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Quantum charging advantage based on power bounds can be deceptive

Sreeram PG, J. Bharathi Kannan, M. S. Santhanam

TL;DR

This work investigates whether upper bounds on quantum charging power can falsely indicate a quantum advantage in a 2-local all-to-all spin-chain quantum battery. By analyzing a kicked spin-chain charger, the authors show that the Robertson-type bound can nearly saturate a quadratic scaling of power without long-range couplings, but a deeper analysis in the energy eigenspace using Fisher information reveals that the actual charging rate does not scale superextensively with $N$. The bound based on $I_E$, while tighter, can still be misleading in certain dynamical scenarios, and may diverge at turning points where $P(t)=0$. The work argues for validating claimed quantum advantages by directly computing $P(t)$ and the required resources, rather than relying on bounds alone.

Abstract

We demonstrate that an all-to-all coupled spin-chain model of a quantum battery with 2-local interactions exhibits superextensive charging when analysed using the upper bound derived from the uncertainty principle. Unlike the previously studied models in the literature, the contribution to this apparent quantum advantage arises from both the battery and the charger, and it does not require long-range couplings. However, on closer analysis of the charging using the battery evolution in the energy eigenspace, the advantage vanishes. Moreover, this tighter bound can also fail in certain physical situations. One has to exercise caution and compute the actual power transferred before claiming a quantum advantage.

Quantum charging advantage based on power bounds can be deceptive

TL;DR

This work investigates whether upper bounds on quantum charging power can falsely indicate a quantum advantage in a 2-local all-to-all spin-chain quantum battery. By analyzing a kicked spin-chain charger, the authors show that the Robertson-type bound can nearly saturate a quadratic scaling of power without long-range couplings, but a deeper analysis in the energy eigenspace using Fisher information reveals that the actual charging rate does not scale superextensively with . The bound based on , while tighter, can still be misleading in certain dynamical scenarios, and may diverge at turning points where . The work argues for validating claimed quantum advantages by directly computing and the required resources, rather than relying on bounds alone.

Abstract

We demonstrate that an all-to-all coupled spin-chain model of a quantum battery with 2-local interactions exhibits superextensive charging when analysed using the upper bound derived from the uncertainty principle. Unlike the previously studied models in the literature, the contribution to this apparent quantum advantage arises from both the battery and the charger, and it does not require long-range couplings. However, on closer analysis of the charging using the battery evolution in the energy eigenspace, the advantage vanishes. Moreover, this tighter bound can also fail in certain physical situations. One has to exercise caution and compute the actual power transferred before claiming a quantum advantage.
Paper Structure (10 sections, 18 equations, 4 figures)

This paper contains 10 sections, 18 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Kicked spin chain model of quantum battery and superextensive power bound
  3. Energy space activity and the vanishing power advantage
  4. Does More energy space activity always mean better charging?
  5. $I_E$ does not recognize the magnitude of energy transfer
  6. $I_E$ does not recognize wasteful discharge of the battery
  7. $I_E$ can be large due to dynamics within a degenerate subspace.
  8. $I_E$ can diverge at a turning point where $P(t)=0.$
  9. Discussion and conclusion
  10. acknowledgements

Figures (4)

  • Figure 1: A schematic of an all-to-all interacting spin chain model with 2-local interactions. The chain shows only $N=4$ spins for clarity.
  • Figure 2: (a) Mean eigenvalue and (b) variance of the eigenvalues of $H_C$ at the kicks ($H_C= \frac{\pi}{2} J_y+ \frac{7}{2j}J_z^2$) and in between the kicks ($H_C= \frac{\pi}{2} J_y$).
  • Figure 3: Power scaling in the spin chain battery with the periodically kicked charging, averaged over 50 time steps is close to quadratic ($\sim N^{1.9}$). The $N^1$ line shows the classical scaling. The inset shows the individual scalings of the battery and the charger variances.
  • Figure 4: KL divergence averaged over 50 time steps, as a function of the number of spins.