On decaying rate of a quantum state

Stabilization of decaying states and quantum vortices

A two-dimensional model of an electron moving under the influence of an attractive zero-range potential as well as external magnetic and electric fields is analyzed. We prove by numerical investigations that there are formed such resonances which manifest a peculiar dependance on the electric field intensity, i.e., although the electric field increases, the lifetime of these resonance states grows up. It is explained that this phenomenon, called further \textit{the stabilization}, is a close consequence of \textit{quantum-mechanical vortices} induced by the magnetic field and controlled by the…

指数衰减的含噪声设备量子模拟误差

Exponentially Decaying Quantum Simulation Error with Noisy Devices

该研究证明含噪量子设备中单步Trotter误差随电路深度指数衰减，推导最优步数与噪声要求，并展示资源节省，为量子模拟优势提供系统见解。

Contextuality and Nonlocality in Decaying Multipartite Systems

Everyday experience supports the existence of physical properties independent of observation in strong contrast to the predictions of quantum theory. In particular, existence of physical properties that are independent of the measurement context is prohibited for certain quantum systems. This property is known as contextuality. This paper studies whether the process of decay in space-time generally destroys the ability of revealing contextuality. We find that in the most general situation the decay property does not diminish this ability. However, applying certain constraints due to the space-…

用于误差缓解量子计算的均匀衰减子空间

Uniformly Decaying Subspaces for Error Mitigated Quantum Computation

本文提出均匀衰减子空间理论，利用 Lindblad 方程耗散结构构造无偏估计量，在无需完全了解噪声的情况下消除一阶衰减率偏差，改进双轨量子比特误差缓解并优于概率误差消除。

通过平衡态下的衰减相互作用产生负Wigner函数

Negative Wigner function by decaying interaction from equilibrium

提出一种仅通过相互作用突然衰减在平衡态下产生负Wigner函数叠加态的新方法，并展示其可检测性与量子相干性，且增加量子比特可增强效果。

Robust quantum searching with spontaneously decaying qubits

We present a modification of the standard single-item quantum search procedure that acquires robustness from spontaneous decay of the qubits. This damps the usual oscillation of populations, driving the system to a steady state with a strongly enhanced population of the solution. Numerical evaluation of the steady state was performed for up to 36 qubits. The huge size of the state space in our analysis is dealt with by exploiting a symmetry in the master equation that reduces the scaling of computer resources from exponential to polynomial. Based on these results we estimate that an error-free…

Fractional Entropy Decaying and the Third Law of Thermodynamics

The quantum thermodynamic property of the fractional damping system is investigated extensively. A fractional power-law decaying entropy function is revealed which presents another evidence for the validity of the third law of thermodynamics in the quantum dissipative region. Several non-trivial characters are excavated such as that the entropy varies from a non-linear diverging function to a semi-linear decaying function of the fractional exponent as the temperature tends to absolute zero.

The quantum Bernoulli map

The classical Bernoulli and baker maps are two simple models of deterministic chaos. On the level of ensembles, it has been shown that the time evolution operator for these maps admits generalized spectral representations in terms of decaying eigenfunctions. We introduce the quantum version of the Bernoulli map. We define it as a projection of the quantum baker map. We construct a quantum analogue of the generalized spectral representation, yielding quantum decaying states represented by density matrices. The quantum decaying states develop a quasi-fractal shape limited by the quantum uncertai…

张量网络最优采样：针对波函数快速衰减尾部

Optimal sampling of tensor networks targeting wave function's fast decaying tails

提出一种针对等距张量网络态的最优采样方法，利用精确累积边界函数避免样本重复，实现指数级加速，并在多个数值示例中验证了超过一个数量级的性能提升。

周期场中量子行走速度的指数衰减界

Exponentially decaying velocity bounds of quantum walks in periodic fields

本文研究带局部场的一维CMV量子行走，证明通过引入足够大周期的周期场可使渐近速度任意小，并给出速度随周期长度指数衰减的上界，从而在长时间步数后仍表现出类局域化效应。

Deviation from the exponential decay law in relativistic quantum field theory: the example of strongly decaying particles

We show that a short-time regime, in which a deviation from the exponential decay law occurs, exists also in the framework of a superrenormalizable relativistic quantum field theory. This, in turn, implies the possibility of a quantum Zeno effect also for elementary decays. The attention is then focused on the typical order of magnitude of strong decay rates of mesons: for these particles, strong deviations from the exponential decay law are present during a period of time comparable with their mean life time. As a concrete example, the case of the $ρ$ meson is studied.

Generalized Effective Operator Formalism for Decaying Systems

Systems of neutral kaons can be used to observe entanglement and the violation of Bell inequalities. The decay of these particles poses some problems, however, and recently an effective formalism for treating such systems has been derived. We generalize this formalism and make it applicable to other quantum systems that can be made to behave in a similar manner. As examples, we discuss two possible implementations of the generalized formalism using trapped ions such as $^{171}$Yb or $^{172}$Yb, which may be used to simulate kaonic behavior in a quantum optical system.

Non-hermitian approach to decaying ultracold bosonic systems

A paradigm model of modern atom optics is studied, strongly interacting ultracold bosons in an optical lattice. This many-body system can be artificially opened in a controlled manner by modern experimental techniques. We present results based on a non-hermitian effective Hamiltonian whose quantum spectrum is analyzed. The direct access to the spectrum of the metastable many-body system allows us to easily identify relatively stable quantum states, corresponding to previously predicted solitonic many-body structures.

从双指数衰减光子发射数据中提取光物理过程速率的框架

A framework for extracting the rates of photophysical processes from biexponentially decaying photon emission data

提出一个包含载流子俘获和释放的模型，解释低维半导体中中性激子光致发光的双指数衰减，无需近似即可确定所有跃迁速率的似然区间，并在高温极限下给出具体速率值，优于简化模型。

Rapidly Decaying Wigner Functions are Schwartz Functions

We show that if the Wigner function of a (possibly mixed) quantum state decays toward infinity faster than any polynomial in the phase space variables $x$ and $p$, then so do all of its derivatives, i.e., it is a Schwartz function on phase space. This is equivalent to the condition that the Husimi function is a Schwartz function, that the quantum state is a Schwartz operator in the sense of Keyl et al., and, in the case of a pure state, that the wavefunction is a Schwartz function on configuration space. We discuss the interpretation of this constraint on Wigner functions and provide explicit …

Breit-Wigner distribution, quantum beats and GSI Anomaly

The relationship between Breit-Wigner distribution as an underlying basis for decaying unstable quantum systems and GSI experiment (anomaly) has not been addressed properly in the literatures. We show that quantum beats can be obtained using a superposition of two Breit-Wigner distributions. This modified distribution can explain the GSI time anomaly with quantum beats resulting from the existence of two energy levels of the decaying ion.

Time Asymmetric Quantum Theory - III. Decaying States and the Causal Poincare Semigroup

A relativistic resonance which was defined by a pole of the $S$-matrix, or by a relativistic Breit-Wigner line shape, is represented by a generalized state vector (ket) which can be obtained by analytic extension of the relativistic Lippmann-Schwinger kets. These Gamow kets span an irreducible representation space for Poincaré transformations which, similar to the Wigner representations for stable particles, are characterized by spin (angular momentum of the partial wave amplitude) and complex mass (position of the resonance pole). The Poincaré transformations of the Gamow kets, as well as of …

Many-Body Quantum Optics with Decaying Atomic Spin States: ($γ$, $κ$) Dicke model

We provide a theory for quantum-optical realizations of the open Dicke model with internal, atomic spin states subject to spontaneous emission with rate $γ$. This introduces a second decay channel for excitations to irreversibly dissipate into the environment, in addition to the photon loss with rate $κ$, which is composed of individual atomic decay processes and a collective atomic decay mechanism. The strength of the latter is determined by the cavity geometry. We compute the mean-field non-equilibrium steady states for spin and photon observables in the long-time limit, $t\rightarrow \infty…

Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems

Thermal states are the bedrock of statistical physics. Nevertheless, when and how they actually arise in closed quantum systems is not fully understood. We consider this question for systems with local Hamiltonians on finite quantum lattices. In a first step, we show that states with exponentially decaying correlations equilibrate after a quantum quench. Then we show that the equilibrium state is locally equivalent to a thermal state, provided that the free energy of the equilibrium state is sufficiently small and the thermal state has exponentially decaying correlations. As an application, we…

Can a charged decaying particle serve as an ideal clock in the presence of the magnetic field?

We investigate a model of a supposedly ideal clock based on the decay rate of a charged particle in circular motion in a constant magnetic field. We show that the time measured by an ideal clock depends on the acceleration. However, the effect becomes visible at an order of magnitude of 10^{28} g, therefore confirming the validity of the ideal clock hyphotesis for realistic accelerations.

On polynomial Lieb-Robinson bounds for the XY chain in a decaying random field

We consider the isotropic XY quantum spin chain in a random external field in the $z$ direction, with single site distributions given by i.i.d. random variables times the critical decaying envelope $j^{-1/2}$. Our motivation is the study of many-body localization. We investigate transport properties in terms of polynomial Lieb-Robinson (PLR) bounds. We prove a zero-velocity PLR bound for large disorder strength $λ$ and for small $λ$ we show a partial converse, which suggests the existence of non-trivial transport in the model.

In search of an observational quantum signature of the primordial perturbations in slow-roll and ultra slow-roll inflation

In the standard inflationary paradigm, cosmological density perturbations are generated as quantum fluctuations in the early Universe, but then undergo a quantum-to-classical transition. A key role in this transition is played by squeezing of the quantum state, which is a result of the strong suppression of the decaying mode component of the perturbations. Motivated by ever improving measurements of the cosmological perturbations, we ask whether there are scenarios where this decaying mode is nevertheless still observable in the late Universe, ideally leading to a ``smoking gun'' signature of …

Time Asymmetric Quantum Theory - II. Relativistic Resonances from S-Matrix Poles

Relativistic resonances and decaying states are described by representations of Poincaré transformations, similar to Wigner's definition of stable particles. To associate decaying state vectors to resonance poles of the $S$-matrix, the conventional Hilbert space assumption (or asymptotic completeness) is replaced by a new hypothesis that associates different dense Hardy subspaces to the in- and out-scattering states. Then one can separate the scattering amplitude into a background amplitude and one or several ``relativistic Breit-Wigner'' amplitudes, which represent the resonances per se. Thes…

Pulsed and continuous measurements of exponentially decaying systems

We study the influence of a detector on the decay law of a quantum state whose "undisturbed" survival probability is purely exponential. In particular, we consider a detector with a finite energy band of detection, i.e. it interacts only with decay products having an energy within a certain range of values. In one case, we assume that the detector performs many repeated measurements at short time intervals in all of which a collapse of the wave function occurs (bang-bang or pulsed-type measurements). In the second case, we assume a continuous measurement which preserves unitarity. We confirm t…

幂律衰减本征态中的涌现多重分形

Emergent multifractality in power-law decaying eigenstates

本文提出基于本征态幂律衰减的通用原则以区分分形相与真正的多重分形相，并在一维非均匀紧束缚模型中解析计算分形维数谱，与数值模拟吻合。

量子集中不等式与热力学系综的等价性：一种最优质量输运方法

Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal mass transport approach

本研究提出量子自旋系统的新型集中不等式，引入局域W₁距离并证明输运成本不等式，最终证明了量子统计力学中系综等价性与弱本征态热化假说。

Finitely Repeated Adversarial Quantum Hypothesis Testing

We formulate a passive quantum detector based on a quantum hypothesis testing framework under the setting of finite sample size. In particular, we exploit the fundamental limits of performance of the passive quantum detector asymptotically. Under the assumption that the attacker adopts separable optimal strategies, we derive that the worst-case average error bound converges to zero exponentially in terms of the number of repeated observations, which serves as a variation of quantum Sanov's theorem. We illustrate the general decaying results of miss rate numerically, depicting that the `naive' …

在超外围离子碰撞中衰变粒子的方位角纠缠

Azimuthal angular entanglement between decaying particles in ultra-peripheral ion collisions

研究超外围离子碰撞中衰变粒子的方位角纠缠，通过比较经典与量子计算揭示多粒子纠缠的量子相关性。