Quantum vs Classical Erasure: Equal Bounds but Unequal Costs
Abstract
Irreversibility has a fundamental thermodynamic cost, erasing information inevitably generates heat. This connection is quantified by the Landauer bound, which gives the minimum dissipation needed to erase a single bit of information. While this bound applies in both classical and quantum settings, it is saturated only in idealised limits of infinite resources. Here, we provide a unified first principles description of finite-resource erasure in both classical and quantum systems. We begin by proving the communal folklore that in the idealised regime the erasure cost of a bit encoded in a quantum or classical system is the same. Despite this, we show that their practical implementation differs substantially: achieving comparable erasure quality in quantum systems requires more control, larger accessible energy gaps and longer operation times. Classical protocols can achieve the erasure of a comparable quantum protocol under far weaker constraints which we expose in trade-off relations. Our results explain why practical erasure schemes fall short of Landauer's bound and show that classical systems enjoy several fundamental thermodynamic advantages.
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BibTeX
@misc{neuser2026quantum,
title = {{Quantum vs Classical Erasure: Equal Bounds but Unequal Costs}},
author = {Jan Neuser and Jake Xuereb and Pharnam Bakhshinezhad and Marcus Huber},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.27341},
eprint = {2607.27341},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.27341},
}
RIS
TY - UNPB
TI - Quantum vs Classical Erasure: Equal Bounds but Unequal Costs
AU - Jan Neuser
AU - Jake Xuereb
AU - Pharnam Bakhshinezhad
AU - Marcus Huber
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2607.27341
UR - https://arxiv.org/abs/2607.27341
AB - Irreversibility has a fundamental thermodynamic cost, erasing information inevitably generates heat. This connection is quantified by the Landauer bound, which gives the minimum dissipation needed to erase a single bit of information. While this bound applies in both classical and quantum settings, it is saturated only in idealised limits of infinite resources. Here, we provide a unified first principles description of finite-resource erasure in both classical and quantum systems. We begin by proving the communal folklore that in the idealised regime the erasure cost of a bit encoded in a quantum or classical system is the same. Despite this, we show that their practical implementation differs substantially: achieving comparable erasure quality in quantum systems requires more control, larger accessible energy gaps and longer operation times. Classical protocols can achieve the erasure of a comparable quantum protocol under far weaker constraints which we expose in trade-off relations. Our results explain why practical erasure schemes fall short of Landauer's bound and show that classical systems enjoy several fundamental thermodynamic advantages.
ER -