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Invalidity of the Landauer inequality for information erasure in the quantum regime

M. Nieuwenhuizen

Published Jun 5, 2002• 1 citation
OpenAlex

Abstract

A known aspect of the Clausius inequality is that an equilibrium system subjected to a squeezingdS < 0 of its entropy must release at least an amount |d¯Q| = T|dS| of heat. This serves as a basisfor the Landauer principle, which puts a lower bound T ln2 for the heat generated by erasure of onebit of information. Here we show that in the world of quantum entanglement this law is broken,suggesting that quantum carriers of information can be more efficient than assumed so far.

Related papers

Invalidity of the Landauer inequality for information erasure in the quantum regime

ARMEN E. ALLAHVERDYAN, Theo M. Nieuwenhuizen

A known aspect of the Clausius inequality is that an equilibrium system subjected to a squeezing $\d S<0$ of its entropy must release at least an amount $|\dbarrm Q|=T|\d S|$ of heat. This serves as a basis for the Landauer principle, which puts a lower bound $T\ln 2$ for the heat generated by erasure of one bit of information. Here we show that in the world of quantum entanglement this law is broken, suggesting that quantum carriers of information can be more efficient than assumed so far.

arXiv:cond-mat/0206052•Jun 5, 2002•0 citations

Breakdown of the Landauer bound for information erasure in the quantum regime

ARMEN E. ALLAHVERDYAN, Theo M. Nieuwenhuizen

A known aspect of the Clausius inequality is that an equilibrium system subjected to a squeezing dS < 0 of its entropy must release at least an amount the absolute value of dQ = T times the absolute value of dS of heat. This serves as a basis for the Landauer principle, which puts a lower bound T ln 2 for the heat generated by erasure of one bit of information. Here we show that in the world of quantum entanglement this law is broken. A quantum Brownian particle interacting with its thermal bath can either generate less heat or even absorb heat during an analogous squeezing process, due to entanglement with the bath. The effect exists even for weak but fixed coupling with the bath, provided that temperature is low enough. This invalidates the Landauer bound in the quantum regime, and suggests that quantum carriers of information can be more efficient than assumed so far.

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Quantum vs Classical Erasure: Equal Bounds but Unequal Costs

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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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The first law of thermodynamics, which governs energy conservation, is traditionally formulated as an equality. Surprisingly, we demonstrate that the first law alone implies a universal Landauer-like inequality linking changes in system entropy and energy. However, contrasting with the Landauer principle derived from the second law of thermodynamics, our obtained Landauer-like inequality solely relies on system information and is applicable in scenarios where implementing the Landauer principle becomes challenging. Furthermore, the Landauer-like inequality can complement the Landauer principle by establishing a dual {\it upper} bound on heat dissipation. We illustrate the practical utility of the Landauer-like inequality in dissipative quantum state preparation and quantum information erasure applications. Our findings offer new insights into identifying thermodynamic constraints relevant to the fields of quantum thermodynamics and the energetics of quantum information processing and more specifically, this approach could facilitate investigations into systems coupled to non-thermal baths or scenarios where access to bath information is limited.

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Effect of Quantum Coherence on Landauer’s Principle

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Landauer's principle provides a fundamental lower bound for energy dissipation occurring 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 off-diagonal (coherence) elements of the density matrix are decoupled. In this paper, we aimed to broaden the comparative study to include the influence of quantum coherence induced by the tilted system-reservoir interaction direction. By examining their dependence on the initial state of the information-bearing system, we find that the following properties of the bounds are generically held regardless of whether the influence of the coherence is present or not: the entropic bound serves as the tighter bound for a sufficiently mixed initial state, while the thermodynamic bound is tighter when the purity of the initial state is sufficiently high. The exception is the case where the system dynamics involve only phase relaxation; in this case, the two bounds coincide when the initial coherence is zero; otherwise, the thermodynamic bound serves the tighter bound. We also find the quantum information erasure inevitably accompanies constant energy dissipation caused by the creation of system-reservoir correlation, which may cause an additional source of energetic cost for the erasure.

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Quantum measurements and Landauer’s principle

Vladimir I Shevchenko

Information processing systems must obey laws of physics. One of particular examples of this general statement is known as Landauer’s principle - irreversible operations (such as erasure) performed by any computing device at finite temperature have to dissipate some amount of heat bound from below. Together with other results of this kind, Landauer’s principle represents a fundamental limit any modern or future computer must obey.

EPJ Web of Conferences•Jan 1, 2015•0 citations
A known aspect of the Clausius inequality is that an equilibrium system subjected to a squeezingdS < 0 of its entropy must release at least an amount |d¯Q| = T|dS| of heat. This serves as a basisfor the Landauer principle, which puts a lower bound T ln2 for the heat generated by erasure of onebit of information. Here we show that in the world of quantum entanglement this law is broken,suggesting that quantum carriers of information can be more efficient than assumed so far.
A known aspect of the Clausius inequality is that an equilibrium system subjected to a squeezing $\d S<0$ of its entropy must release at least an amount $|\dbarrm Q|=T|\d S|$ of heat. This serves as a basis for the Landauer principle, which puts a lower bound Tln⁡2T\ln 2Tln2 for the heat generated by erasure of one bit of information. Here we show that in the world of quantum entanglement this law is broken, suggesting that quantum carriers of information can be more efficient than assumed so far.
A known aspect of the Clausius inequality is that an equilibrium system subjected to a squeezing dS < 0 of its entropy must release at least an amount the absolute value of dQ = T times the absolute value of dS of heat. This serves as a basis for the Landauer principle, which puts a lower bound T ln 2 for the heat generated by erasure of one bit of information. Here we show that in the world of quantum entanglement this law is broken. A quantum Brownian particle interacting with its thermal bath can either generate less heat or even absorb heat during an analogous squeezing process, due to entanglement with the bath. The effect exists even for weak but fixed coupling with the bath, provided that temperature is low enough. This invalidates the Landauer bound in the quantum regime, and suggests that quantum carriers of information can be more efficient than assumed so far.
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.
The first law of thermodynamics, which governs energy conservation, is traditionally formulated as an equality. Surprisingly, we demonstrate that the first law alone implies a universal Landauer-like inequality linking changes in system entropy and energy. However, contrasting with the Landauer principle derived from the second law of thermodynamics, our obtained Landauer-like inequality solely relies on system information and is applicable in scenarios where implementing the Landauer principle becomes challenging. Furthermore, the Landauer-like inequality can complement the Landauer principle by establishing a dual {\it upper} bound on heat dissipation. We illustrate the practical utility of the Landauer-like inequality in dissipative quantum state preparation and quantum information erasure applications. Our findings offer new insights into identifying thermodynamic constraints relevant to the fields of quantum thermodynamics and the energetics of quantum information processing and more specifically, this approach could facilitate investigations into systems coupled to non-thermal baths or scenarios where access to bath information is limited.
Landauer's principle provides a fundamental lower bound for energy dissipation occurring 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 off-diagonal (coherence) elements of the density matrix are decoupled. In this paper, we aimed to broaden the comparative study to include the influence of quantum coherence induced by the tilted system-reservoir interaction direction. By examining their dependence on the initial state of the information-bearing system, we find that the following properties of the bounds are generically held regardless of whether the influence of the coherence is present or not: the entropic bound serves as the tighter bound for a sufficiently mixed initial state, while the thermodynamic bound is tighter when the purity of the initial state is sufficiently high. The exception is the case where the system dynamics involve only phase relaxation; in this case, the two bounds coincide when the initial coherence is zero; otherwise, the thermodynamic bound serves the tighter bound. We also find the quantum information erasure inevitably accompanies constant energy dissipation caused by the creation of system-reservoir correlation, which may cause an additional source of energetic cost for the erasure.