Does decoherence in the thermodynamic limit exist?

Sharpening the Second Law of Thermodynamics with the Quantum Bayes' Theorem

We prove a generalization of the classic Groenewold-Lindblad entropy inequality, combining decoherence and the quantum Bayes theorem into a simple unified picture where decoherence increases entropy while observation decreases it. This provides a rigorous quantum-mechanical version of the second law of thermodynamics, governing how the entropy of a system (the entropy of its density matrix, partial-traced over the environment and conditioned on what is known) evolves under general decoherence and observation. The powerful tool of spectral majorization enables both simple alternative proofs of …

Classical states and decoherence by unitary evolution in the thermodynamic limit

It is shown how classical states, meant as states representing a classical object, can be produced in the thermodynamic limit, retaining the unitary evolution of quantum mechanics. Besides, using a simple model of a single spin interacting with a spin-bath, it is seen how decoherence, with the off-diagonal terms in the density matrix going to zero, can be obtained when the number of the spins in the bath is taken to go formally to infinity. In this case, indeed, the system appears to flop at a frequency being formally infinity that, from a physical standpoint, can be proved equivalent to a tim…

Work done in a decoherence process

We investigate the thermodynamics of a quench realized by turning on an interaction generating pure decoherence. We characterize the work probability distribution function, also with a fluctuation relation, a lower bound of the work and by considering some physical examples.

退相干的热力学

Thermodynamics of decoherence

本文研究纯退相干的非平衡热力学，揭示退相干本身可导致具有积分涨落关系且与熵产生相关的非平凡热耗散，并通过超冷费米气体中的量子比特退相干实例加以验证。

保持对称性：通过退相干实现自发对称性破缺

Preserving Symmetry: Spontaneous Symmetry Breaking through Decoherence

本文针对有限量子系统的局域化问题，通过量子化环境，利用退相干分支实现局域化，复合系统态矢量仍保持平移对称，可恢复半经典描述并预测实验可区分修正。

On reduction of the wave-packet, decoherence, irreversibility and the second law of thermodynamics

We prove a quantum version of the second law of thermodynamics: the (quantum) Boltzmann entropy increases if the initial (zero time) density matrix decoheres, a condition generally satisfied in Nature. It is illustrated by a model of wave-packet reduction, the Coleman-Hepp model, along the framework introduced by Sewell in his approach to the quantum measurement problem. Further models illustrate the monotonic-versus-non-monotonic behavior of the quantum Boltzmann entropy in time. As a last closely related topic, decoherence, which was shown by Narnhofer and Thirring to enforce macroscopic pur…

Thermodynamic Limit and Decoherence: Rigorous Results

Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is considered. These results translate in a set of theorems proving that these effects can be effectively at work producing an emerging classical world without recurring to any external entity that in some cases cannot be properly defined. In a many-body system has been recently shown that Gaussian decay of the coherence is the rule with a duration of recurrence m…

Thermodynamics of quantum coherence

Quantum decoherence is seen as an undesired source of irreversibility that destroys quantum resources. Quantum coherences seem to be a property that vanishes at thermodynamic equilibrium. Away from equilibrium, quantum coherences challenge the classical notions of a thermodynamic bath in a Carnot engines, affect the efficiency of quantum transport, lead to violations of Fourier's law, and can be used to dynamically control the temperature of a state. However, the role of quantum coherence in thermodynamics is not fully understood. Here we show that the relative entropy of a state with quantum …

Chaos, Thermodynamics and Quantum Mechanics: an Application to Celestial Dynamics

We address the issue of the quantum-classical correspondence in chaotic systems using, as recently done by Zurek [e-print quant-ph/9802054], the solar system as a whole as a case study: this author shows that the classicality of the planetary motion is ensured by the environment-induced decoherence. We show that equivalent results are provided by the theories of spontaneous fluctuations and that these latter theories, in some cases, result in a still faster process of decoherence. We show that, as an additional benefit, the assumption of spontaneous fluctuation makes it possible to genuinely d…

Entropy Defined, Entropy Increase and Decoherence Understood, and Some Black-Hole Puzzles Solved

Statistical mechanics explains thermodynamics in terms of (quantum) mechanics by equating the entropy of a microstate of a closed system with the logarithm of the number of microstates in the macrostate to which it belongs, but the question `what is a macrostate?' has never been answered except in a vague, subjective, way. However Hawking's discovery of black hole evaporation led to a formula for black hole entropy with no subjective element. In this letter, we argue from this result, together with the assumption that `black hole thermodynamics is just ordinary thermodynamics applied to black …

Decoherence suppression via environment preparation

To protect a quantum system from decoherence due to interaction with its environment, we investigate the existence of initial states of the environment allowing for decoherence-free evolution of the system. For models in which a two-state system interacts with a dynamical environment, we prove that such states exist if and only if the interaction and self-evolution Hamiltonians share an eigenstate. If decoherence by state preparation is not possible, we show that initial states minimizing decoherence result from a delicate compromise between the environment and interaction dynamics.

Open-system approach to nonequilibrium quantum thermodynamics at arbitrary coupling

We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths beyond perturbation theory. Our approach is based on the exact time-local quantum master equation for the reduced open system states, and on a principle of minimal dissipation. This principle leads to a unique prescription for the decomposition of the master equation into a Hamiltonian part representing coherent time evolution and a dissipator part describing dissipation and decoherence. Employing this decomposition we demonstrate how to define work, heat, and entropy production…

低密度具有内部结构的气体中热力学一致的碰撞主方程

Thermodynamically consistent collisional master equation in a low-density gas with internal structure

本文提出一种量子系统与具有内部自由度的稀薄热气体发生非弹性散射的动力学主方程，证明了气体在热平衡时的热力学一致性，并揭示了气体内部与运动状态温度不同时作为非平衡储层产生能量的机制。

A Quantum Many-Body Instability in the Thermodynamic Limit

Intrinsic decoherence in the thermodynamic limit is shown for a large class of many-body quantum systems in the unitary evolution in NMR and cavity QED. The effect largely depends on the inability of the system to recover the phases. Gaussian decaying in time of the fidelity is proved for spin systems and radiation-matter interaction.

空间量子比特中由空气分子散射导致的退相干率表达式

Decoherence rate expression due to air molecule scattering in spatial qubits

该研究给出空气分子散射导致空间量子比特退相干的求解方案，复现已知波长极限，对比现有插值方法并评估宏观空间叠加态相关参数，还分析了干涉仪中退相干率的时间依赖性。

Correlations transference and apparition of a metastable decoherence-free subspace in dissipative reservoirs

The dynamic of correlations in a system composed of a two-mode quantum field coupled with the environment is studied. The quantum field corresponds to two entangled coherent states whose amplitude we vary up to the mesoscopic regime. We show that under the onset of decoherence, correlations in the quantum field are not lost but transferred to the environment. We also found that sudden transitions in the decoherence regimes appear along with the dynamics depending on the coherent states' amplitude. Increasing the amplitude of the entangled coherence state results in the apparition of a metastab…

Decoherence, Einselection, and the Existential Interpretation (the Rough Guide)

The roles of decoherence and environment-induced superselection in the emergence of the classical from the quantum substrate are described. The stability of correlations between the einselected quantum pointer states and the environment allows them to exist almost as objectively as classical states were once thought to exist: There are ways of finding out what is the pointer state of the system which utilize redundancy of their correlations with the environment, and which leave einselected states essentially unperturbed. This relatively objective existence of certain quantum states facilitates…

Decoherence-free subspaces for a quantum register interacting with a spin environment

We study a model of a quantum spin register interacting with an environment of spin particles in quantum-measurement limit. In the limit of collective decoherence we obtain the form of state vectors that constitute high-dimensional decoherence-free subspaces (DFS). In a more general setting we present sufficient and necessary conditions for existence of low-dimensional DFSs that can be used to construct subspaces of higher dimension.

广义多级振幅阻尼通道及其热力学性能

Generalized multilevel amplitude damping channels and their thermodynamic performances

本文引入广义多级振幅阻尼（GMAD）通道来模拟与热环境耦合的qudit中的噪声和退相干效应，通过评估功泛函和ergotropic电容研究GMAD下能量资源的退化，揭示了ergotropic电容随环境温度非单调变化以及马尔可夫Mpemba效应等反直觉现象。

Lie Algebras and Suppression of Decoherence in Open Quantum Systems

Since there are many examples in which no decoherence-free subsystems exist (among them all cases where the error generators act irreducibly on the system Hilbert space), it is of interest to search for novel mechanisms which suppress decoherence in these more general cases. Drawing on recent work (quant-ph/0502153) we present three results which indicate decoherence suppression without the need for noiseless subsystems. There is a certain trade-off; our results do not necessarily apply to an arbitrary initial density matrix, or for completely generic noise parameters. On the other hand, our c…

A Master Equation for Gravitational Decoherence: Probing the Textures of Spacetime

We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis, in contrast to most existing theories of gravitational decoherence. We poi…

量子态抗退相干的普遍保护

Universal Protection of Quantum States from Decoherence

本文提出一种无需预先知识的量子态保护协议，通过扩展希尔伯特空间实现对任意量子态的退相干保护。

Universal Quantum Computation in a Neutral Atom Decoherence Free Subspace

In this paper, we propose a way to achieve protected universal computation in a neutral atom quantum computer subject to collective dephasing. Our proposal relies on the existence of a Decoherence Free Subspace (DFS), resulting from symmetry properties of the errors. After briefly describing the physical system and the error model considered, we show how to encode information into the DFS and build a complete set of safe universal gates. Finally, we provide numerical simulations for the fidelity of the different gates in the presence of time-dependent phase errors and discuss their performance…

Decoherence-Free Entropic Gravity: Model and Experimental Tests

Erik Verlinde's theory of entropic gravity [arXiv:1001.0785], postulating that gravity is not a fundamental force but rather emerges thermodynamically, has garnered much attention as a possible resolution to the quantum gravity problem. Some have ruled this theory out on grounds that entropic forces are by nature noisy and entropic gravity would therefore display far more decoherence than is observed in ultra-cold neutron experiments. We address this criticism by modeling linear gravity acting on small objects as an open quantum system. In the strong coupling limit, when the model's unitless f…

基于相位耦合的量子极限环：面向NISQ热力学器件的框架

Quantum limit cycles from phase coupling: A framework for NISQ thermodynamic devices

该研究提出基于相位耦合的量子极限环框架，将Kuramoto模型与Van der Pol振荡器量子化后耦合量子比特，在量子热力学环境中实现稳定极限环，观测到新颖效应，为NISQ热力学器件提供新方案。

通过通用统计力学映射理解局域退相干下的稳定子码

Understanding Stabilizer Codes Under Local Decoherence Through a General Statistical Mechanics Mapping

本研究通过两种方法构建稳定子码退相干基态矩到经典统计力学模型的映射，证明信息容量度量对应热力学量，分析了3D toric code等的解码阈值，揭示了映射的去规范性质。

退相干下CSS码的相干信息

Coherent information for CSS codes under decoherence

本文通过将一般CSS码在局部非相干Pauli错误下的密度矩阵对角化并映射到经典统计力学模型，解析计算了相干信息，从而严格建立了量子码解码转变与经典随机模型相变之间的联系，并证明最优解码器可达到基本阈值。

Dynamical disappearance of superposition states in the thermodynamic limit

It is shown that a macroscopic superposition state of radiation, strongly interacting with an ensemble of two-level atoms, is removed generating a coherent state describing a classical radiation field, when the thermodynamic limit is taken on the unitary evolution obtained by the Schroedinger equation. Decoherence appears as a dynamical effect in agreement with a recent proposal [M. Frasca, Phys. Lett. A 283, 271 (2001)]. To prove that this effect is quite general, we show that this same behavior appears when a superposition of two Fock number states is also considered. Higher order correction…

Quantum digital-to-analog conversion algorithm using decoherence

We consider the problem of mapping digital data encoded on a quantum register to analog amplitudes in parallel. It is shown to be unlikely that a fully unitary polynomial-time quantum algorithm exists for this problem; NP becomes a subset of BQP if it exists. In the practical point of view, we propose a nonunitary linear-time algorithm using quantum decoherence. It tacitly uses an exponentially large physical resource, which is typically a huge number of identical molecules. Quantumness of correlation appearing in the process of the algorithm is also discussed.

Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit

In this work we examine the effect of phase-space noncommutativity on some typically quantum properties such as quantum beating, quantum information, and decoherence. To exemplify these issues we consider the two-dimensional noncommutative quantum harmonic oscillator whose components behavior we monitor in time. This procedure allows us to determine how the noncommutative parameters are related to the missing information quantified by the linear quantum entropy and by the mutual information between the relevant Hilbert space coordinates. Particular questions concerning the thermodynamic limit …

Decoherence of massive superpositions induced by coupling to a quantized gravitational field

We present a simple calculation leading to the quantum gravitationally-induced decoherence of a spatial superposition of a massive object in the linear coupling regime. The point of this calculation is to illustrate that the gravitationally-induced collapse could be of the same origin as any other collapse, i.e. due to the entanglement between the system (here a massive object) and its environment (in this case gravity, but it could well be the electromagnetic or any other field). We then point out that, in some cases, one has to be careful when concluding that matter-wave interference of larg…

测量由量子真空涨落引起的退相干

Measuring Decoherence Due to Quantum Vacuum Fluctuations

本研究计算了粒子电荷突然开关时由真空涨落引起的领头阶退相干效应，并提出实验装置以检测该效应，旨在深入理解真空涨落本质并作为退相干理论的新精度测试。