The power of noisy fermionic quantum computation

Melo, Fernando de; Ćwikliński, Piotr; Terhal, Barbara M.

doi:10.1088/1367-2630/15/1/013015

Cited by 33 publications

(84 citation statements)

References 34 publications

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“…Is there anything else? We will prove that for one mode, any channel satisfying (27) can be written as a dilatation composed with a completely positive channel, possibly composed with the transposition (29), see Fig. 2.…”

Section: Characterization Of Gaussian-to-gaussian Mapsmentioning

confidence: 97%

“…Another example of transformation not fulfilling the CP requirement (45) but respecting (27) is the (complete) transposition…”

Section: Characterization Of Gaussian-to-gaussian Mapsmentioning

confidence: 99%

“…For one mode, σ ≥ 0 satisfies σ ≥ ±i∆ iff det σ ≥ 1, and condition (27) can be rewritten as To prove (49) =⇒ (48) consider first the case det K = 0. Choosing σ such that…”

Section: One Modementioning

confidence: 99%

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Normal form decomposition for Gaussian-to-Gaussian superoperators

Palma

Mari

Giovannetti

et al. 2015

Journal of Mathematical Physics

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In this paper we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition.While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.1

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Section: Characterization Of Gaussian-to-gaussian Mapsmentioning

confidence: 97%

“…Another example of transformation not fulfilling the CP requirement (45) but respecting (27) is the (complete) transposition…”

Section: Characterization Of Gaussian-to-gaussian Mapsmentioning

confidence: 99%

See 1 more Smart Citation

Normal form decomposition for Gaussian-to-Gaussian superoperators

Palma

Mari

Giovannetti

et al. 2015

Journal of Mathematical Physics

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“…From the proof of Proposition 1 ( [12]) and the proof of Theorem 2 that we provide later, one can lower bound ǫ as a function of m. We can say that for any state ρ ∈ C 2m there exists ǫ ≥…”

Section: Set Upmentioning

confidence: 99%

“…Both criteria are based on the notion of 'extendibility' and approach the target set (convex-Gaussian or separable states) from the outside. The criterion in [12] is presented in the form of a sequence of solvable semi-definite programs. The authors in [14] presented another characterization of the set of convex-Gaussian states in a particular case when a state space is on 4 fermionic modes, i.e.…”

Section: Introductionmentioning

confidence: 99%

Complete criterion for convex-Gaussian-state detection

Vershynina

2014

Phys. Rev. A

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We present a new criterion that determines whether a fermionic state is a convex combination of pure Gaussian states. This criterion is complete and characterizes the set of convex-Gaussian states from the inside. If a state passes a program it is a convex-Gaussian state and any convex-Gaussian state can be approximated with arbitrary precision by states passing the criterion. The criterion is presented in the form of a sequence of solvable semidefinite programs. It is also complementary to the one developed by de Melo,Ćwikliński and Terhal, which aims at characterizing the set of convex-Gaussian states from the outside. Here we present an explicit proof that criterion by de Melo et al. is complete, by estimating a distance between an n-extendible state, a state that passes the criterion, to the set of convex-Gaussian states.

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A fermionic de Finetti theorem

Krumnow

Zimborás

Eisert

2017

Journal of Mathematical Physics

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Quantum versions of de Finetti's theorem are powerful tools, yielding conceptually important insights into the security of key distribution protocols or tomography schemes and allowing to bound the error made by mean-field approaches. Such theorems link the symmetry of a quantum state under the exchange of subsystems to negligible quantum correlations and are well understood and established in the context of distinguishable particles. In this work, we derive a de Finetti theorem for finite sized Majorana fermionic systems. It is shown, much reflecting the spirit of other quantum de Finetti theorems, that a state which is invariant under certain permutations of modes loses most of its anti-symmetric character and is locally well described by a mode separable state. We discuss the structure of the resulting mode separable states and establish in specific instances a quantitative link to the quality of Hartree-Fock approximation of quantum systems. We hint at a link to generalized Pauli principles for one-body reduced density operators. Finally, building upon the obtained de Finetti theorem, we generalize and extend the applicability of Hudson's fermionic central limit theorem.Comment: 15 pages, 1 figure, tiny change

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The power of noisy fermionic quantum computation

Cited by 33 publications

References 34 publications

Normal form decomposition for Gaussian-to-Gaussian superoperators

Normal form decomposition for Gaussian-to-Gaussian superoperators

Complete criterion for convex-Gaussian-state detection

A fermionic de Finetti theorem

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