Claus Kiefer
It is shown how the programme of decoherence can be applied in the context of quantum field theory. To illustrate the role of gauge invariance, we first discuss the charge superselection rule in quantum electrodynamics in some detail. We then present an example where macroscopic electromagnetic fields are ``measured" through interaction with charges and thereby rendered classical.
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Proposals to solve the problems of quantum measurement via non-linear CPT-violating modifications of quantum dynamics are argued to provide a possible fundamental explanation for the irreversibility of statistical mechanics as well. The argument is expressed in terms of collapse-free accounts. The reverse picture, in which statistical irreversibility generates quantum irreversibility, is argued to be less satisfactory because it leaves the Born probability rule unexplained.
Universal trade-off structure between symmetry, irreversibility, and quantum coherence in quantum processes
该研究提出了对称性、不可逆性与量子相干性间的普适权衡关系，揭示了改变局部守恒荷必然导致不可逆性且可被相干性缓解，广泛适用于非平衡物理、量子信息处理及黑洞信息问题。
The issue of irreversibility in a universe with time-reversal-symmetric laws is a central problem in physics. % , and, in particular, to statistical mechanics, information theory and quantum thermodynamics. In this letter, we discuss for the first time how irreversibility can emerge within the recently proposed constructor theory framework. Here irreversibility is expressed as the requirement that a task is possible, while its inverse is not. In particular, we demonstrate that this irreversibility is compatible with quantum theory's time reversal symmetric laws, by exploiting a specific model,…
We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation - quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under LOCC for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distilla…
The Halting problem of a quantum computer is considered. It is shown that if halting of a quantum computer takes place the associated dynamics is described by an irreversible operator.
A hypothetical formulation of quantum mechanics is presented so as to reconcile it with macro-realism. On the analogy drawn from thermodynamics, an objective description of wave packet reduction is postulated, in which a characteristic energy scale and a time scale are introduced to separate the quantum and classical conceptions.
Fluctuations and Irreversibility: Historical and Modern Perspectives
本文综述了量子波动理论与线性响应理论的联系，探讨了量子系统中耗散功对非经典效应的影响，以及其在量子技术发展中的重要性。
It is argued that setting isolated systems as primary scope of field theory and looking at particles as derived entities, the problem of an objective anchorage of quantum mechanics can be solved and irreversibility acquires a fundamental role. These general ideas are checked in the case of the Boltzmann description of a dilute gas.
Quantum mechanics in the Rigged Hilbert Space formulation describes quasistationary phenomena mathematically rigorously in terms of Gamow vectors. We show that these vectors exhibit microphysical irreversibility, related to an intrinsic quantum mechanical arrow of time, which states that preparation of a state has to precede the registration of an observable in this state. Moreover, the Rigged Hilbert Space formalism allows the derivation of an exact golden rule describing the transition of a pure Gamow state into a mixture of interaction-free decay products.
In classical thermodynamic processes the unavoidable presence of irreversibility, quantified by the entropy production, carries two energetic footprints: the reduction of extractable work from the optimal, reversible case, and the generation of a surplus of heat that is irreversibly dissipated to the environment. Recently it has been shown that in the quantum regime an additional quantum irreversibility occurs that is linked to decoherence into the energy basis. Here we employ quantum trajectories to construct distributions for classical heat and quantum heat exchanges, and show that the heat …
We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal g…
Thermodynamics of quantum coherence has attracted growing attention recently, where the thermodynamic advantage of quantum superposition is characterized in terms of quantum thermodynamics. We investigate thermodynamic effects of quantum coherent driving in the context of the fluctuation theorem. We adopt a quantum-trajectory approach to investigate open quantum systems under feedback control. In these systems, the measurement backaction in the forward process plays a key role, and therefore the corresponding time-reversed quantum measurement and post-selection must be considered in the backwa…
We show that some classically chaotic quantum systems uncoupled from noisy environments may generate intrinsic decoherence with all its associated effects. In particular, we have observed time irreversibility and high sensitivity to small perturbations in the initial conditions in a quasiperiodic version of the kicked rotor. The existence of simple quantum systems with intrinsic decoherence clarifies the quantum--classical correspondence in chaotic systems.
We investigate temporal evolution of von Neumann's entropy in exemplary quantum mechanical systems and show that it grows in systems evolving with incrementally increasing decoherence during scattering processes. We demonstrate that the origin of irreversibility lies in complexity of preparing time-reversed quantum states due to entanglement and in partitioning of the wave function of the evolving system.
Universal tradeoff relations between resource cost and irreversibility of channels: General-resource Wigner-Araki-Yanase theorems and beyond
该研究在量子资源理论框架下证明了量子信道资源成本与不可逆性的普适权衡关系，推导了能量/自由能成本权衡、拓展版Wigner-Araki-Yanase定理等关键结论，揭示了量子性与不可逆性的普遍关联。
Quantifying Irreversibility via Bayesian Subjectivity for Classical & Quantum Linear Maps
本文通过贝叶斯主观性量化经典和量子线性映射的不可逆性，探讨信息损失对初始状态回溯预测的影响，揭示不可逆过程的直观与微妙洞察。
The aim of these lectures is to investigate the transfer of information occurring in course of quantum interactions. In particular, I shall explore circumstances in which such an information transfer with the quantum environment of the considered quantum system leads to the destruction of the phase coherence between the states of the privileged basis in the system Hilbert space. This basis shall be called the pointer basis. I shall argue that states of this pointer basis correspond to the ``classical'' states of the observables of the quantum system in question.
Counterfactuals in Macroscopic Quantum Physics: Irreversibility, Measurement and Locality
本论文利用反事实推理、构造子理论与量子信息理论，探讨了量子理论在宏观尺度下的不可逆性、测量与定域性挑战，揭示了量子热力学新特征及量子算符非对易性影响，强化了普适量子理论对微观与宏观系统的一致描述能力。
We consider thermal relaxation process of a quantum system attached to a single or multiple reservoirs. Quantifying the degree of irreversibility by entropy production, we prove that the irreversibility of the thermal relaxation is lower-bounded by a relative entropy between the unitarily-evolved state and the final state. The bound characterizes the state discrepancy induced by the non-unitary dynamics, thus reflecting the dissipative nature of irreversibility. Intriguingly, the bound can be evaluated solely in terms of the initial and final states and the system Hamiltonian; hence, providing…
Irreversibility is a fundamental concept with important implications at many levels. It pinpoints the fundamental difference between the intrinsically reversible microscopic equations of motion and the unidirectional arrow of time that emerges at the macroscopic level. More pragmatically, a full quantification of the degree of irreversibility of a given process can help in the characterisation of the performance of thermo-machines operating at the quantum level. Here, we review the concept of entropy production, which is commonly intended as {\it the} measure of thermodynamic irreversibility o…
Fluctuation theorems are relations constraining the out-of-equilibrium fluctuations of thermodynamic quantities like the entropy production that were initially introduced for classical or quantum systems in contact with a thermal bath. Here we show, in the absence of thermal bath, the dynamics of continuously measured quantum systems can also be described by a fluctuation theorem, expressed in terms of a recently introduced arrow of time measure. This theorem captures the emergence of irreversible behavior from microscopic reversibility in continuous quantum measurements. From this relation, w…
Clausius inequality has deep implications for reversibility and the arrow of time. Quantum theory is able to extend this result for closed systems by inspecting the trajectory of the density matrix on its manifold. Here we show that this approach can provide an upper and lower bound to the irreversible entropy production for open quantum systems as well. These provide insights on the thermodynamics of the information erasure. Limits of the applicability of our bounds are discussed, and demonstrated in a quantum photonic simulator.
We investigate the link between the irreversibility generated by a stationary dissipative process and the correlations established within a composite quantum system. We provide two equivalent expressions for the entropy generated in the non-equilibrium steady state of coupled quantum harmonic oscillators that allow for a simple interpretation of the onset of irreversibility. We then unveil a quantitative relation between the entropy production rate and correlations, both total and quantum, built between the two oscillators. In the small-coupling limit, the entropy production rate is shown to b…
We argue that two distinct probes of quantum chaos, i.e., the growth of noncommutativity of two unequal-time operators and the degree of irreversibility in a time-reversal test, are equivalent for initially localized states. We confirm this for interacting nonintegrable many-body systems and a quantum kicked rotor. Our results show that three-point out-of-time-ordered correlators dominate the growth of the squared commutator for initially localized states, in stark contrast to four-point out-of-time-ordered correlators that have extensively been studied for thermal initial states.
We identify and explore the intriguing property of resource resonance arising within resource theories of entanglement, coherence and thermodynamics. While the theories considered are reversible asymptotically, the same is generally not true in realistic scenarios where the available resources are bounded. The finite-size effects responsible for this irreversibility could potentially prohibit small quantum information processors or thermal machines from achieving their full potential. Nevertheless, we show here that by carefully engineering the resource interconversion process any such losses …
Irreversibility in quantum measurements is considered from the point of quantum information theory. For that purpose the information transfer between the measured object S and measuring system O is analyzed. It's found that due to the principal constraints of quantum-mechanical origin, the information about the purity of S state isn't transferred to O during the measurement of arbitraryS observable V. Consequently O can't discriminate the pure and mixed S ensembles with the same <V>. As the result, the random outcomes should be detected by O in V measurement for S pure ensemble of V eigenstate…
Entropy production characterizes irreversibility. This viewpoint allows us to consider the thermodynamic uncertainty relation, which states that a higher precision can be achieved at the cost of higher entropy production, as a relation between precision and irreversibility. Considering the original and perturbed dynamics, we show that the precision of an arbitrary counting observable in continuous measurement of quantum Markov processes is bounded from below by Loschmidt echo between the two dynamics, representing the irreversibility of quantum dynamics. When considering particular perturbed d…
We study the problem of irreversibility when the dynamical evolution of a many-body system is described by a stochastic quantum circuit. Such evolution is more general than a Hamiltonian one, and since energy levels are not well defined, the well-established connection between the statistical fluctuations of the energy spectrum and irreversibility cannot be made. We show that the entanglement spectrum provides a more general connection. Irreversibility is marked by a failure of a disentangling algorithm and is preceded by the appearance of Wigner-Dyson statistical fluctuations in the entanglem…
We derive quantum nonequilibrium equalities in absolutely irreversible processes. Here by absolute irreversibility we mean that in the backward process the density matrix does not return to the subspace spanned by those eigenvectors that have nonzero weight in the initial density matrix. Since the initial state of a memory and the postmeasurement state of the system are usually restricted to a subspace, absolute irreversibility occurs during the measurement and feedback processes. An additional entropy produced in absolute irreversible processes needs to be taken into account to derive nonequi…
The analysis of dissipation and dephasing in driven mesoscopic devices requires a distinction between two notions of quantum irreversibility. One ("Loschmidt echo") is related to "time reversal", while the other is related to "driving reversal". In the latter context the time of maximum return (compensation) should substitute the inappropriate notion of "echo" time. Non-perturbative features manifest themselves in the energy spreading process. This is demonstrated for the prototype random-matrix Wigner model, where the compensation time and the system response exhibit a non-universal scaling b…
The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of system's physical properties. In addition, strong interactions in many-body systems strikingly affect the energy-fluctuation statistics along a non-equilibrium dynamics. By driving transient currents to oppose the precursor to metal-Mott insulator transition in a diversity of dynamical regimes, we show how increasing correlations dramatically affect the statistics of energy fluctuations and consequently the quantum work distribu…
We demonstrate the irreversibility of asymptotic entanglement manipulation under quantum operations that completely preserve the positivity of partial transpose (PPT), resolving a major open problem in quantum information theory. Our key tool is a new efficiently computable additive lower bound for the asymptotic relative entropy of entanglement with respect to PPT states, which can be used to evaluate the entanglement cost under local operations and classical communication (LOCC). We find that for any rank-two mixed state supporting on the $3\otimes3$ antisymmetric subspace, the amount of dis…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the appearance of irreversibility that applies to coherent, isolated systems in a pure quantum state. This equilibration mechanism requires only an assumption of sufficiently complex internal dynamics and natural information-theoretic constraints arising from the infeasibility of collecting an astronomical amount of measurement data. Remarkably, we are able to …
Irreversibility of decorrelating processes: an experimental assessment in cavity QED
本文通过腔量子电动力学实验，测量了在消除量子相干性和完全去相关局部状态过程中产生的熵产，从而评估了量子不可逆性。
The formalism of quantum systems with diagonal singularities is applied to describe scattering processes. Well defined states are obtained for infinite time, which are related to a ''weak form'' of intrinsic irreversibility. Real and complex generalized spectral decompositions of the Liouville-Von Neumann superoperator are computed. The physical meaning of ''Gamov states'' is discussed.
The idea of perturbation independent decay (PID) has appeared in the context of survival-probability studies, and lately has emerged in the context of quantum irreversibility studies. In both cases the PID reflects the Lyapunov instability of the underlying semiclassical dynamics, and it can be distinguished from the Wigner-type decay that holds in the perturbative regime. The theory of the survival probability is manifestly related to the parametric theory of the local density of states (LDOS). In this Paper we demonstrate that in spite of the common "ideology", the physics of quantum irrever…
The Doppler effect of moving atoms can create irreversibility of light. We show that the laser field in electromagnetic induced transparency (EIT) scheme with atomic motion can control the directional propagation of two counter-propagating probe fields in atomic gas cell. The quantum coherence effect serves as an optical transistor. Interference of the two output fields from the cell shows useful feature for determining the mean atomic velocity and can be useful as quantum velocimeter. We also find that the sign of the dispersive phase in EIT has a unique property, which helps to explain certa…
We derive quantitative relations among several naturally defined measures of classical and nonclassical correlations in a bipartite quantum state. We also obtain an upper bound of entanglement irreversibility and a sufficient condition for reversible entanglement. The additivity of entanglement of formation is directly related to the additivity of quantum discord as well as a certain measure of classical correlation.
The quantum measurement problem considered for measuring system (MS) model which consist of measured state S (particle), detector D and information processing device O. For spin chains and other O models the state evolution for MS observables measurements studied. It's shown that specific O states structure forbids the measurement of MS interference terms which discriminate pure and mixed S states. It results in the reduction MS Hilbert space to O representation in which MS evolution is irreversible, which in operational formalism corresponds to S state collapse. In radiation decoherence O mod…
The inception of a universal gravity-related irreversibility took place originally in quantum cosmology. The ultimate reason of universal irreversibility is thought to come from black holes close to the Planck scale. Completely different instances of irreversibilities are quantum state reductions unrelated to gravity or relativity but related to measurement devices. However, an intricate relationship between Newton gravity and quantized matter might result in fundamental and spontaneous quantum state reduction --- in the non-relativistic Schrödinger-Newton context. The above two concepts of fu…
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…
The relation between the thermodynamic entropy production and non-Markovian evolutions is matter of current research. Here, we study the behavior of the stochastic entropy production in open quantum systems undergoing unital non-Markovian dynamics. In particular, for the family of Pauli channels we show that in some specific time intervals both the average entropy production and the variance can decrease, provided that the quantum dynamics fails to be P-divisible. Although the dynamics of the system is overall irreversible, our result may be interpreted as a transient tendency towards reversib…
The discussion on time-reversal in quantum mechanics exists at least since Wigner's ``Uber die Operation der Zeitumkehr in der Quantenmechanik'' paper in 1932. If and how the dynamics of the quantum world is time-reversible has been the subject of many controversies. Some have seen quantum mechanics as fundamentally time-irreversible, see for example von Neumann, and some have seen in that the ultimate cause of time's arrow and second law behavior. In his best-selling book ``The Emperor's New Mind'', Roger Penrose argues similarly and concludes that ``our sought-for quantum gravity must be a t…
Error and Disturbance as Irreversibility with Applications: Unified Definition, Wigner--Araki--Yanase Theorem and Out-of-Time-Order Correlator
本文提出利用不可逆性定义误差与扰动的框架，通过量子梳结构将测量不可逆性转化为辅助量子比特系统的不可逆性，并揭示不可逆性与非时间序相关子符之间的操作联系。
Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field and experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergen…
Irreversibility in an optical parametric driven optomechanical system
本文研究光学参量振荡器非线性对混合光机械系统熵产生率与量子关联的影响，推导修正熵产生率，发现小失谐下不可逆性显著偏离，并证明可通过调节非线性相位降低系统不可逆性。
The main idea of "Quantum Chaos" studies is that Quantum Mechanics introduces two energy scales into the study of chaotic systems: One is obviously the mean level spacing $Δ\propto\hbar^d$, where $d$ is the dimensionality; The other is $Δ_b\propto\hbar$, which is known as the non-universal energy scale, or as the bandwidth, or as the Thouless energy. Associated with these two energy scales are two special quantum-mechanical (QM) regimes in the theory of driven system. These are the QM adiabatic regime, and the QM non-perturbative regime respectively. Otherwise Fermi golden rule applies, and li…
After a review of the arrows of time, we describe the possibilities of a time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's bra-ket formalism, allows the choice of asymmetric boundary conditions analogous to the retarded solutions of the Maxwell equations for the radiation arrow of time. This led to irreversibility on the microphysical level as exemplified by decaying states or resonances. Resonances are mathematically represented by Gamow kets, functionals over a space of very well-behaved…
A generalization of the Gibbs-von Neumann relative entropy is proposed based on the quantum BBGKY [Bogolyubov-Born-Green-Kirkwood-Yvon] hierarchy as the nonequilibrium entropy for an N-body system. By using a generalization of the Liouville-von Neumann equation describing the evolution of a density super- operator, it is demonstrated that the entropy production for an isolated system is non-negative, which provides an arrow of time. Moreover, following the procedure of non-equilibrium thermodynamics a master matrix is introduced for which a mi- croscopic expression is obtained. Then, the quant…
The time reversal and irreversibility in conventional quantum mechanics are compared with those of the rigged Hilbert space quantum mechanics. We discuss the time evolution of Gamow and Gamow-Jordan vectors and show that the rigged Hilbert space case admits a new kind of irreversibility which does not appear in the conventional case. The origin of this irreversibility can be traced back to different initial-boundary conditions for the states and observables. It is shown that this irreversibility does not contradict the experimentally tested consequences of the time-reversal invariance of the c…
The polarization emerging in the subsequent scattering processes can never exceed $1$ which corresponds to the fully polarized pure state. This property is shown to be provided by the addition rule similar to that for relativistic velocities never exceeding the speed of light. The cases of spin $1/2$ and $1$ are considered. The photon linear polarization in Thomson scattering is monotonically increasing. This directness is shown to be a consequence of spin measurement procedure and may be the particular example of ithe anticipated relation between quantum measurement and time irreversibility. …
The Loschmidt echo -- also known as fidelity -- is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is perturbation independent, and given by the classical Lyapunov exponent. But observation of the Lyapunov decay depends strongly on the type of initial state upon which an average is done. This dependence can be removed by averaging the fid…
Quantum irreversibility of quasistatic protocols for finite-size quantized systems
该研究针对有限尺寸量子系统准静态过程的可逆性问题，分析了扫描转移凝聚玻色子协议中绝热输运与混沌辅助耗散的作用，揭示了量子涨落主导区的量子-经典对应破缺，指出双轨道近似及多体Landau-Zener范式的局限性。
Very Strong Irreversibility of Quantum Entanglement
该研究证明量子纠缠的不可逆性在指数强逆层面依然存在，解决了Lami与Regula的猜想，还推导了非纠缠操作下指数强逆成本的半定规划下界，并构造了展现该特性的反对称态族。
When a physical system is put in contact with a very large thermal bath, it undergoes a dissipative (i.e., an apparently irreversible) process that leads to thermal equilibrium. This dynamical process can be described fully within quantum physics, involving only unitary, therefore reversible, maps. The information, initially present in the system, is not erased, but is diluted in the bath because of entanglement. Irreversibility may arise if, after quantum information has been thus diluted, some classical information is lost. This paper reviews a model for thermalization that displays these fe…
Interrelation of Non-Classicality, Entropy, Irreversibility and Work extraction in Open Quantum Systems
本研究在多种开放量子系统中揭示了非经典体积与熵、熵产生与ergotropy之间的普遍对比关系，并发现储库初始状态的影响，从而连接了量子信息与热力学。
Recently probabilistic hysteresis in isolated Hamiltonian systems of ultracold atoms has been studied in the limit of large particle numbers, where a semiclassical treatment is adequate. The origin of irreversibility in these sweep experiments, where a control parameter is slowly (adiabatically) tuned back and forth, turned out to be a passage blue back and forth across a separatrix (integrable case) or a passage in and out of a chaotic sea in phase space (chaotic case). Here we focus on the full quantum mechanical description of the integrable system and show how the semiclassical results eme…
Macroscopic quantum distinguishablity, identity and irreversibility
本文在局部时间方案中表明，宏观多粒子系统可自然获得可区分性与个体性，其动力学轨迹不可逆，并推导出非指数衰变定律，需进一步分析相对论因果性与宇宙学背景。
Quantitative measure of disorder or randomness based on the entropy production characterizes thermodynamical irreversibility, which is relevant to the conventional second law of thermodynamics. Here we report, in a quantum mechanical fashion, the first theoretical prediction and experimental exploration of an information-theoretical bound on the entropy production. Our theoretical model consists of a simplest two-level dissipative system driven by a purely classical field, and under the Markovian dissipation, we find that such an information-theoretical bound, not fully validating quantum rela…
We test Boltzmann's H-theorem for several models of particle random walk. We study the influence of interaction between the particle and reservoir/detectors on entropy and find entropy increasing in time for some models and behaving non-monotonically for others. The key mechanism affecting the entropy growth is the quantum entanglement between the system and the reservoir. We discuss the details of the system-reservoir interaction, such as presence of the interference in the system and number of interactions with detector parts, and their impact on the monotonicity of entropy.
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