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Quantum advantage from negativity of work quasiprobability distributions

Gianluca Francica

TL;DR

The work establishes a concrete link between a quantum battery's charging advantage and the negativity of the work quasiprobability distribution in a subinterval of the process. By analyzing a sudden-quench charging protocol with noncommuting $H_1$, the authors show that negativity of the quasiprobability at $q=\tfrac{1}{2}$ implies unbounded higher cumulants in the large-$N$ limit, triggering a sufficient condition that drives $\tau$ to zero as $N\to\infty$. They illustrate the mechanism with a fermionic random-coupling model, where $p_{1/2}(w)$ can become negative while $p_0(w)$ remains nonnegative, and derive scaling laws for the charging time, $\tau\sim N^{-z}$. The results offer a practical route to diagnose and harness quantum advantage in battery charging via measurable quasiprobabilities, connecting abstract nonclassical statistics to tangible performance in quantum technologies.

Abstract

Quantum batteries can be charged by performing a work ``instantaneously'' in the limit of large number of cells. In general, the work exhibits statistics that can be represented by a quasiprobability in the presence of initial quantum coherence in the energy basis. Here we show that these two concepts of quantum thermodynamics, which apparently appear disconnected, show a simple relation. Specifically, if the work distribution shows negativity in some time interval, then we can surely get quantum advantage in the charging process.

Quantum advantage from negativity of work quasiprobability distributions

TL;DR

The work establishes a concrete link between a quantum battery's charging advantage and the negativity of the work quasiprobability distribution in a subinterval of the process. By analyzing a sudden-quench charging protocol with noncommuting , the authors show that negativity of the quasiprobability at implies unbounded higher cumulants in the large- limit, triggering a sufficient condition that drives to zero as . They illustrate the mechanism with a fermionic random-coupling model, where can become negative while remains nonnegative, and derive scaling laws for the charging time, . The results offer a practical route to diagnose and harness quantum advantage in battery charging via measurable quasiprobabilities, connecting abstract nonclassical statistics to tangible performance in quantum technologies.

Abstract

Quantum batteries can be charged by performing a work ``instantaneously'' in the limit of large number of cells. In general, the work exhibits statistics that can be represented by a quasiprobability in the presence of initial quantum coherence in the energy basis. Here we show that these two concepts of quantum thermodynamics, which apparently appear disconnected, show a simple relation. Specifically, if the work distribution shows negativity in some time interval, then we can surely get quantum advantage in the charging process.

Paper Structure

This paper contains 9 sections, 1 theorem, 27 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Charging process
  3. Sufficient condition for quantum advantage
  4. Quasiprobability distribution
  5. Quantum advantage and work quasiprobability
  6. Leggett-Garg inequality
  7. Main result
  8. Example
  9. Conclusions

Key Result

Theorem 1

For the charging process of Sec. sec.process, for $t_1\in (0,\tau)$ and $t_2=\tau$, if for $q=1/2$ the quasiprobability distribution of the work $w$ done in the time interval $[t_1,t_2]$ also takes negative values, i.e., $p_{\frac{1}{2}}(w)<0$ for some $w$, then there is quantum advantage in the cha

Figures (1)

  • Figure 1: The histograms of quasiprobability distributions $p_0(w)$ (top panel) and $p_{1/2}(w)$ (bottom panel) for a single realization of the disorder. We assume $\vert\psi(\tau)\rangle\approx \vert E^0_{max}\rangle$ and put $C_2=N^\alpha$ with $\alpha=1$, $N=8$ and $\epsilon_0=1$.

Theorems & Definitions (1)

  • Theorem 1