Local symmetry properties of pure 3-qubit states

A Sudbery; H A Carteret

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Local symmetry properties of pure 3-qubit states

H A Carteret, A Sudbery

Quantum Physics · Submitted 25 Jan 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations.

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arXiv listing abstract v5. Results and the main claim are underlined; show every role.

Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilisers.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations.	contribution 0.51	0.69	0.18	asserted 1.00
s1	It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a stationary value for some local invariant.	result 0.98	0.91	0.38	asserted 0.98
s2	We describe all the exceptional states with enlarged stabilisers.	contribution 0.87	0.93	0.22	asserted 0.97

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The paper

Original abstract

Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilisers.

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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Three qubits can be entangled in two inequivalent ways
quant-ph 2000-05 accept novelty 8.0 of 10

Pure three-qubit states fall into exactly six stochastic-LOCC classes, of which only two (GHZ and W) carry genuine tripartite entanglement and are mutually inaccessible.
Entanglement groups for mixed states
quant-ph 2025-07 conditional novelty 7.0 of 10

For mixed quantum states, entanglement can be characterized by a quotient group of local unitary stabilizers of the density matrix, and any nontriviality for separable states must come from multipartite entanglement w...

How the literature uses it

9 arXiv papers cite this in 17 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 8 sentences without a confident label

Builds on it 1 paper

Inspired by ideas originally laid out for 3-qubit systems [ref] , the authors of the present paper have achieved a number of results for systems of arbitrary numbers of qubits on the structure of stabilizer Lie subalgebras and in particular, those stabilizers that have maximum possible dimension.

Classification of nonproduct states with maximum stabilizer dimension · Introduction · 0.81

Uses its method or tool 1 paper

The results presented in this article arise from the following framework, utilized in [ref] for 3-qubit systems and developed further by the authors in [ref] for $n$ qubits, for approaching local unitary equivalence classification.

Multiparty quantum states stabilized by the diagonal subgroup of the local unitary group · Introduction · 0.82

Compares with it 1 paper

However the definition of entanglement in terms of entanglement groups leads to a characterization of two-party and three-party entanglement for these states which is very different from [ref] .

Entanglement groups · Examples · 0.99

Cites it as background 4 papers

Progress has been made, however, in understanding aspects of the local unitary orbits and their dimensions [ref] .

Maximum stabilizer dimension for nonproduct states · Introduction · 0.94
A seemingly different approach to classifying states according to entanglement was initiated in [ref] .

Entanglement groups · Strata · 0.92
A discussion of more conventional entanglement measures may be found in [ref] .

Black Holes, Qubits and Octonions · U-duality · 0.98

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