Precision and Work Fluctuations in Gaussian Battery Charging

Nicolai Friis1,2 and Marcus Huber1

1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
2Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria

One of the most fundamental tasks in quantum thermodynamics is extracting energy from one system and subsequently storing this energy in an appropriate battery. Both of these steps, work extraction and charging, can be viewed as cyclic Hamiltonian processes acting on individual quantum systems. Interestingly, so-called passive states exist, whose energy cannot be lowered by unitary operations, but it is safe to assume that the energy of any not fully charged battery may be increased unitarily. However, unitaries raising the average energy by the same amount may differ in qualities such as their precision, fluctuations, and charging power. Moreover, some unitaries may be extremely difficult to realize in practice. It is hence of crucial importance to understand the qualities that can be expected from practically implementable transformations. Here, we consider the limitations on charging batteries when restricting to the feasibly realizable family of Gaussian unitaries. We derive optimal protocols for general unitary operations as well as for the restriction to easier implementable Gaussian unitaries. We find that practical Gaussian battery charging, while performing significantly less well than is possible in principle, still offers asymptotically vanishing relative charge variances and fluctuations.

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► Cited by (beta)

[1] Niels Lörch, Christoph Bruder, Nicolas Brunner, Patrick P Hofer, "Optimal work extraction from quantum states by photo-assisted Cooper pair tunneling", Quantum Science and Technology 3, 035014 (2018).

[2] Emma McKay, Nayeli A. Rodríguez-Briones, Eduardo Martín-Martínez, "Fluctuations of work cost in optimal generation of correlations", Physical Review E 98, 032132 (2018).

[3] Ludovico Lami, Bartosz Regula, Xin Wang, Rosanna Nichols, Andreas Winter, Gerardo Adesso, "Gaussian quantum resource theories", Physical Review A 98, 022335 (2018).

(The above data is from Crossref's cited-by service. Unfortunately not all publishers provide suitable and complete citation data so that some citing works or bibliographic details may be missing.)