Sub- and super-fidelity as bounds for quantum fidelity

Miszczak, Jarosław Adam; Puchała, Zbigniew; Horodecki, Paweł; Uhlmann, Armin; Życzkowski, Karol

doi:10.26421/qic9.1-2-7

Cited by 78 publications

(146 citation statements)

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“…In this paper, we derive lower and upper bounds for the geometric measure of coherence for arbitrary dimension d, by using the concepts of sub-fidelity and super-fidelity introduced in Ref. [29,30,31,32,33]. These bounds are shown to be tight for a class of maximally coherent mixed states.…”

Section: Introductionmentioning

confidence: 99%

Estimation on Geometric Measure of Quantum Coherence

Zhang

Chen

et al. 2017

Commun. Theor. Phys.

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Section: Introductionmentioning

confidence: 99%

Estimation on Geometric Measure of Quantum Coherence

Zhang

Chen

et al. 2017

Commun. Theor. Phys.

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“…and later studied independently in [79] by the name of super-fidelity, where ρ and σ represent two density matrices that belong to L +,1 (H N ). With respect to F N (ρ, σ) the connection with the discrete Wigner functions W ρ (µ, ν) and W σ (µ, ν) can be promptly established as follows:…”

Section: Discussionmentioning

confidence: 99%

Representations of two-qubit and ququart states via discrete Wigner functions

Marchiolli,

Galetti

2019

Preprint

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By means of a well-grounded mapping scheme linking Schwinger unitary operators and generators of the special unitary group SU(N), it is possible to establish a self-consistent theoretical framework for finite-dimensional discrete phase spaces which has the discrete SU(N) Wigner function as a legitimate by-product. In this paper, we apply these results with the aim of putting forth a detailed study on the discrete SU(2) ⊗ SU(2) and SU(4) Wigner functions, in straight connection with experiments involving, among other things, the tomographic reconstruction of density matrices related to the two-qubit and ququart states. Next, we establish a formal correspondence between both the descriptions that allows us to visualize the quantum correlation effects of these states in finite-dimensional discrete phase spaces. Moreover, we perform a theoretical investigation on the twoqubit X-states, which combines discrete Wigner functions and their respective marginal distributions in order to obtain a new function responsible for describing qualitatively the quantum correlation effects. To conclude, we also discuss possible extensions to the discrete Husimi and Glauber-Sudarshan distribution functions, as well as future applications on spin chains.

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“…, we can extract F G (ρ θ ) from the coefficient of the quadratic term. In the present single-qubit case, the superfidelity is equivalent to the Uhlmann-Jozsa fidelity for both pure and mixed states [40]; we thus obtain the exact QFI through F θ = F G (ρ θ ); see Eq. ( 3).…”

Section: Fig 1 (A)mentioning

confidence: 92%

Experimental estimation of the quantum Fisher information from randomized measurements

Yu,

Li,

Wang

et al. 2021

Preprint

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The quantum Fisher information (QFI) represents a fundamental concept in quantum physics. On the one hand, it quantifies the metrological potential of quantum states in quantum-parameter-estimation measurements. On the other hand, it is intrinsically related to the quantum geometry and multipartite entanglement of manybody systems. Here, we explore how the QFI can be estimated via randomized measurements, an approach which has the advantage of being applicable to both pure and mixed quantum states. In the latter case, our method gives access to the sub-quantum Fisher information, which sets a lower bound on the QFI. We experimentally validate this approach using two platforms: a nitrogen-vacancy center spin in diamond and a 4-qubit state provided by a superconducting quantum computer. We further perform a numerical study on a many-body spin system to illustrate the advantage of our randomized-measurement approach in estimating multipartite entanglement, as compared to quantum state tomography. Our results highlight the general applicability of our method to general quantum platforms, including solid-state spin systems, superconducting quantum computers and trapped ions, hence providing a versatile tool to explore the essential role of the QFI in quantum physics.

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Sub- and super-fidelity as bounds for quantum fidelity

Cited by 78 publications

References 0 publications

Estimation on Geometric Measure of Quantum Coherence

Estimation on Geometric Measure of Quantum Coherence

Representations of two-qubit and ququart states via discrete Wigner functions

Experimental estimation of the quantum Fisher information from randomized measurements

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