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One-body entanglement as a quantum resource in fermionic systems
Quantum Physics · Submitted 10 Jan 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource.
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The abstract, sentence by sentence
We show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource. The associated theory has SDs and their convex hull as free states, and number conserving fermion linear optics operations (FLO), which include one-body unitary transformations and measurements of the occupancy of single-particle modes, as the basic free operations. We first provide a bipartitelike formulation of one-body entanglement, based on a Schmidt-like decomposition of a pure $N$-fermion state, from which the SPDM [together with the $(N-1)$-body density matrix] can be derived. It is then proved that under FLO operations, the initial and postmeasurement SPDMs always satisfy a majorization relation, which ensures that these operations cannot increase, on average, the one-body entanglement. It is finally shown that this resource is consistent with a model of fermionic quantum computation which requires correlations beyond antisymmetrization. More general free measurements and the relation with mode entanglement are also discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource. | contribution 0.80 | 0.91 | 0.84 | asserted 0.99 |
| s1 | The associated theory has SDs and their convex hull as free states, and number conserving fermion linear optics operations (FLO), which include one-body unitary transformations and measurements of the occupancy of single-particle modes, as the basic free operations. | method 0.48 | 0.52 | 0.09 | asserted 1.00 |
| s2 | We first provide a bipartitelike formulation of one-body entanglement, based on a Schmidt-like decomposition of a pure $N$-fermion state, from which the SPDM [together with the $(N-1)$-body density matrix] can be derived. | method 0.60 | 0.93 | 0.05 | asserted 1.00 |
| s3 | It is then proved that under FLO operations, the initial and postmeasurement SPDMs always satisfy a majorization relation, which ensures that these operations cannot increase, on average, the one-body entanglement. | result 0.98 | 0.90 | 0.19 | asserted 1.00 |
| s4 | It is finally shown that this resource is consistent with a model of fermionic quantum computation which requires correlations beyond antisymmetrization. | interpretation 0.59 | 0.89 | 0.27 | hedged possibility 0.59 |
| s5 | More general free measurements and the relation with mode entanglement are also discussed. | contribution 0.91 | 0.65 | 0.03 | unclear 0.65 |
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Original abstract
We show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource. The associated theory has SDs and their convex hull as free states, and number conserving fermion linear optics operations (FLO), which include one-body unitary transformations and measurements of the occupancy of single-particle modes, as the basic free operations. We first provide a bipartitelike formulation of one-body entanglement, based on a Schmidt-like decomposition of a pure $N$-fermion state, from which the SPDM [together with the $(N-1)$-body density matrix] can be derived. It is then proved that under FLO operations, the initial and postmeasurement SPDMs always satisfy a majorization relation, which ensures that these operations cannot increase, on average, the one-body entanglement. It is finally shown that this resource is consistent with a model of fermionic quantum computation which requires correlations beyond antisymmetrization. More general free measurements and the relation with mode entanglement are also discussed.
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How the literature uses it
3 arXiv papers cite this in 6 sentences
Papers citing it · 5 sentences without a confident label
Cites it as background 1 paper
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This definition underlies different approaches [ref] that use entanglement criteria and entanglement measures and apply them to entanglement manipulation [ref] and to several condensed matter systems [ref] .
Entanglement in indistinguishable particle systems · Entanglement-II · 0.80
What it cites
Cites as background 2 papers
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Several studies on the relation between these types of entanglement [ref] and on whether exchange correlations can be associated with entanglement [ref] have been recently made.
Entanglement between identical particles is a useful and consistent resource · Introduction · 0.96
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There is also a growing interest in quantum chemistry simulations based on optical lattices [ref] , which would benefit from a detailed characterization of fermionic correlations.
Quantum Simulation of 2D Quantum Chemistry in Optical Lattices · Introduction · 0.83
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