This article discusses the concept of information and its intimate relationship with physics. After an introduction of all the necessary quantum mechanical and information theoretical concepts we analyze Landauer's principle that states that the erasure of information is inevitably accompanied by the generation of heat. We employ this principle to rederive a number of results in classical and quantum information theory whose rigorous mathematical derivations are difficult. This demonstrates the usefulness of Landauer's principle and provides an introduction to the physical theory of information.
Quantum state engineering and quantum computation rely on information erasure procedures that, up to some fidelity, prepare a quantum object in a pure state. Such processes occur within Landauer's framework if they rely on an interaction between the object and a thermal reservoir. Landauer's principle dictates that this must dissipate a minimum quantity of heat, proportional to the entropy reduction that is incurred by the object, to the thermal reservoir. However, this lower bound is only reachable for some specific physical situations, and it is not necessarily achievable for any given reser…
Information is physical but information is also processed in finite time. Where computing protocols are concerned, finite-time processing in the quantum regime can dynamically generate coherence. Here we show that this can have significant thermodynamic implications. We demonstrate that quantum coherence generated in the energy eigenbasis of a system undergoing a finite-time information erasure protocol yields rare events with extreme dissipation. These fluctuations are of purely quantum origin. By studying the full statistics of the dissipated heat in the slow driving limit, we prove that coh…
Information is central to thermodynamics, providing the grounds to the formulation of the theory in powerful abstract statistical terms. One must not forget, however, that, as put by Landauer, {\it information is physical}. This means that the processing of information will be unavoidably linked to the costs of manipulating the real physical systems carrying the information. Here we will focus on the particular process of erasing information, which plays a fundamental role in the description of heat engines. We will review Landauer's principle and the associated erasure energy cost. We will al…
Quantum vs Classical Erasure: Equal Bounds but Unequal Costs
Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien（维也纳量子科学与技术中心，原子研究所，维也纳工业大学）；Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）
Landauer's erasure principle is a cornerstone of thermodynamics and information theory. According to this principle, erasing information incurs a minimum energy cost. Recently, Vaccaro and Barnett [Proc. R. Soc {\bf 467}, 1770 (2011)] explored information erasure in the context of multiple conserved quantities and showed that the erasure cost can be solely in terms of spin angular momentum. As Landauer's erasure principle plays a fundamental role in heat engines, their result considerably widens the possible configurations that heat engines can have. Motivated by this, we propose here a novel …
One of the outstanding challenges to information processing is the eloquent suppression of energy consumption in execution of logic operations. Landauer principle sets an energy constraint in deletion of a classical bit of information. Although some attempts have been paid to experimentally approach the fundamental limit restricted by this principle, exploring Landauer principle in a purely quantum mechanical fashion is still an open question. Employing a trapped ultracold ion, we experimentally demonstrate a quantum version of Landauer principle, i.e., an equality associated with energy cost …
We consider state changes in quantum theory due to "conditional action" and relate these to the discussion of entropy decrease due to interventions of "intelligent beings" and the principles of Szilard and Landauer/Bennett. The mathematical theory of conditional actions is a special case of the theory of "instruments" which describes changes of state due to general measurements and will therefore be briefly outlined in the present paper. As a detailed example we consider the imperfect erasure of a qubit that can also be viewed as a conditional action and will be realized by the coupling of a s…
Quantum Landauer's principle provides a fundamental lower bound for energy dissipation occurred with information erasure in the quantum regime. While most studies have related the entropy reduction incorporated with the erasure to the lower bound~(entropic bound), recent efforts have also provided another lower bound associated with the thermal fluctuation of the dissipated energy~(thermodynamic bound). The coexistence of the two bounds has stimulated comparative studies of their properties; however, these studies were performed for systems where the time-evolution of diagonal (population) and…
We consider two bottlenecks in quantum computing: limited memory size and noise caused by heat dissipation. Trying to optimize both, we investigate "on-the-go erasure" of quantum registers that are no longer needed for a given algorithm: freeing up auxiliary qubits as they stop being useful would facilitate the parallelization of computations. We study the minimal thermodynamic cost of erasure in these scenarios, applying results on the Landauer erasure of entangled quantum registers. For the class of algorithms solving the Abelian hidden subgroup problem, we find optimal on-the-go erasure pro…
We introduce a simple single-system game inspired by the Clauser-Horne-Shimony-Holt (CHSH) game. For qubit systems subjected to unitary gates and projective measurements, we prove that any strategy in our game can be mapped to a strategy in the CHSH game, which implies that Tsirelson's bound also holds in our setting. More generally, we show that the optimal success probability depends on the reversible or irreversible character of the gates, the quantum or classical nature of the system and the system dimension. We analyse the bounds obtained in light of Landauer's principle, showing the entr…
Erasure is fundamental for information processing. It is also key in connecting information theory and thermodynamics, as it is a logically irreversible task. We provide a new angle on this connection, noting that there may be an additional cost to erasure, that is not captured by standard results such as Landauer's principle. To make this point we use a model of irreversibility based on Constructor Theory - a recently proposed generalization of the quantum theory of computation. The model uses a machine called the "quantum homogenizer", which has the ability to approximately realise the trans…
Landauer's principle states that erasure of each bit of information in a system requires at least a unit of energy $k_B T \ln 2$ to be dissipated. In return, the blank bit may possibly be utilized to extract usable work of the amount $k_B T \ln 2$, in keeping with the second law of thermodynamics. While in principle any collection of spins can be utilized as information storage, work extraction by utilizing this resource in principle requires specialized engines that are capable of using this resource. In this work, we focus on heat and charge transport in a quantum spin Hall device in the pre…
The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this study, we investigate the heat dissipation associated with finite-time information erasure and the effect of quantum coherence in such processes. By considering a scenario wherein information is encoded in an open quantum system whose dynamics are described by the Markovian Lindblad equation, we show that the dissipated heat is lower-bounded by the conventional Landauer cost, as well as a correction term inversely proportional to the operational …
We demonstrate an information erasure protocol that resets $N$ qubits at once. The method displays exceptional performances in terms of energy cost (it operates nearly at Landauer energy cost $kT \ln 2$), time duration ($\sim μs$) and erasure success rate ($\sim 99,9\%$). The method departs from the standard algorithmic cooling paradigm by exploiting cooperative effects associated to the mechanism of spontaneous symmetry breaking which are amplified by quantum tunnelling phenomena. Such cooperative quantum erasure protocol is experimentally demonstrated on a commercial quantum annealer and cou…
Starting from Landauer's slogan "information is physical," we revise and modify Landauer's principle stating that the erasure of information has a minimal price in the form of a certain quantity of free energy. We establish a direct link between the erasure cost and the work value of a piece of information, and show that the former is essentially the length of the string's best compression by a reversible computation. We generalize the principle by deriving bounds on the free energy to be invested for --- or gained from, for that matter --- a general computation. We then revisit the second law…
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Laboratory（MajuLab，法国国家科研中心-南法大学-首尔大学-新加坡国立大学-南洋理工大学国际联合实验室）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；ICREA - Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚高级研究学院）；Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), CONICET（布宜诺斯艾利斯大学，布宜诺斯艾利斯物理研究所，阿根廷国家科学研究委员会）
In a generalized framework for the Landauer erasure protocol, we study bounds on the heat dissipated in typical nonequilibrium quantum processes. In contrast to thermodynamic processes, quantum fluctuations are not suppressed in the nonequilibrium regime and cannot be ignored, making such processes difficult to understand and treat. Here we derive an emergent fluctuation relation that virtually guarantees the average heat produced to be dissipated into the reservoir either when the system or reservoir is large (or both) or when the temperature is high. The implication of our result is that for…
Landauer's erasure principle puts a fundamental constraint on the amount of work required to erase information using thermal reservoirs. Recently this bound was improved to include corrections for finite-sized thermal reservoirs. In conventional information-erasure schemes, conservation of energy plays a key role with the cost of erasure. However, it has been shown that erasure can be achieved through the manipulation of spin angular momentum rather than energy, using a reservoir composed of energy-degenerate spin particles under the constraint of the conservation of spin angular momentum, in …
In this work we explore the use of thermodynamic length to improve the performance of experimental protocols. In particular, we implement Landauer erasure on a driven electron level in a semiconductor quantum dot, and compare the standard protocol in which the energy is increased linearly in time with the one coming from geometric optimisation. The latter is obtained by choosing a suitable metric structure, whose geodesics correspond to optimal finite-time thermodynamic protocols in the slow driving regime. We show experimentally that geodesic drivings minimise dissipation for slow protocols, …
Quantum Szilard engine constitutes an adequate interplay of thermodynamics, information theory and quantum mechanics. Szilard engines are in general operated by a Maxwell's Demon where Landauer's principle resolves the apparent paradoxes. Here we propose a Szilard engine setup without featuring an explicit Maxwell's demon. In a demonless Szilard engine, the acquisition of which-side information is not required, but erasure and the related heat dissipation still take place implicitly by the very nature of the work extraction process. We see that the insertion of the partition in a quantum Szila…
We define the deconstruction cost of a tripartite quantum state on systems $ABE$ as the minimum rate of noise needed to apply to the $AE$ systems, such that there is negligible disturbance to the marginal state on the $BE$ systems, while the system $A$ of the resulting state is locally recoverable from the $E$ system alone. We refer to such actions as deconstruction operations and protocols implementing them as state deconstruction protocols. State deconstruction generalizes Landauer erasure of a single-party quantum state as well the erasure of correlations of a two-party quantum state. We fi…
Investigating principles for storage of quantum information at finite temperature with minimal need for active error correction is an active area of research. We bear upon this question in two-dimensional holographic conformal field theories via the quantum null energy condition (QNEC) that we have shown earlier to implement the restrictions imposed by quantum thermodynamics on such many-body systems. We study an explicit encoding of a logical qubit into two similar chirally propagating excitations of finite von-Neumann entropy on a finite temperature background whose erasure can be implemente…
