H-theorem in quantum physics

Lesovik, G. B.; Лебедев, А. В.; Sadovskyy, Ivan; Suslov, M. V.; Vinokur, V. M.

doi:10.1038/srep32815

Cited by 30 publications

(29 citation statements)

References 29 publications

(36 reference statements)

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“…One might then wonder whether the Landauer limit still remains applicable to such situations, and if phenomena such as quantum tunnelling can help to reduce the energy-time cost of a computation. Such questions concern the thermodynamics of quantum systems and are a priori non-trivial 13,14 . Here, we provide an experimental framework that allows us to explore them.…”

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confidence: 99%

Quantum Landauer erasure with a molecular nanomagnet

et al. 2018

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The erasure of a bit of information is an irreversible operation whose minimal entropy production of k B ln 2 is set by the Landauer limit 1 . This limit has been verified in a variety of classical systems, including particles in traps 2,3 and nanomagnets 4 . Here, we extend it to the quantum realm by using a crystal of molecular nanomagnets as a quantum spin memory and showing that its erasure is still governed by the Landauer principle. In contrast to classical systems, maximal energy efficiency is achieved while preserving fast operation owing to its high-speed spin dynamics. The performance of our spin register in terms of energy-time cost is orders of magnitude better than existing memory devices to date. The result shows that thermodynamics sets a limit on the energy cost of certain quantum operations and illustrates a way to enhance classical computations by using a quantum system.While a computation performed with an ideal binary logic gate (for example, NOT) has no lower energy dissipation limit [5][6][7] , one carried out in a memory device does. The reason is that in the former the bit is merely displaced isentropically in the space of states, whereas in the latter the minimal operation, called Landauer erasure, entails resetting the memory irrespective of its initial state. Let us see how this erasure applies to a classical N-bit register (Fig. 1a, left) and how the Landauer limit comes about. In the first stage, each bit of the register, in a definite state '0' or '1' , is allowed to explore the two binary states by lowering the potential barrier and through the action of temperature fluctuations. This doubling of the phase space is accompanied by an entropy production Δ S = k B ln 2 per bit, where k B is the Boltzmann constant. In the second stage, a work W ≥ TΔ S is required to reduce the register's entropy and phase space to their initial values 8 . The limit W = TΔ S is reached only if this reduction is carried out reversibly. This can be achieved when using a frictionless system in a quasi-static fashion (that is, at timescales slower than its relaxation time τ rel ), so that unwanted memory and hysteresis effects are avoided. For this reason, slow (fast) operation-with respect to the system-dependent τ rel -is generally associated with a lower (higher) dissipation.This complementarity between work and time suggests considering the product Wτ rel -rather than either of the two-as the figure of merit assessing the energy-time cost of a computation. On one hand, driven by the demand for speed, effort has been put into pursuing fast-switching storage devices. This has successfully produced stateof-the-art systems with picosecond timescales, although operating far (≳ 10 6 ) above the reversible limit [9][10][11][12] . On the other hand, reducing W down to the Landauer limit, at the expense of slow operation, has been beautifully demonstrated using small particles in traps 2,3 or single-domain nanomagnets 4 as envisioned by Landauer and Bennett 1,8 . All of the mentioned systems are large enough to ...

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confidence: 99%

Quantum Landauer erasure with a molecular nanomagnet

et al. 2018

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“…At the same time, these terms guarantee the unitarity of the evolution. Let us consider the evolution of the compound system within the framework and terminology of the quantum H-theorem [1]. Namely, we focus on the third and the fourth stages of the cycle.…”

Section: Quantum Version Of Maxwell Demon Based On a Single Qubitmentioning

confidence: 99%

“…This relation is the central result of Ref. [1]. It allows to formulate the quantum H-theorem as follows: If the r.h.s.…”

Section: Introductionmentioning

confidence: 99%

“…To determine whether the evolution belongs to the class of unital channels, implying that the system evolves with a non-negative entropy gain ∆S = S (Φ(ρ)) − S (ρ) ≥ 0, one has to check if Φ(1) =1. Using the unitarity ofÛ, one finds [1] …”

Section: Introductionmentioning

confidence: 99%

“…Recently, building on the mathematical formalism of quantum information theory (QIT), we have formulated a quantum H-theorem in terms of physical observables [1]. Consider a fixed-energy subspace E of the system's Hilbert space spanned by the orthonormal basis states |ψ i,E ⟩,Ĥ S |ψ i,E ⟩ = E |ψ i,E ⟩, where the index i denotes all of the system's remaining non-energy degrees of freedom andĤ S denotes the system Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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H-theorem and Maxwell demon in quantum physics

Kirsanov

Лебедев

Sadovskyy

et al. 2018

AIP Conference Proceedings

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Abstract. The Second Law of Thermodynamics states that temporal evolution of an isolated system occurs with non-diminishing entropy. In quantum realm, this holds for energy-isolated systems the evolution of which is described by the so-called unital quantum channel. The entropy of a system evolving in a non-unital quantum channel can, in principle, decrease. We formulate a general criterion of unitality for the evolution of a quantum system, enabling a simple and rigorous approach for finding and identifying the processes accompanied by decreasing entropy in energy-isolated systems. We discuss two examples illustrating our findings, the quantum Maxwell demon and heating-cooling process within a two-qubit system.

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Experimental Realization of Optimal Time‐Reversal on an Atom Chip for Quantum Undo Operations

et al. 2022

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The authors report the use of the dressed chopped random basis optimal control algorithm to realize time‐reversal procedures. The latter are aimed for the implementation of quantum undo operations in quantum technology contexts as quantum computing and quantum communications. The last performed operation can be time‐reversed via the undo command so as to perfectly restore a condition in which any new operation, chosen by the external user, can be applied. By generalizing this concept, the undo command can also allow for the reversing of a quantum operation in a generic time instant of the past. Here, thanks to optimal time‐reversal routines, all these functionalities are experimentally implemented on the fivefold F=2$F=2$ Hilbert space of a Bose–Einstein condensate of non‐interacting 87Rb atoms in the ground state, realized with an atom chip. Each time‐reversal transformation is attained by designing an optimal modulated radio frequency field, achieving on average an accuracy of around 92% in any performed test. The experimental results are accompanied by a thermodynamic interpretation based on the Loschmidt echo. These findings are expected to promote the implementation of time‐reversal operations in a real scenario of gate‐based quantum computing with a more complex structure than the five‐level system considered here.

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H-theorem in quantum physics

Cited by 30 publications

References 29 publications

Quantum Landauer erasure with a molecular nanomagnet

Quantum Landauer erasure with a molecular nanomagnet

H-theorem and Maxwell demon in quantum physics

Experimental Realization of Optimal Time‐Reversal on an Atom Chip for Quantum Undo Operations

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