Heisenberg’s uncertainty relation may be violated in a single measurement

The well-known Heisenberg’s uncertainty relation is an inequality between uncertainties of canonically conjugate observables in a given state. In this interpretation, the Heisenberg’s uncertainty relation is a rigorous mathematical theorem and is, therefore, always valid. However, the same inequality is often applied in the situation of measurement, where it is illustrated in a quite different way. The uncertainty relation is then an inequality connecting the precision (resolution) of the measurement of one observable and the uncertainty of the conjugate observable in the state arising after the measurement. It turns out that in such an interpretation the Heisenberg’s inequality may be violated for some measurement readouts that emerge with small but finite probabilities. Making use of the uncertainties averaged in a special way over all possible measurement readouts, one may formulate an inequality of the type of Heisenberg’s inequality but valid for any measurement. Paper submitted by the author in English on 28 April 2006.     

Complementary relation between quantum entanglement and entropic uncertainty

Quantum entanglement is regarded as one of the core concepts,which is used to describe the nonclassical correlation between subsystems,and entropic uncertainty relation plays a vital role in quantum precision measurement.It is well known that entanglement of formation can be expressed by von Neumann entropy of subsystems for arbitrary pure states.An interesting question is naturally raised:is there any intrinsic correlation between the entropic uncertainty relation and quantum entanglement?Or if the relation can be applied to estimate the entanglement.In this work,we focus on exploring the complementary relation between quantum entanglement and the entropic uncertainty relation.The results show that there exists an inequality relation between both of them for an arbitrary two-qubit system,and specifically the larger uncertainty will induce the weaker entanglement of the probed system,and vice versa.Besides,we use randomly generated states as illustrations to verify our results.Therefore,we claim that our observations might offer and support the validity of using the entropy uncertainty relation to estimate quantum entanglement.     

Heisenberg's uncertainty relation of position and momentum in experiments without mutual disturbance

Arranging target atoms in a plane monolayer, one may produce by atomic or nuclear reaction an ensemble of particles with small initial position spread without disturbing their momentum spread. This would either allow a violation of Heisenberg's uncertainty relation, by creating a situation not described by quantum mechanics hence rendering quantum mechanics incomplete, or, if the uncertainty relation should hold also in this non-disturbative situation, it would mean a permanent violation of energy conservation. Thus an uncertainty relation for position and momentum and energy conservation appear to be mutually exclusive.1. Recently also Croca [5] proposed another way of determining a x without interfering with p_X.2. To forbid even speaking of an initial position spread smaller than that indicated by the wave function [6] would amount to circular reasoning and the denial of a falsification of quantum mechanics.     

Deriving a kinetic uncertainty relation for piecewise deterministic processes: from classical to quantum

From the perspective of Markovian piecewise deterministic processes (PDPs), we investigate the derivation of a kinetic uncertainty relation (KUR), which was originally proposed in Markovian open quantum systems. First, stationary distributions of classical PDPs are explicitly constructed. Then, a tilting method is used to derive a rate functional of large deviations. Finally, based on an improved approximation scheme, we recover the KUR. These classical results are directly extended to the open quantum systems. We use a driven two-level quantum system to exemplify the quantum results.     

Quantum correlation and entropic uncertainty in a quantum-dot system

We explore the dynamical behaviors of the measurement uncertainty and quantum correlation for a vertical quantum-dot system in the presence of magnetic field, including electron-electron interaction and Coulomb-blocked systems. Stemming from the quantum-memory-assisted entropic uncertainty relation, the uncertainty of interest is associated with temperature and parameters related to the magnetic field. Interestingly, the temperature has two kinds of influences on the variation of measurement uncertainty with respect to the magnetic-field-related parameters. We also discuss the relation between the lower bound of Berta et al. and the quantum discord. It is found that there is a natural competition between the quantum discord and the entropy min_Πi^BS_Πi^B(ρ_A|B). Finally, we bring in two improved bounds to offer a more precise limit to the entropic uncertainty.     

Relativistic motion on Gaussian quantum steering for two-mode localized Gaussian states

Realistic quantum systems always exhibit gravitational and relativistic features. In this paper, we investigate the properties of Gaussian steering and its asymmetry by the localized two-mode Gaussian quantum states, instead of the traditional single-mode approximation method in the relativistic setting. We find that the one-side Gaussian quantum steering will monotonically decrease with increasing observers of acceleration. Meanwhile, our results also reveal the interesting behavior of the Gaussian steering asymmetry, which increases for a specific range of accelerated parameter and then gradually approaches to a finite value. Such finding is well consistent and explained by the well-known Unruh effect, which could significantly destroy the one-side Gaussian quantum steering. Finally, our results could also be applied to the dynamical studies of Gaussian steering between the Earth and satellites, since the effects of acceleration are equal to the effects of gravity according to the equivalence principle.     

Geometric phase under the Unruh effect with intermediate statistics

Utilizing the geometric phase (GP) acquired in a quantum evolution, we manifest the thermality and quantum nature of the Unruh effect of an accelerating detector. We consider an UDW detector coupling to a conformal field in Minkowski spacetime, whose response spectrum exhibits an intermediate statistics of (1+1) anyon field. We find that comparing to an inertial moving detector, the GP in accelerating frame is modified after the nonunitary evolution of the detector due to the Unruh effect. We show that such modification can distinguish the different thermalizing ways of the detector, which depends on the scaling dimension of the conformal primary field. Finally, we estimate the difference between the GP under the Unruh radiation and that in a thermal bath for a static observer, which reveals the quantum origin of the Unruh effect rather than a conventional thermal noise.     

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic "Landau" potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.     

An uncertainty relation for joint position-momentum measurements

It is shown that the lower bound in the uncertainty relation for joint position-momentum measurements is twice as large as that in the usual Heisenberg uncertainty principle for separate measurements.     

Efficient quantum simulation of open quantum dynamics at various Hamiltonians and spectral densities

Simulation of open quantum dynamics for various Hamiltonians and spectral densities are ubiquitous for studying various quantum systems. On a quantum computer, only log₂N qubits are required for the simulation of an N-dimensional quantum system, hence simulation in a quantum computer can greatly reduce the computational complexity compared with classical methods. Recently, a quantum simulation approach was proposed for studying photosynthetic light harvesting [npj Quantum Inf. 4, 52 (2018)]. In this paper, we apply the approach to simulate the open quantum dynamics of various photosynthetic systems. We show that for Drude–Lorentz spectral density, the dimerized geometries with strong couplings within the donor and acceptor clusters respectively exhibit significantly improved efficiency. We also demonstrate that the overall energy transfer can be optimized when the energy gap between the donor and acceptor clusters matches the optimum of the spectral density. The effects of different types of baths, e.g., Ohmic, sub-Ohmic, and super-Ohmic spectral densities are also studied. The present investigations demonstrate that the proposed approach is universal for simulating the exact quantum dynamics of photosynthetic systems.     

量子开系统理论及其应用

量子物理是当代科学发展的基石,多次引发高技术革命.它与信息科学结合,产生了交叉学科——量子信息,为突破计算机芯片的尺度极限提供了全新的解决思路.自1987年起,文章作者及其合作者对量子开系统理论、量子退相干及其相关的量子物理基本问题进行了系统的探索,契合了最近10年量子信息研究的快速发展.文章首先结合上世纪70年代末彭桓武先生关于量子开系统(阻尼谐振子的量子化)的重要研究工作,介绍了量子开系统的基本概念及其研究的科学意义,同时简略介绍了文章作者及其合作者在量子开系统理论及其在量子信息应用方面的系列研究工作.     

量子开系统理论及其应用

量子物理是当代科学发展的基石,多次引发高技术革命.它与信息科学结合, 产生了交叉学科——量子信息,为突破计算机芯片的尺度极限提供了全新的解决思路.自1987年起,文章作者及其合作者对量子开系统理论、量子退相干及其相关的量子物理基本问题进行了系统的探索,契合了最近10年量子信息研究的快速发展.文章首先结合上世纪70年代末彭桓武先生关于量子开系统（阻尼谐振子的量子化）的重要研究工作, 介绍了量子开系统的基本概念及其研究的科学意义,同时简略介绍了文章作者及其合作者在量子开系统理论及其在量子信息应用方面的系列研究工作.     

Generalization of uncertainty relation for quantum and stochastic systems

The generalized uncertainty relation applicable to quantum and stochastic systems is derived within the stochastic variational method. This relation not only reproduces the well-known inequality in quantum mechanics but also is applicable to the Gross–Pitaevskii equation and the Navier–Stokes–Fourier equation, showing that the finite minimum uncertainty between the position and the momentum is not an inherent property of quantum mechanics but a common feature of stochastic systems. We further discuss the possible implication of the present study in discussing the application of the hydrodynamic picture to microscopic systems, like relativistic heavy-ion collisions.     

海森堡XYZ自旋链系统的热纠缠与局域量子不确定性研究

研究了热平衡温度,自旋交换相互作用,Dzyaloshinskii-Moriya(DM)相互作用及外加非一致性磁场对两比特海森堡XYZ自旋链量子系统的热纠缠与局域量子不确定度的影响,对比分析了并发度量子纠缠与局域量子不确定度描述自旋链系统量子关联的差别.结果表明自旋链系统的量子纠缠在热平衡温度,DM相互作用及外加磁场的非一致性参数的变化情况下均会出现纠缠突然死亡的再生现象,而自旋链系统的局域量子不确定度随着这些参数呈连续变化现象.并且,自旋交换相互作用,DM相互作用及外加横向磁场作用强度较小时,他们的变化对自旋链系统的量子纠缠与局域量子不确定度的影响有着明显的差别.     

Unification theory of classical statistical uncertainty relation and quantum uncertainty relation and its applications

General classical statistical uncertainty relation is deduced and generalized to quantum uncertainty relation. We give a general unification theory of the classical statistical and quantum uncertainty relations, and prove that the classical limit of quantum mechanics is just classical statistical mechanics. It is shown that the classical limit of the general quantum uncertainty relation is the general classical uncertainty relation. Also, some specific applications show that the obtained theory is self-consistent and coincides with those from physical experiments.     

The uncertainty and quantum correlation of measurement in double quantum-dot systems

In this work, we study the entropic uncertainty and quantum discord in two double-quantum-dot (DQD) system coupled via a transmission line resonator (TLR). Explicitly, the dynamics of the systemic quantum correlation and measured uncertainty are analysed with respect to a general X-type state as the initial state. Interestingly, it is found that the different parameters, including the eigenvalue α of the coherent state, detuning amount δ, frequency ω and the coupling constant g, have subtle effects on the dynamics of the entropic uncertainty, such as the oscillation period of the uncertainty. It is clear to reveal that the quantum discord and the lower bound of the entropic uncertainty are anti-correlated when the initial state of the system is the Werner-type state, while quantum discord and the lower bound of the entropic uncertainty are not anti-correlated when the initial state of the system is the Bell-diagonal state. Thereby, we claim that the current investigation would provide an insight into the entropic uncertainty and quantum correlation in DQDs system, and are basically of importance to quantum precision measurement in practical quantum information processing.     

Application of non-Hermitian Hamiltonian model in open quantum optical systems

Non-Hermitian systems have observed numerous novel phenomena and might lead to various applications. Unlike standard quantum physics, the conservation of energy guaranteed by the closed system is broken in the non-Hermitian system, and the energy can be exchanged between the system and the environment. Here we present a scheme for simulating the dissipative phase transition with an open quantum optical system. The competition between the coherent interaction and dissipation leads to the second-order phase transition. Furthermore, the quantum correlation in terms of squeezing is studied around the critical point. Our work may provide a new route to explore the non-Hermitian quantum physics with feasible techniques in experiments.     

电子衍射中的位置-动量不确定度关系讨论

通过求解薛定谔方程,获得电子在二维衍射中的波函数,在此基础上,利用傅里叶变换,计算电子的位置-动量不确定度并对相关问题进行讨论.     

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in multi-component quantum system (Kim et al. (2018) [28]). This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg XY model. Two distinct situations are considered. The first one concerns the anisotropic XY model and the second situation concerns isotropic XY model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.