Fundamental Limitations on the Reliabilities of Power and Work in Quantum Batteries

TL;DR

This paper establishes fundamental quantum limits on the reliability of quantum batteries, revealing a trade-off between power and work fluctuations governed by quantum uncertainty, and analyzes how different charging schemes affect this reliability.

Contribution

It introduces universal bounds on work and power fluctuations in quantum batteries and uncovers a quantum uncertainty relation that limits simultaneous suppression of these fluctuations.

Findings

Reliability bounds depend on charging speed.

Quantum uncertainty forbids simultaneous suppression of work and power fluctuations.

Hybrid charging schemes optimize the balance between power and reliability.

Abstract

Quantum batteries, microscopic devices designed to address energy demands in quantum technologies, promise high power during charging and discharging processes. Yet their practical usefulness and performance depend critically on reliability, quantified by the noise-to-signal ratios (NSRs), i.e., normalized fluctuations of work and power, where reliability decreases inversely with increasing NSR. We establish fundamental limits to this reliability: both work and power NSRs are universally bounded from below by a function of charging speed, imposing a reliability limit inherent to any quantum battery. More strikingly, we find that a quantum mechanical uncertainty relation forbids the simultaneous suppression of work and power fluctuations, revealing a fundamental trade-off that also limits the reliability of quantum batteries. We analyze the trade-off and limits, as well as their scaling behavior, across parallel (local), collective {(fully non-local)}, and hybrid (semi-local) charging schemes for many-body quantum batteries, finding that increasing power by exploiting stronger entanglement comes at the cost of diminished reliability of power. Similar trends are also observed in the charging of quantum batteries utilizing transverse Ising-like interactions. These suggest that achieving both high power and reliability require neither parallel nor collective charging, but a hybrid charging scheme with an intermediate range of interactions. Therefore, our analysis shapes the practical and efficient design of reliable and high-performance quantum batteries.