Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Precision bounds for bosonic quantum batteries

Beatriz Polo, Federico Centrone

TL;DR

This paper formulates a finite-energy, bosonic quantum-battery framework in which precision charging is quantified by the signal-to-noise ratio $\Gamma=\delta N/\Delta N$. It derives a state-level classical bound tied to antibunching via $g^{(2)}(0)$ and a finite-temperature Gaussian bound $\Gamma_G(\nu,\epsilon)$ whose violation certifies non-Gaussianity, subsequently identifying experimentally feasible non-Gaussian resources that surpass the bound. A linear photodetection model is developed to translate these witnesses to electrical statistics, enabling practical, near-term tests of quantum advantage in energy conversion. The study further extends to multimode configurations, showing how non-Gaussian resources can yield scalable precision gains, and discusses implementability with photodiodes and realistic loss/noise, including a TUR-based benchmark for detectors. Overall, the work provides a concrete, testable route to achieving and certifying quantum-enhanced precision charging in thermodynamically motivated nanoscopic loads.

Abstract

We study precision charging in bosonic quantum batteries under a finite-energy constraint, using the signal-to-noise ratio (SNR) of delivered excitations as an operational metric directly tied to the energy measured at a load. At the state level, we derive a classical bound whose violation is equivalent to antibunching and certifies non-classicality, and a Gaussian bound whose violation certifies non-Gaussianity under fixed temperature and energy-input constraints. We identify experimentally accessible non-Gaussian families that surpass this Gaussian bound at finite temperature, thereby establishing non-Gaussianity as a resource for enhanced charging precision. Finally, we introduce a linear photodetection model which, under standard linear-response assumptions, propagates these bounds to the photocurrent level and enables both witnesses to be evaluated solely from electrical statistics. Together, these results provide a realistic route to demonstrating an operational quantum advantage-defined as surpassing classical and Gaussian precision bounds-in a thermodynamically motivated energy-conversion task, with plausible near-term applications to the precision charging of fragile nanoscopic loads.

Precision bounds for bosonic quantum batteries

TL;DR

This paper formulates a finite-energy, bosonic quantum-battery framework in which precision charging is quantified by the signal-to-noise ratio . It derives a state-level classical bound tied to antibunching via and a finite-temperature Gaussian bound whose violation certifies non-Gaussianity, subsequently identifying experimentally feasible non-Gaussian resources that surpass the bound. A linear photodetection model is developed to translate these witnesses to electrical statistics, enabling practical, near-term tests of quantum advantage in energy conversion. The study further extends to multimode configurations, showing how non-Gaussian resources can yield scalable precision gains, and discusses implementability with photodiodes and realistic loss/noise, including a TUR-based benchmark for detectors. Overall, the work provides a concrete, testable route to achieving and certifying quantum-enhanced precision charging in thermodynamically motivated nanoscopic loads.

Abstract

We study precision charging in bosonic quantum batteries under a finite-energy constraint, using the signal-to-noise ratio (SNR) of delivered excitations as an operational metric directly tied to the energy measured at a load. At the state level, we derive a classical bound whose violation is equivalent to antibunching and certifies non-classicality, and a Gaussian bound whose violation certifies non-Gaussianity under fixed temperature and energy-input constraints. We identify experimentally accessible non-Gaussian families that surpass this Gaussian bound at finite temperature, thereby establishing non-Gaussianity as a resource for enhanced charging precision. Finally, we introduce a linear photodetection model which, under standard linear-response assumptions, propagates these bounds to the photocurrent level and enables both witnesses to be evaluated solely from electrical statistics. Together, these results provide a realistic route to demonstrating an operational quantum advantage-defined as surpassing classical and Gaussian precision bounds-in a thermodynamically motivated energy-conversion task, with plausible near-term applications to the precision charging of fragile nanoscopic loads.

Paper Structure

This paper contains 20 sections, 3 theorems, 78 equations, 8 figures.

Table of Contents

  1. I. Introduction
  2. II. Bosonic batteries
  3. III. Results
  4. A. Classical bound
  5. B. Gaussian limitations
  6. C. Non-Gaussian states
  7. D. Multimode states
  8. IV. Implementability
  9. V. Detectable precision
  10. VI. Discussion and outlook
  11. Appendix A: Covariance matrix formalism for Gaussian states
  12. Appendix B: Optimal signal-to-noise ratio $\Gamma$ for Gaussian states
  13. Appendix C: Expectation values on non-Gaussian states
  14. Appendix D: Kitten states example
  15. Appendix E: Minimum Ergotropy of non-Gaussian states
  16. ...and 5 more sections

Key Result

Theorem A

For any classical output state, the following bound holds: equivalently $g^{(2)}(0)\ge 1$ via Eq. g_intermsof_gamma. Hence any observed violation of eq:ClassicalWitness (equivalently, $g^{(2)}(0)<1$) certifies non-classical (sub-Poissonian) light in our precision metric.

Figures (8)

  • Figure 1: Scheme of the charging precision in a photonic-based battery. Energy fluctuations are attenuated when employing non-classical light.
  • Figure 2: Maximum photon-number SNR attainable for Gaussian states, $\Gamma_G(\nu,\epsilon)$, as a function of temperature (via $\nu$) and maximum energy input $\epsilon$. The dashed line marks $g^{(2)}(0)=1$ (classical/non-classical boundary).
  • Figure 3: SNR of a photon-added squeezed thermal state as a function of thermal fluctuations and squeezing. The pure Fock state $|1\rangle$ corresponds to no squeezing ($z=1$) and zero temperature.
  • Figure 4: Best-achieved SNR $\Gamma$ versus temperature for different non-Gaussian families (optimized over $U_G$), compared against the Gaussian bound (black dashed line). The energetic constraint has been set at $\epsilon = 5$ (dimensionless).
  • Figure 5: Solution to \ref{['optimization']} for the optimal squeezing and displacement through the Lagrange multipliers method.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Theorem A
  • Theorem B
  • Lemma 1