Quantum channel-estimation with particle loss: GHZ versus W states

Fraïsse, Julien Mathieu Elias; Braun, Daniel

doi:10.1515/qmetro-2016-0009

Cited by 6 publications

(5 citation statements)

References 15 publications

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“…Expression (92) generalizes well-known variance-based formulas [24]. At t = 0, state |ϕ ω 〉 coincides with ψ ω 0 and thus we recover the QFI for a single unitary, Eq.…”

Section: Qfi For a Bogoliubov Transformation Followed By A Hamiltonia...supporting

confidence: 52%

Quantum parameter estimation with many-body fermionic systems and application to the Hall effect

Giraud,

Goerbig,

Braun

2024

SciPost Phys.

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We calculate the quantum Fisher information for a generic many-body fermionic system in a pure state depending on a parameter. We discuss the situations where the parameter is imprinted in the basis states, in the state coefficients, or both. In the case where the parameter dependence of coefficients results from a Hamiltonian evolution, we derive a particularly simple expression for the quantum Fisher information. We apply our findings to the quantum Hall effect, and evaluate the quantum Fisher information associated with the optimal measurement of the magnetic field for a system in the ground state of the effective Hamiltonian. The occupation of electron states with high momentum enforced by the Pauli principle leads to a ``super-Heisenberg’’ scaling of the sensitivity with a power law that depends on the geometry of the sensor.

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“…Expression (92) generalizes well-known variance-based formulas [24]. At t = 0, state |ϕ ω 〉 coincides with ψ ω 0 and thus we recover the QFI for a single unitary, Eq.…”

Section: Qfi For a Bogoliubov Transformation Followed By A Hamiltonia...supporting

confidence: 52%

Quantum parameter estimation with many-body fermionic systems and application to the Hall effect

Giraud,

Goerbig,

Braun

2024

SciPost Phys.

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“…Let us consider a possibility of non-invertible intermediate transformations of Lqubit states, i.e., non-invertible gates, which are described by the 2 L × 2 L matrices U(r) of (possibly) less than full rank 1 ≤ r ≤ 2 L . This can be related to the production of "degenerate" states (see, e.g., [43]), "particle loss" [53][54][55], and the role of ranks in multiparticle entanglement [56,57].…”

Section: Invertible and Noninvertible Quantum Gatesmentioning

confidence: 99%

Polyadic Braid Operators and Higher Braiding Gates

Duplij

Vogl

2021

Universe

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A new kind of quantum gates, higher braiding gates, as matrix solutions of the polyadic braid equations (different from the generalized Yang--Baxter equations) is introduced. Such gates lead to another special multiqubit entanglement that can speed up key distribution and accelerate algorithms. Ternary braiding gates acting on three qubit states are studied in detail. We also consider exotic non-invertible gates, which can be related with qubit loss, and define partial identities (which can be orthogonal), partial unitarity, and partially bounded operators (which can be non-invertible). We define two classes of matrices, star and circle ones, such that the magic matrices (connected with the Cartan decomposition) belong to the star class. The general algebraic structure of the introduced classes is described in terms of semigroups, ternary and $5$-ary groups and modules. The higher braid group and its representation by the higher braid operators are given. Finally, we show, that for each multiqubit state, there exist higher braiding gates that are not entangling, and the concrete conditions to be non-entangling are given for the obtained binary and ternary gates.Yang--Baxter equation; braid group; qubit; ternary; polyadic; braiding quantum gate.

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“…This can be related to the production of "degenerate" states (see, e.g. [42]), "particle loss" [52][53][54], and the role of ranks in multiparticle entanglement [55,56].…”

Section: Invertible and Noninvertible Quantum Gatesmentioning

confidence: 99%

Polyadic braid operators and higher braiding gates

Duplij,

Vogl

2021

Preprint

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Higher braiding gates, a new kind of quantum gate, are introduced. These are matrix solutions of the polyadic braid equations (which differ from the generalized Yang-Baxter equations). Such gates support a special kind of multi-qubit entanglement which can speed up key distribution and accelerate the execution of algorithms. Ternary braiding gates acting on three qubit states are studied in detail. We also consider exotic non-invertible gates which can be related to qubit loss, and define partial identities (which can be orthogonal), partial unitarity, and partially bounded operators (which can be non-invertible). We define two classes of matrices, the star and circle types, and find that the magic matrices (connected with the Cartan decomposition) belong to the star class. The general algebraic structure of the classes introduced here is described in terms of semigroups, ternary and 5-ary groups and modules. The higher braid group and its representation by higher braid operators are given. Finally, we show that for each multi-qubit state there exist higher braiding gates which are not entangling, and the concrete conditions to be non-entangling are given for the binary and ternary gates discussed. CONTENTS I. Introduction II. Yang-Baxter operators A. Yang-Baxter maps and braid group B. Constant matrix solutions to the Yang-Baxter equation C. Partial identity and unitarity D. Permutation and parameter-permutation 4-vertex Yang-Baxter maps E. Group structure of 4-vertex and 8-vertex matrices F. Star 8-vertex and circle 8-vertex Yang-Baxter maps G. Triangle invertible 9and 10-vertex solutions III. Polyadic braid operators and higher braid equations IV. Solutions to the ternary braid equations A. Constant matrix solutions B. Permutation and parameter-permutation 8-vertex solutions C. Group structure of the star and circle 8-vertex matrices D. Group structure of the star and circle 16-vertex matrices E. Pauli matrix presentation of the star and circle 16-vertex constant matrices F. Invertible and non-invertible 16-vertex solutions to the ternary braid equations G. Higher 2 n -vertex constant solutions to n-ary braid equations V. Invertible and noninvertible quantum gates VI. Binary braiding quantum gates VII. Higher braiding quantum gates VIII. Entangling braiding gates A. Entangling binary braiding gates B. Entangling ternary braiding gates References

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Quantum channel-estimation with particle loss: GHZ versus W states

Cited by 6 publications

References 15 publications

Quantum parameter estimation with many-body fermionic systems and application to the Hall effect

Quantum parameter estimation with many-body fermionic systems and application to the Hall effect

Polyadic Braid Operators and Higher Braiding Gates

Polyadic braid operators and higher braiding gates

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