Completely positive maps for reduced states of indistinguishable particles

Souza, Leonardo da Silva; Debarba, Tiago; Ferreira, Diego L. B.; Iemini, Fernando; Vianna, Reinaldo O.

doi:10.1103/physreva.98.052135

Cited by 4 publications

(5 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 1. The measurement of the occupancy of a singleparticle state |ki = c † k |0i ∈ H, described by the operators (27), is a ONG operation.…”

Section: Fermion Linear Optics Operations As Ongmentioning

confidence: 99%

“…Different approaches have been considered, like mode entanglement [3][4][5], where subsystems correspond to a set of single-particle (SP) states in a given basis; extensions based on correlations between observables [6][7][8][9][10]; and entanglement beyond symmetrization [11][12][13][14][15][16][17][18][19][20][21], which is independent of the choice of SP basis. Several studies on the relation between these types of entanglement [5,16,20,[22][23][24][25][26][27][28] and on whether exchange correlations can be associated with entanglement [29][30][31][32][33] have been recently made. There is also a growing interest in quantum chemistry simulations based on optical lattices [34,35], which would benefit from a detailed characterization of fermionic correlations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

One-body entanglement as a quantum resource in fermionic systems

2020

View full text Add to dashboard Cite

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 Nfermion 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.

show abstract

“…Theorem 1. The measurement of the occupancy of a singleparticle state |ki = c † k |0i ∈ H, described by the operators (27), is a ONG operation.…”

Section: Fermion Linear Optics Operations As Ongmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

One-body entanglement as a quantum resource in fermionic systems

2020

View full text Add to dashboard Cite

show abstract

“…Such entanglement is of course independent of the choice of sp basis (it is not a modeentanglement) and in fact also of the choice of M-fermion creation operators, as long as they satisfy Eqs. ( 26) and (27).…”

Section: Discussionmentioning

confidence: 99%

“…Expressions similar or equivalent to (75) have been previously derived in Refs. [27,36,38], with [38] discussing its extension to states with no fixed fermion number. These results, together with Eqs.…”

Section: ααmentioning

confidence: 99%

“…Different approaches to this problem have been considered, like mode entanglement [3][4][5], extensions based on correlations between observables [6][7][8][9][10], and entanglement beyond symmetrization [11][12][13][14][15][16][17][18][19][20][21], which is independent of the choice of a single-particle (sp) basis. The relation between these forms of entanglement has been analyzed by different authors [2,5,16,20,[22][23][24][25][26][27][28][29], as well as the question regarding whether symmetrization correlations should be addressed as entanglement [30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Many-body entanglement in fermion systems

2021

View full text Add to dashboard Cite

We discuss a general bipartitelike representation and Schmidt decomposition of an arbitrary pure state of N indistinguishable fermions, based on states of M < N and (N-M ) fermions. It is directly connected with the reduced M-and (N-M )-body density matrices (DMs), which have the same spectrum in such states. The concept of M-body entanglement emerges naturally in this scenario, generalizing that of one-body entanglement. Rigorous majorization relations satisfied by the normalized M-body DM are then derived, which imply that the associated entropy will not increase, on average, under a class of operations which have these DMs as postmeasurement states. Moreover, such entropy is an upper bound to the bipartite entanglement entropy generated by a class of operations which map the original state to a bipartite state of M and N − M effectively distinguishable fermions. Analytic evaluation of the spectrum of M-body DMs in some strongly correlated fermionic states is also provided.

show abstract

Fermionic entanglement in the Lipkin model

et al. 2019

View full text Add to dashboard Cite

We examine the fermionic entanglement in the ground state of the fermionic Lipkin model and its relation with bipartite entanglement. It is first shown that the one-body entanglement entropy, which quantifies the minimum distance to a fermionic Gaussian state, behaves similarly to the mean-field order parameter and is essentially proportional to the total bipartite entanglement between the upper and lower modes, a quantity meaningful only in the fermionic realization of the model. We also analyze the entanglement of the reduced state of four single-particle modes (two up-down pairs), showing that its fermionic concurrence is strongly peaked at the phase transition and behaves differently from the corresponding up-down entanglement. We finally show that the first measures and the up-down reduced entanglement can be correctly described through a basic mean-field approach supplemented with symmetry restoration, whereas the concurrence requires at least the inclusion of RPA-type correlations for a proper prediction. Fermionic separability is also discussed.

show abstract

Completely positive maps for reduced states of indistinguishable particles

Cited by 4 publications

References 30 publications

One-body entanglement as a quantum resource in fermionic systems

One-body entanglement as a quantum resource in fermionic systems

Many-body entanglement in fermion systems

Fermionic entanglement in the Lipkin model

Contact Info

Product

Resources

About