representation. Then we prove that there exists no larger BSM on two qubits by showing that no six-outcome BSM is possible. We also determine the most distinguishable set of six equiangular maximally entangled states and show that it falls only somewhat short of forming a valid quantum measurement. Finally, we study the nonprojective BSM in the contexts of both local state discrimination and entanglement-assisted quantum communication. Our results put forward natural forms of nonprojective joint measurements and provide insight into the geometry of entangled quantum states.

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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review A
volume
110
issue
4
article number
042206
publisher
American Physical Society
external identifiers
  • scopus:85206326104
ISSN
2469-9926
DOI
10.1103/PhysRevA.110.042206
language
English
LU publication?
yes
id
0545bbc5-de3a-4093-a4a8-f4b5a19cfe79
date added to LUP
2024-12-11 10:43:29
date last changed
2025-04-04 14:30:19
@article{0545bbc5-de3a-4093-a4a8-f4b5a19cfe79,
  abstract     = {{<p>The Bell-state measurement (BSM) is the projection of two qubits onto four orthogonal maximally entangled states. Here we first propose how to appropriately define more general BSMs, which have more than four possible outcomes, and then study whether they exist in quantum theory. We observe that nonprojective BSMs can be defined in a systematic way in terms of equiangular tight frames of maximally entangled states, i.e., a set of maximally entangled states, where every pair is equally, and in a sense maximally, distinguishable. We show that there exists a five-outcome BSM through an explicit construction and find that it admits a simple geometric representation. Then we prove that there exists no larger BSM on two qubits by showing that no six-outcome BSM is possible. We also determine the most distinguishable set of six equiangular maximally entangled states and show that it falls only somewhat short of forming a valid quantum measurement. Finally, we study the nonprojective BSM in the contexts of both local state discrimination and entanglement-assisted quantum communication. Our results put forward natural forms of nonprojective joint measurements and provide insight into the geometry of entangled quantum states.</p>}},
  author       = {{Wei, Amanda and Cobucci, Gabriele and Tavakoli, Armin}},
  issn         = {{2469-9926}},
  language     = {{eng}},
  number       = {{4}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review A}},
  title        = {{Nonprojective Bell-state measurements}},
  url          = {{http://dx.doi.org/10.1103/PhysRevA.110.042206}},
  doi          = {{10.1103/PhysRevA.110.042206}},
  volume       = {{110}},
  year         = {{2024}},
}