Kent A. Peacock
I tentatively suggest that the superposition principle of quantum mechanics is explicable in a mathematically natural way if it is possible to understand probability amplitudes as complex-valued logarithms. This notion is inspired by the fact that the quantum state may be interpreted as a measure of information.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
The paper is withdrawn due to an error in Section 2.
The superposition principle of two qubit states is formulated as nonlinear addition rule of mean spinprojection onto three perpendicular directions. The explicit expression for the mean value determining the superposition state in term of the two initial pure states of the qubit is obtained. Possibility to check the superposition expression in experiments is discussed.
Laser absorption spectroscopy to probe the superposition principle in atomic translational motion
该研究提出少原子多普勒敏感吸收光谱方案，用于判别原子量子平动运动是否具有叠加性及其测量是否导致坍缩。
This is a comment to the paper, Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics by C Cisneros et al 1998 Eur. J. Phys. 19 237. doi:10.1088/0143-0807/19/3/005. The proof that the authors construct for the limitation on the superposition of state vectors corresponding to different sectors of the Hilbert space, partitioned by a superoperator has a flaw as outlined below.
Interpretation of the superposition principle and locality loophole in Bell experiments
本文揭示叠加原理与局域性的联系，提出自洽解释表明量子力学可为局域统计理论，指出贝尔不等式违反无法区分局域性，并提议新实验以闭合局域性漏洞。
The superposition principle is a very basic ingredient of quantum theory. What may come as a surprise to many students, and even to many practitioners of the quantum craft, is tha superposition has limitations imposed by certain requirements of the theory. The discussion of such limitations arising from the so-called superselection rules is the main purpose of this paper. Some of their principal consequences are also discussed. The univalence, mass and particle number superselection rules of non-relativistic quantum mechanics are also derived using rather simple methods.
No extension of the Quantum Tensor Product admits a Superposition principle
该研究在广义概率理论框架内定义叠加，构建三条叠加原理，证明量子张量积是满足所有原理的量子系统最大复合规则，还将纠缠等非经典特征归为叠加的特殊形式。
For three given probability distributions describing positions of three classical coins the quantum density matrix of spin-$1/2$ state is constructed and its matrix elements are associated with triada of Malevich's squares. The superposition principle of spin-$1/2$ states is presented in the form of nonlinear addition rule for these classical coin probabilities. We illustrate the formulas by the statement"God does not play dice - God plays coins".
We discuss the propagation of laser radiation through a medium of quantum prepared Λ-type atoms in order to enhance the insight into the physics of QS-PT generator suggested in Phys. Rev. A 80, 035801 (2009). We obtain analytical results which give a qualitatively corerct description of the outcoming series of ultrashort optical pulses and show that for the case of alkali vapor medium QS-PT generation may be implemented under ordinary experimental conditions.
By sending a classical two-level system, one can transfer information about only \emph{two} distinguishable outcomes. Here we show that in quantum mechanics, using both the spin and path degrees of freedom of a spin-1/2 particle, and a Mach-Zehnder type interferometric arrangement with two suitable Stern-Gerlach detectors, it is possible to transfer information about \emph{four} distinguishable outcomes. This procedure does \emph{not} require using quantum entanglement as a resource as in the well-known protocol of dense coding, but instead hinges entirely on the quantum superposition principl…
We show that scattering a quantum particle on a one-dimensional potential barrier as well as scattering the electromagnetic wave on a quasi-one-dimensional layered structure (both represent scattering problems with one 'source' and two 'sinks') violate the superposition principle; the role of nonlinear elements is played here by the potential barrier and the layered structure, splitting the incident (probability and electromagnetic) wave into two parts (transmitted and reflected). This explains why all attempts to solve the tunneling time problem within the framework of the standard (linear) m…
The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The ana…
Collective behavior in quantum interference: an alternative superposition principle
本文提出一种干涉仪集体模型，其未耦合组件集体作用，展示了与标准诠释在多体系统叠加原理上的差异，揭示了量子与半经典理论间的联系，为多体叠加原理测试提供新见解。
There are four reasons why our present knowledge and understanding of quantum mechanics could be regarded as incomplete. Firstly, the principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. Secondly, there is no universally agreed upon explanation for the process of quantum measurement. Thirdly, there is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. Fourthly, and perhaps most importantly, the concept of time is…
The quantum superposition principle: a reconsideration
该研究基于量子力学绝热定理、非绝热缀饰态及实验证据重新审视量子叠加原理，揭示了其物理机制与特性，深化了对量子叠加的认知。
A role of the superposition principle is discussed for the quantum-mechanical Carnot engine introduced by Bender, Brody, and Meister [J. Phys. A 33, 4427 (2000)]. It is shown that the efficiency of the engine can be enhanced by superposition of quantum states. A finite-time process is also discussed, and the condition of the maximum power output is presented. Interestingly, the efficiency at the maximum power is lower than that without superposition.
The connection of unbroken SUSY quantum mechanics in its strictly isospectral form with the nonlinear Riccati superposition principle is pointed out
We challenge the view that there is a basic conflict between the fundamental principles of Quantum Theory and General Relativity, and in particular the fact that a superposition of massive bodies would lead to a violation of the Equivalence Principle. It has been argued that this violation implies that such a superposition must inevitably spontaneously collapse (like in the Diósi-Penrose model). We identify the origin of such an assertion in the impossibility of finding a local, classical reference frame in which Einstein's Equivalence Principle would hold. In contrast, we argue that the formu…
The Feynman Path Integral formalism has long been used for calculations of probability amplitudes. Over the last few years, it has been extensively used to theoretically demonstrate that the usual application of the superposition principle in slit based interference experiments is often incorrect. This has caveat in both optics and quantum mechanics where it is often naively assumed that the boundary condition represented by slits opened individually is same as them being opened together. The correction term comes from exotic sub leading terms in the Path Integral which can be described by wha…
We reconsider a well known problem of quantum theory, i.e. the so called measurement (or macro-objectification) problem, and we rederive the fact that it gives rise to serious problems of interpretation. The novelty of our approach derives from the fact that the relevant conclusion is obtained in a completely general way, in particular, without resorting to any of the assumptions of ideality which are usually done for the measurement process. The generality and unescapability of our assumptions (we take into account possible malfunctionings of the apparatus, its unavoidable entanglement with t…
Characterizing the superposition of arbitrary random quantum states and a known quantum state
本文研究了未知量子比特态相对于已知态的叠加问题，刻画了可叠加态集合位于布洛赫球上的圆内，并指出高维情形下叠加协议几乎对所有态违反不可克隆原理。
We propose a simple experimental test of the quantum equivalence principle introduced by Zych and Brukner [arXiv:1502.00971], which generalises the Einstein equivalence principle to superpositions of internal energy states. We consider a harmonically-trapped spin-$\frac12$ atom in the presence of both gravity and an external magnetic field and show that when the external magnetic field is suddenly switched off, various violations of the equivalence principle would manifest as otherwise forbidden transitions. Performing such an experiment would put bounds on the various phenomenological violati…
The superposition principle forms the very backbone of quantum theory. The resulting linear structure of quantum theory is structurally so rigid that tampering with it may have serious, seemingly unphysical, consequences. This principle has been succesful at even the highest available accelerator energies. Is this aspect of quantum theory forever then? The present work is an attempt to understand the attitude of the founding fathers, particularly of Bohr and Dirac, towards this principle. The Heisenberg matrix mechanics on the one hand, and the Schrodinger wave mechanics on the other, are crit…
Quantum Superposition Principle and Geometry
本文针对量子态空间非线性导致常规叠加原理难以纳入几何表述的问题，提出区分投影叠加原理与分解原理的方案，以自旋1/2系统和双缝实验为例说明其合理性。
Recently, there has been a discussion on the origin of the quantum probability rules (Deutsch quant-ph/9906015, Polley quant-ph/9906124, Barnum et al. quant-ph/9907024, Finkelstein quant-ph/9907004). This contribution, which is a slightly reformulated version of a paper published in Int.J.Theor.Phys. 33, 171 (1994), points out the follwoing: To an experimenter the world is a persistent stream of discrete data. All that is certain is that with each observation he/she knows more than before, simply because he/she can now answer the question "Which of the possible outcomes have you just registere…
Breeding the Cat Through Superposition of Two Schrodinger Kittens Based on Coupled Waveguides
针对高振幅光学薛定谔猫态难以制备的问题，提出在耦合波导中叠加两个小猫态并使其干涉增长的方案，实现高概率、可片上集成的大振幅猫态生成。
The Einstein Equivalence Principle (EEP) has a central role in the understanding of gravity and space-time. In its weak form, or Weak Equivalence Principle (WEP), it directly implies equivalence between inertial and gravitational mass. Verifying this principle in a regime where the relevant properties of the test body must be described by quantum theory has profound implications. Here we report on a novel WEP test for atoms. A Bragg atom interferometer in a gravity gradiometer configuration compares the free fall of rubidium atoms prepared in two hyperfine states and in their coherent superpos…
Quantum coherence is important in quantum mechanics, and its essence is from superposition principle. We study the coherence of any two pure states and that of their arbitrary superposition, and obtain the relationship between them. In the case that the two states have support on orthogonal subspaces, the relationship is simple, that is, the difference between the coherence of their superposition state and the average coherence of them is smaller than 1. In other cases, we obtain different and a little more complicated relationships. Furthermore, we also obtain the lower bound of coherence of …
With the exception of superselection rules, there are no known explicit violations of the Principle of quantum Superposition. However, quantum measurement and the emergence of classicality seem to imply that the Principle of Superposition is not universal, so perhaps new superselection rules or something similar wait to be found. This invites us to search for explicit violations of superposition, even in places where we expect it to hold. Given that many quantum measurement devices rely on atoms absorbing photons, these processes are natural places for a first search for such violations. We pr…
Quantum Interference Needs Convention: Overlap-Determinability and Unified No-Superposition Principle
本文提出重叠可确定性概念，统一无叠加原理，揭示相位约定对量子叠加实现的关键作用，并展示其对量子计算基础和效率的影响。
The principle of linear superposition is a hallmark of quantum theory. It has been confirmed experimentally for photons, electrons, neutrons, atoms, for molecules having masses up to ten thousand amu, and also in collective states such as SQUIDs and Bose-Einstein condensates. However, the principle does not seem to hold for positions of large objects! Why for instance, a table is never found to be in two places at the same time? One possible explanation for the absence of macroscopic superpositions is that quantum theory is an approximation to a stochastic nonlinear theory. This hypothesis may…
New technological developments allow to explore the quantum properties of very complex systems, bringing the question of whether also macroscopic systems share such features, within experimental reach. The interest in this question is increased by the fact that, on the theory side, many suggest that the quantum superposition principle is not exact, departures from it being the larger, the more macroscopic the system. Here we propose a novel way to test the possible violation of the superposition principle, by analyzing its effect on the spectral properties of a generic two-level system. We wil…
The quantization of time-reparametrization invariant systems such as general relativity is plagued by an ambiguity relating to the role of time in the theory. If one parametrizes observables by the (unobservable) time, and then relies on the existence of an approximate "clock" degree of freedom to give physical meaning to the observables, one finds multiple quantum states that yield the same predictions yet interfere with each other.
The abstract framework of quantum mechanics (QM) causes the well-known weirdness, which leads to the field of foundation of QM. We constructed the new concept, i.e., scope, to lay the foundation of quantum coherence and openness, also the principles of superposition and entanglement. We studied analytically and quantitatively the quantum correlations and information, also we discussed the physical essence of the existed entanglement measures. We compared with several other approaches to the foundation of QM, and we stated that the concept of scope is unique and has not been demonstrated before…
Two of us (CM and VV) recently showed how the quantum character of a physical system, in particular the gravitational field, can in principle be witnessed without directly measuring observables of that system, solely by its ability to mediate entanglement between two other systems. Here we propose a variant of that scheme, where the entanglement is again generated via gravitational interaction, but now between two particles both at sharp locations (very close to each other) but each in a superposition of two different masses. We discuss an in-principle example using two hypothetical massive, n…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulati…
Quantum entanglement is the quintessence of quantum information processing mostly limited to the microscopic regime governed by Heisenberg uncertainty principle. For practical applications, however, macroscopic entanglement gives great benefits in both photon loss and sensitivity. Recently, a novel method of macroscopic entanglement generation has been proposed and demonstrated in a coupled interferometric system using classical laser light, where superposition between binary bases in each interferometric system plays a key role. Here, the function of path superposition applied to independent …
Quantum steering is an important correlation in quantum information theory. A recent work [Nat. Commun. 12, 2410 (2021)] showed that quantum steering is also useful for quantum metrology. Here, we extend the exploration of steering-enhanced quantum metrology from single noiseless phase shifts to superpositions of noisy phase shifts. As concrete examples, we consider a control system that manipulates a target system to pass through a superposition of either dephased or depolarized phase shifts channels. We show that using such superpositions of noisy phase shifts can suppress the effects of noi…
The principle of superposition is a key ingredient for quantum mechanics. A recent work [M. Oszmaniec et al., Phys. Rev. Lett. 116, 110403 (2016)] has shown that a quantum adder that deterministically generates a superposition of two unknown states is forbidden. Here we propose a probabilistic approach for creating a superposition state of two arbitrary states encoded in two three-dimensional cavities. Our implementation is based on a three-level superconducting transmon qubit dispersively coupled to two cavities. Numerical simulations show that high-fidelity generation of the superposition of…
In this paper, we are exploring the feasibility of observing non-classical features of gravity in a low-energy regime in a quantum optomechanical experiment. If gravity is to have an underlying quantum nature, it should hold the most fundamental quantum characteristics such as the superposition principle and entanglement. Despite the weakness of gravity, in principle there is a chance, to observe such a quantum signature of the gravity by exploiting the quantum optomechanical techniques, without direct observation of graviton. We are investigating a new dynamical scheme called, gravitational q…
The superposition principle is fundamental to quantum theory. Yet a recent no-go theorem has proved that quantum theory forbids superposition of unknown quantum states, even with nonzero probability. The implications of this result, however, remain poorly understood so far. In this paper we show that the existence of a protocol that superposes two unknown pure states with nonzero probability (allowed to vary over input states) leads to violation of other no-go theorems. In particular, such a protocol can be used to perform certain state discrimination and cloning tasks that are forbidden not o…
Quantum interferences between non-orthogonal states are the best approximation of a joint realization of the non-commuting physical properties represented by the two states. As I have shown recently, such interferences can be used to demonstrate that quantum physics deviates from classical causality in the limit of small action. Here, I point out that this proof constitutes a failure of the principle of least action and consider possible implications for our understanding of fundamental physics.
In this paper we attempt to provide a physical representation of quantum superpositions. For this purpose we discuss the constraints of the quantum formalism to the notion of possibility and the necessity to consider a potential realm independent of actuality. Taking these insights into account and from the basic principles of quantum mechanics itself we advance towards the definition of the notions of power and potentia. Assuming these notions as a standpoint we analyze the meaning of 'observation' and 'interaction'. As a conclusion we provide a set of axioms which comprise our interpretation…
English translation of a Russian article from 1928. Translator's abstract: The article presents general considerations on the validity of the superposition principle for light in vacuo from out a quantum theoretic point of view. It contains a report on an optical experiment designed to detect the phenomenon of photon-photon scattering. To understand the negative result of the performed experiment, a consideration of the solar corona is undertaken in order to derive an empirical upper limit on the photon-photon scattering rate. Source details: S. I. Vavilov: Zamechaniya ob empiricheskoi tochnos…
We show that the maximum quantum violation of the Klyachko-Can-Binicioglu-Shumovsky (KCBS) inequality is exactly the maximum value satisfying the following principle: The sum of probabilities of pairwise exclusive events cannot exceed 1. We call this principle "global exclusivity," since its power shows up when it is applied to global events resulting from enlarged scenarios in which the events in the inequality are considered jointly with other events. We identify scenarios in which this principle singles out quantum contextuality, and show that a recent proof excluding nonlocal boxes follows…
Superpositions of thermalisations in relativistic quantum field theory
本文利用相对论非惯性参考系量子场论框架，解释了量子控制热化下系统无法热化的现象，通过分析场模相互作用验证解释，并建立量子信息、相对论物理与量子热力学的联系。
A general orbital angular momentum (OAM) mode selection principle is put forward involving the rotationally symmetric superposition of chiral states. This principle is not only capable of explaining the operation of spiral zone plate holograms and suggesting that naturally occurring rotationally symmetric patterns could be inadvertent sources of vortex beams, but more importantly, it enables the systematic and flexible generation of structured OAM waves in general. This is demonstrated both experimentally and theoretically in the context of electron vortex beams using rotationally symmetric bi…
The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability Principle) and Spectral Theory of observables are discussed in this non linear geometrical context.
Einstein's Equivalence principle for superpositions of gravitational fields and quantum reference frames
本文提出爱因斯坦等效原理可推广至量子参考系及量子叠加引力场，通过限制引力场非经典性类型建立框架，扩展了该原理的适用范围。
Superpositional Gradient Descent: Harnessing Quantum Principles for Model Training
本文提出叠加梯度下降方法，通过量子原理提升模型训练效率，实验证明其在序列分类和LLM微调中表现优于AdamW。
Probing gravity-related decoherence with a 16 $μ$g Schrödinger cat state
本研究通过16微克机械谐振子的薛定谔猫态退相干实验，检验了与引力相关的Diósi-Penrose波函数坍缩模型，探讨宏观叠加态破坏的机制。
Cellular automata can show well known features of quantum mechanics, such as a linear updating rule that resembles a discretized form of the Schrödinger equation together with its conservation laws. Surprisingly, a whole class of "natural" Hamiltonian cellular automata, which are based entirely on integer-valued variables and couplings and derived from an Action Principle, can be mapped reversibly to continuum models with the help of Sampling Theory. This results in "deformed" quantum mechanical models with a finite discreteness scale $l$, which for $l\rightarrow 0$ reproduce the familiar cont…
Self-Configuring Quantum Networks with Superposition of Trajectories
本文提出了一种自配置量子网络方法，利用叠加路径和变分量子优化技术，在未知噪声环境下实现高保真度连接。
Communication in a network generally takes place through a sequence of intermediate nodes connected by communication channels. In the standard theory of communication, it is assumed that the communication network is embedded in a classical spacetime, where the relative order of different nodes is well-defined. In principle, a quantum theory of spacetime could allow the order of the intermediate points between sender and receiver to be in a coherent superposition. Here we experimentally realise a table-top simulation of this exotic possibility on a photonic system, demonstrating high-fidelity t…
Quantum Machine Learning Using Quantum Illumination With Quantum Enhanced Interference
本文提出利用量子增强技术分析量子比特叠加状态，构建量子神经网络反向传播技术以提升量子优化和搜索算法性能。
According to Bohr's principle of complementarity, a quanton can behave either as a wave or a particle, depending on the choice of the experimental setup. Some recent two-path interference experiments have devised methods where one can have a quantum superposition of the two choices, thus indicating that a quanton may be in a superposition of wave and particle nature. These experiments have been of interest from the point of view of Wheeler's delayed-choice experiment. However, it has also been claimed that this experiment can violate complementarity. Here we theoretically analyze a multipath i…
Intro to Quantum Harmony: Chords in Superposition
本文探讨了量子计算原理与音乐和谐之间的关联，指出量子叠加原理与音乐意义的诠释密切相关，并在量子计算模拟中直接应用叠加原理辅助计算机生成音乐作曲的决策过程。
Whether quantum physics is universally valid is an open question with far-reaching implications. Intense research is therefore invested into testing the quantum superposition principle with ever heavier and more complex objects. Here we propose a radically new, experimentally viable route towards studies at the quantum-to-classical borderline by probing the orientational quantum revivals of a nanoscale rigid rotor. The proposed interference experiment testifies a macroscopic superposition of all possible orientations. It requires no diffraction grating, uses only a single levitated particle, a…
Physicians define death as the "irreversible" breakdown of all brain-functions including brain-stem. By "irreversible" they mean a damage that is beyond the human capacity to restore the patient's healthy state. In the same line I propose to complete the definition of quantum physics in [1] by Principle D (Detection): "Detection outcomes (like death) are ordinarily irreversible and observer-independent". It is then argued that this principle excludes generalization of quantum superposition to visible objects bearing observer-dependent outcomes. However this exclusion is not absolute: It rather…
Quantum $n$-body correlations cannot be explained with $(n-1)$-body nonlocality. However, this genuine $n$-body nonlocality cannot surpass certain bounds. Here we address the problem of identifying the principles responsible for these bounds. We show that, for any $n \ge 2$, the exclusivity principle, as derived from axioms about sharp measurements, and a technical assumption give the exact bounds predicted by quantum theory. This provides a unified explanation of the bounds of single-body contextuality and $n$-body nonlocality, and connects two programs towards understanding quantum theory.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。