Two types of arguments concerning (im)possibility of constructing a scalable, exponentially stable quantum memory equipped with Hamiltonian controls are discussed. The first type concerns ergodic properties of open Kitaev models which are considered as promising candidates for such memories. It is shown that, although the 4D Kitaev model provides stable qubit observables, the Hamiltonian control is not possible. The thermodynamical approach leads to the new proposal of the revised version of Landauer's principle and suggests that the existence of quantum memory implies the existence of the perpetuum mobile of the second kind. Finally, a discussion of the stability property of information and its implications is presented.
Landauer's principle states that the erasure of information generates a corresponding amount of entropy in the environment. We show that Landauer's principle provides an intuitive basis for Holevo bound on the classical capacity of a quantum channel.
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 informatio…
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 study the validity of Landauer principle in the non-Markovian regime by means of collision models where the intracollisions inside the reservoir cause memory effects generating system-environment correlations. We adopt the system-environment correlations created during the dynamical process to assess the effect of non-Markovianity on the Landauer principle. Exploiting an exact equality for the entropy change of the system, we find the condition for the violation of the Landauer principle, which occurs when the established system-environment correlations become larger than the entropy produc…
Classical and quantum error correction are presented in the form of Maxwell's demon and their efficiency analyzed from the thermodynamic point of view. We explain how Landauer's principle of information erasure applies to both cases. By then extending this principle to entanglement manipulations we rederive upper bounds on purification procedures thereby linking the ''no local increase of entanglement'' principle to the Second Law of thermodynamics.
We demonstrate the validity of Landauer's erasure principle in the strong coupling quantum regime by treating the system-reservoir interaction in a consistent way. We show that the initial coupling to the reservoir modifies both energy and entropy of the system and provide explicit expressions for the latter in the case of a damped quantum harmonic oscillator. These contributions are related to the Hamiltonian of mean force and dominate in the strong damping limit. They need therefore to be fully taken into account in any low-temperature thermodynamic analysis of quantum systems.
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…
We present a concise derivation of Landauer's erasure principle from the postulates of statistical mechanics, along with a small number of additional but uncontroversial axioms.
Upon reviewing the article by Allahverdyan and Nieuwenhuizen in PRE, we conclude that neither the Landauer principle nor the counterexamples presented by the authors have any relation (i) to thermodynamics, and (ii) to the interdependence of nonstatistical quantum physics and thermodynamics.
In a recent paper [Mar05] it is argued that to properly understand the thermodynamics of Landauer's Principle it is necessary extend the concept of logical operations to include indeterministic operations. Here we examine the thermodynamics of such operations in more detail, extending the work of Landuaer[Lan61] to include indeterministic operations and to include logical states with variable entropies, temperatures and mean energies. We derive the most general statement of Landauer's Principle and prove it's universality, extending considerably the validity of previous proofs. This confirms c…
We confirm Landauer's 1961 hypothesis that reducing the number of possible macroscopic states in a system by a factor of two requires work of at least kT ln 2. Our experiment uses a colloidal particle in a time-dependent, virtual potential created by a feedback trap to implement Landauer's erasure operation. In a control experiment, similar manipulations that do not reduce the number of system states can be done reversibly. Erasing information thus requires work. In individual cycles, the work to erase can be below the Landauer limit, consistent with the Jarzynski equality.
Thermodynamics connects our knowledge of the world to our capability to manipulate and thus to control it. This crucial role of control is exemplified by the third law of thermodynamics, Nernst's unattainability principle, which states that infinite resources are required to cool a system to absolute zero temperature. But what are these resources and how should they be utilized? And how does this relate to Landauer's principle that famously connects information and thermodynamics? We answer these questions by providing a framework for identifying the resources that enable the creation of pure …
Landauer's principle states that the erasure of one bit of information requires the free energy kT ln 2. We argue that the reliability of the bit erasure process is bounded by the accuracy inherent in the statistical state of the energy source (`the resources') driving the process. We develop a general framework describing the `thermodynamic worth' of the resources with respect to reliable bit erasure or good cooling. This worth turns out to be given by the distinguishability of the resource's state from its equilibrium state in the sense of a statistical inference problem. Accordingly, Kullba…
Using the operational framework of completely positive, trace preserving operations and thermodynamic fluctuation relations, we derive a lower bound for the heat exchange in a Landauer erasure process on a quantum system. Our bound comes from a non-phenomenological derivation of the Landauer principle which holds for generic non-equilibrium dynamics. Furthermore the bound depends on the non-unitality of dynamics, giving it a physical significance that differs from other derivations. We apply our framework to the model of a spin-1/2 system coupled to an interacting spin chain at finite temperat…
The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than $kTlog 2$. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system S coupled to an infinitely extended thermal reservoir R. Using Araki's perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint system S+R, that Landauer's bound saturates for adiabatically switched interactions. The recent work of…
Landauer's principle is, roughly, the principle that there is an entropic cost associated with implementation of logically irreversible operations. Though widely accepted in the literature on the thermodynamics of computation, it has been the subject of considerable dispute in the philosophical literature. Both the cogency of proofs of the principle and its relevance, should it be true, have been questioned. In particular, it has been argued that microscale fluctuations entail dissipation that always greatly exceeds the Landauer bound. In this article Landauer's principle is treated within sta…
Landauer's Principle relates entropy decrease and heat dissipation during logically irreversible processes. Most theoretical justifications of Landauer's Principle either use thermodynamic reasoning or rely on specific models based on arguable assumptions. Here, we aim at a general and minimal setup to formulate Landauer's Principle in precise terms. We provide a simple and rigorous proof of an improved version of the Principle, which is formulated in terms of an equality rather than an inequality. The proof is based on quantum statistical mechanics concepts rather than on thermodynamic argume…
Landauer's principle sets fundamental thermodynamical constraints for classical and quantum information processing, thus affecting not only various branches of physics, but also of computer science and engineering. Despite its importance, this principle was only recently experimentally considered for classical systems. Here we employ a nuclear magnetic resonance setup to experimentally address the information to energy conversion in a quantum system. Specifically, we consider a three nuclear spins $S=1/2$ (qubits) molecule ---the system, the reservoir and the ancilla--- to measure the heat dis…
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 model of Unruh-DeWitt detector coupled to the scalar field for finite time is studied. A systematic way of computing finite time corrections in various cases is suggested and nonperturbative effects like thermalization are discussed. It is shown in particular that adiabatic switching off the coupling between the detector and the thermal bath leaves non-vanishing corrections to the detector's levels distribution. Considering the two level detector as an information bearing degree of freedom encoding one bit of information, limits on external work for the detector's (de)couling in finite tim…
Landauer's bound relates changes in the entropy of a system with the inevitable dissipation of heat to the environment. The bound, however, becomes trivial in the limit of zero temperature. Here we show that it is possible to derive a tighter bound which remains non-trivial even as $T\to 0$. As in the original case, the only assumption we make is that the environment is in a thermal state. Nothing is said about the state of the system or the kind of system-environment interaction. Our bound is valid for all temperatures and is always tighter than the original one, tending to it in the limit of…
We investigate the link between information and thermodynamics embodied by Landauer's principle in the open dynamics of a multipartite quantum system. Such irreversible dynamics is described in terms of a collisional model with a finite temperature reservoir. We demonstrate that Landauer's principle holds, for such a configuration, in a form that involves the flow of heat dissipated into the environment and the rate of change of the entropy of the system. Quite remarkably, such a principle for {\it heat and entropy power} can be explicitly linked to the rate of creation of correlations among t…
We study driven finite quantum systems in contact with a thermal reservoir in the regime in which the system changes slowly in comparison to the equilibration time. The associated isothermal adiabatic theorem allows us to control the full statistics of energy transfers in quasi-static processes. Within this approach, we extend Landauer's Principle on the energetic cost of erasure processes to the level of the full statistics and elucidate the nature of the fluctuations breaking Landauer's bound.
Recent papers discussing thermodynamic processes in strongly coupled quantum systems claim a violation of Landauer's principle and imply a violation of the second law of thermodynamics. If true, this would have powerful consequences. Perpetuum mobiles could be build as long as the operating temperature is brought close to zero. It would also have serious consequences on thermodynamic derivations of information theoretic results, such as the Holevo bound. Here we argue why these claims are erroneous. Correlations occurring in the strongly coupled, quantum domain require a rethink of how entropy…
In two recent papers, Maroney and Turgut separately and independently show generalisations of Landauer's erasure principle to indeterministic logical operations, as well as to logical states with variable energies and entropies. Here we show that, although Turgut's generalisation seems more powerful, in that it implies but is not implied by Maroney's and that it does not rely upon initial probability distributions over logical states, it does not hold for non-equilibrium states, while Maroney's generalisation holds even in non-equilibrium. While a generalisation of Turgut's inequality to non-e…
Landauer's principle has seen a boom of interest in the last few years due to the growing interest in quantum information sciences. However, its relevance and validity in the contexts of quantum field theory (QFT) remain surprisingly unexplored. In the present paper, we consider Landauer's principle in qubit-cavity QFT interaction perturbatively, in which the initial state of the cavity QFT is chosen to be a vacuum or thermal state. In the vacuum case, the QFT always absorbs heat and jumps to excited states. For the qubit at rest, its entropy decreases, whereas if the qubit accelerates, it may…
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 study Landauer's Principle for Repeated Interaction Systems (RIS) consisting of a reference quantum system $\mathcal{S}$ in contact with a structured environment $\mathcal{E}$ made of a chain of independent quantum probes; $\mathcal{S}$ interacts with each probe, for a fixed duration, in sequence. We first adapt Landauer's lower bound, which relates the energy variation of the environment $\mathcal{E}$ to a decrease of entropy of the system $\mathcal{S}$ during the evolution, to the peculiar discrete time dynamics of RIS. Then we consider RIS with a structured environment $\mathcal{E}$ disp…
We assess two different non-equilibrium quantum Landauer bounds: the traditional approach based on the change in entropy, referred to as the `entropic bound', and one based on the details of the dynamical map, referred to as the `thermodynamic bound'. By first restricting to a simple exactly solvable model of a single two level system coupled to a finite dimensional thermal environment and by exploiting an excitation preserving interaction, we establish the dominant role played by the population terms in dictating the tightness of these bounds with respect to the dissipated heat, and clearly e…
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 review the physical foundations of Landauer's Principle, which relates the loss of information from a computational process to an increase in thermodynamic entropy. Despite the long history of the Principle, its fundamental rationale and proper interpretation remain frequently misunderstood. Contrary to some misinterpretations of the Principle, the mere transfer of entropy between computational and non-computational subsystems can occur in a thermodynamically reversible way without increasing total entropy. However, Landauer's Principle is not about general entropy transfers; rather, it mor…
We analyze Landauer's principle for repeated interaction systems consisting of a reference quantum system $\mathcal{S}$ in contact with an environment $\mathcal{E}$ which is a chain of independent quantum probes. The system $\mathcal{S}$ interacts with each probe sequentially, for a given duration, and the Landauer principle relates the energy variation of $\mathcal{E}$ and the decrease of entropy of $\mathcal{S}$ by the entropy production of the dynamical process. We consider refinements of the Landauer bound at the level of the full statistics (FS) associated to a two-time measurement protoc…
We study the Landauer's principle of an Unruh-DeWitt detector linearly coupled to Dirac field in $1 + 1$ dimensional cavity. When the initial state of the field is vacuum, we obtain the heat transfer and von Neumann entropy change perturbatively. For the thermal state, the heat transfer and entropy change are approximately obtained in the case where the interaction time is long enough and the Unruh-DeWitt detector is in resonance with one of the field mode. Compared to the real scalar field, we find the results of vacuum initial state differs solely from the helicity of the Dirac field and the…
We consider quantum decoherence and Landauer's principle in qubit-cavity quantum field theory (QFT) interaction, treating the qubit as the system and cavity QFT as the environment. In particular, we investigate the changes that occur in the system with a pure initial state and environment during the decoherence process, with or without energy dissipation, and compare the results with the case in which the initial state of the system is a mixed state and thus decoherence is absent. When we choose an interaction Hamiltonian such that the energy and coherence of the system change simultaneously, …
Landauer's principle provides a link between Shannon's information entropy and Clausius' thermodynamical entropy. We set up here a basic formula for the incremental free energy of a quantum channel, possibly relative to infinite systems, naturally arising by an Operator Algebraic point of view. By the Tomita-Takesaki modular theory, we can indeed describe a canonical evolution associated with a quantum channel state transfer. Such evolution is implemented both by a modular Hamiltonian and a physical Hamiltonian, the latter being determined by its functoriality properties. This allows us to mak…
Fidelity mechanics is formalized as a framework to investigate quantum critical phenomena in quantum many-body systems. This is achieved by introducing fidelity temperature to properly quantify quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer's principle at zero temperature. Fidelity flows are defined and may be interpreted as an alternative form of renormalization group flows. Thus, both stable and unstable f…
We develop the full counting statistics of dissipated heat to explore the relation with Landauer's principle. Combining the two-time measurement protocol for the reconstruction of the statistics of heat with the minimal set of assumptions for Landauer's principle to hold, we derive a general one-parameter family of upper and lower bounds on the mean dissipated heat from a system to its environment. Furthermore, we establish a connection with the degree of non-unitality of the system's dynamics and show that, if a large deviation function exists as stationary limit of the above cumulant generat…
Traditional form of the second law of thermodynamics is strongly restricted by three conditions: One is the initial joint state of the system and surroundings should be a product state, so that there exists no initial correlations. The second is the initial states of surroundings are in equilibrium thermodynamics. And the end is weak couplings between the system and surroundings. This formulation of the second law should be reexamined in order to understand the relations of thermodynamics and information theory, especially, when existing initial correlations. In this work, using the techniques…
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…
It is argued using a Gedankenexperiment that a scalable quantum memory could be used as a perpetuum mobile of the second kind and hence cannot be realized in Nature. The reasoning is based on the assumption that the Landauer's principle for measurements is a consequence of the second law of thermodynamics and not an independent postulate. This implies a modification of the Landauer's principle when applied for discrimination of equilibrium (metastable) states. While identification of the metastable state can be done at the infinitesimally low cost, a change of such a state involves dissipation…
We show that at least 2kTln2 of heat dissipation per qubit occurs in measurement-based quantum computation according to Landauer's principle. This result is derived by using only the fundamental fact that quantum physics respects the no-signaling principle.
We propose a quantum repeater protocol which builds on the well-known DLCZ protocol [L.M. Duan, M.D. Lukin, J.I. Cirac, and P. Zoller, Nature 414, 413 (2001)], but which uses photon pair sources in combination with memories that allow to store a large number of temporal modes. We suggest to realize such multi-mode memories based on the principle of photon echo, using solids doped with rare-earth ions. The use of multi-mode memories promises a speedup in entanglement generation by several orders of magnitude and a significant reduction in stability requirements compared to the DLCZ protocol.
