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  • Letter

End-point measurement approach to assess quantum coherence in energy fluctuations

S. Gherardini, A. Belenchia, M. Paternostro, and A. Trombettoni
Phys. Rev. A 104, L050203 – Published 18 November 2021
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    Abstract

    We discuss the role of quantum coherence in the energy fluctuations of open quantum systems. To this aim, we introduce a protocol to which we refer as the end-point measurement scheme, allowing us to define the statistics of energy changes as a function of energy measurements performed only after the evolution of the initial state. At the price of an additional uncertainty on the initial energies, this approach prevents the loss of initial quantum coherences and enables the estimation of their effects on energy fluctuations. We demonstrate our findings by running an experiment on the IBM Quantum Experience superconducting qubit platform.

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    • Received 16 June 2020
    • Revised 2 July 2021
    • Accepted 29 September 2021

    DOI:https://doi.org/10.1103/PhysRevA.104.L050203

    ©2021 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Quantum thermodynamics
    Quantum Information, Science & TechnologyAtomic, Molecular & OpticalStatistical Physics & Thermodynamics

    Authors & Affiliations

    S. Gherardini1,2,*, A. Belenchia3,4,*, M. Paternostro4, and A. Trombettoni5,2

    • 1Department of Physics and Astronomy & LENS, University of Florence, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
    • 2CNR-IOM DEMOCRITOS Simulation Center and SISSA, Via Bonomea 265, I-34136 Trieste, Italy
    • 3Institut für Theoretische Physik, Eberhard-Karls-Universität Tübingen, 72076 Tübingen, Germany
    • 4Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom
    • 5Department of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, Italy

    • *These authors contributed equally to this work.

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    Vol. 104, Iss. 5 — November 2021

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    • Figure 1
      Figure 1

      Protocol for the quantification of energy fluctuations and the extraction of information about coherence. An ensemble of identical systems, prepared in the initial state ρi, is divided in three subgroups. One is used to obtain piℓ=Tr(ρiΠiℓ) via an initial energy measurement. The second goes through a dephasing channel, returning a state P diagonal in the energy basis. This then undergoes map Φt and is used to determine pPk=Tr(Φtf[P]Πfk). The systems in the third subgroup are not initially measured but subjected to the dynamics and used to obtain pfk=Tr(Φtf[ρi]Πfk).

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    • Figure 2
      Figure 2

      Top: Circuits implemented in IBMQ. The initial state is prepared by applying two identical single-qubit gates U(θ0) onto |00〉 (we use θ0=2 [36]). In TPM, two initial projective measurements destroy any coherence in the computational basis, while in EPM such measurements (enclosed in the dashed red box) are absent. We then implement the controlled gate U(θn), with θn≡nπ/10 and n=0,...,20, followed by two projective measurements in the computational basis. The results are stored in four classical registers to allow the analysis of the energy-change statistics. Bottom: Comparison of the characteristic functions for EPM and TPM. The lines show the theoretical predictions, while the points (with their error bars) the experimental results. Each data point has been obtained from 2048 experimental runs. The solid red line and circles are related to the results obtained by applying TPM. The dashed blue line and squared refer to the EPM characteristic function. Finally, the dotted magenta line and rhombuses (dot-dashed black line and triangles) show the contribution of the diagonal (off-diagonal) parts of the initial state ρi in the computational basis. The inverse (physical) temperature of the diagonal part of the initial state is β=0.443/ε, where ε∼5 MHz is the energy gap for the superconducting qubits, as provided by the IBMQ documentation.

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