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This paper is a new step towards understanding why “quantum nonlocality” is a misleading concept. Metaphorically speaking, “quantum nonlocality” is Janus faced. One face is an apparent nonlocality of the Lüders projection and another face is Bell nonlocality (a wrong conclusion that the violation of Bell type inequalities implies the existence of mysterious instantaneous influences between distant physical systems). According to the Lüders projection postulate, a quantum measurement performed on one of the two distant entangled physical systems modifies their compound quantum state instantaneously. Therefore, if the quantum state is considered to be an attribute of the individual physical system and if one assumes that experimental outcomes are produced in a perfectly random way, one quickly arrives at the contradiction. It is a primary source of speculations about a spooky action at a distance. Bell nonlocality as defined above was explained and rejected by several authors; thus, we concentrate in this paper on the apparent nonlocality of the Lüders projection. As already pointed out by Einstein, the quantum paradoxes disappear if one adopts the purely statistical interpretation of quantum mechanics (QM). In the statistical interpretation of QM, if probabilities are considered to be objective properties of random experiments we show that the Lüders projection corresponds to the passage from joint probabilities describing all set of data to some marginal conditional probabilities describing some particular subsets of data. If one adopts a subjective interpretation of probabilities, such as QBism, then the Lüders projection corresponds to standard Bayesian updating of the probabilities. The latter represents degrees of beliefs of local agents about outcomes of individual measurements which are placed or which will be placed at distant locations. In both approaches, probability-transformation does not happen in the physical space, but only in the information space. Thus, all speculations about spooky interactions or spooky predictions at a distance are simply misleading. Coming back to Bell nonlocality, we recall that in a recent paper we demonstrated, using exclusively the quantum formalism, that CHSH inequalities may be violated for some quantum states only because of the incompatibility of quantum observables and Bohr’s complementarity. Finally, we explain that our criticism of quantum nonlocality is in the spirit of Hertz-Boltzmann methodology of scientific theories.

The EPR paradox was caused by the provision that quantum variables must have pre-existing values. This type of “hidden property realism” was later falsified by Bell’s Theorem. Accordingly, the physical basis for action-at-a-distance between entangled quanta was removed. Yet, modern interpretations present Bell’s inequality as a Locality Criterion, as if Bell violations can only happen at the quantum level, and only with remote interactions. This is a questionable practice, considering that classical joint measurements also violate such inequalities for mutually exclusive wave properties. In particular, consecutive measurements of polarization produce the same coefficients of correlation as parallel measurements with entangled quanta, yet they are explicitly local. Furthermore, it is possible to combine parallel and consecutive measurements of Type I polarization-entangled photons in a single experiment, conclusively showing that quantum Bell violations can be local. Surprisingly, classical phenomena also require nonlocal interpretations if pre-existing properties are taken for granted. Hence, the solution is to reject the models with pre-existing properties for both classical and quantum wave-like phenomena.

This paper is concerned with the new extended (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE), which is regarded as an extension of the well-known (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation and acts a key role in the incompressible fluid. By means of the Cole-Hopf transform, the Hirota bilinear equation of the studied equation is developed. Then based on the Hirota bilinear equation, we give a detailed investigation into the new exact solutions of the BLMPE. Firstly, the linear superposition principle combined with the weight algorithm is utilized to construct the resonant multiple wave solutions by introducing the parameterization for the wave numbers and frequencies. Secondly, the new homoclinic approach is applied to seek for the periodic wave solutions. Finally, the symbolic computation with the ansatz function scheme is adopted to construct the interaction solutions. The 3-D plots and 2-D contours are figured out to reveal the nonlinear dynamic behaviors of the different solutions. To the best of our knowledge, the results obtained in this work are all new and have not been reported elsewhere yet. The attained solutions can help us understand the nonlinear dynamic behaviors of the new extended (3 + 1)-dimensional BLMPE better. What’s more, the proposed methods in this work can be also adopted to study the resonant multiple wave, periodic wave and interaction solutions of the other PDEs arising in physics.

The main orientation of the current research is to look into the generalized (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation (BKPE) for the water waves. By exerting the Cole-Hopf transform, we extract its Hirota bilinear equation. First, the weight algorithm (WA) together with the linear superposition principle(LSP) is carried out to look for the resonant multiple soliton solutions (RMSSs). Two different types of the RMSSs are obtained by introducing the parameterization of the wave numbers and frequencies. Second, the N -soliton solutions (NSSs) are also explored by using Hirota bilinear equation. On this basis, the resonance conditions of the soliton molecules on the (x, y)-, (x, z)- and (y, z)-planes are extracted and the soliton molecules are found. Finally, the ansatz function scheme, together with the symbolic computation is manipulated to look into the interaction solutions (ISs). Two different interaction solutions of the sin-cosh type and cos-cosh type are developed. A comparison between the RMSSs and the N -soliton solutions are elaborated in detail. Additionally, the dynamics of the solutions are displayed graphically to expound the physical interpretation. The proposed methods in this work can be also employed to inquire into the similar exact solutions of the other PDEs.

The superposition principle is the cornerstone of quantum mechanics, leading to a variety of genuinely quantum effects. Whether the principle applies also to macroscopic systems or, instead, there is a progressive breakdown when moving to larger scales is a fundamental and still open question. Spontaneous wavefunction collapse models predict the latter option, thus questioning the universality of quantum mechanics. Technological advances allow to increasingly challenge collapse models and the quantum superposition principle, with a variety of different experiments. Among them, non-interferometric experiments proved to be the most effective in testing these models. We provide an overview of such experiments, including cold atoms, optomechanical systems, X-ray detection, bulk heating and comparisons with cosmological observations. We also discuss avenues for future dedicated experiments, which aim at further testing collapse models and the validity of quantum mechanics. Collapse models predict that the superposition principle of quantum mechanics breaks down at macroscopic scales. This Review discusses constraints on these models from non-interferometric experiments.

Matter-wave interference experiments provide a direct confirmation of the quantum superposition principle, a hallmark of quantum theory, and thereby constrain possible modifications to quantum mechanics1. By increasing the mass of the interfering particles and the macroscopicity of the superposition2, more stringent bounds can be placed on modified quantum theories such as objective collapse models3. Here, we report interference of a molecular library of functionalized oligoporphyrins4 with masses beyond 25,000 Da and consisting of up to 2,000 atoms, by far the heaviest objects shown to exhibit matter-wave interference to date. We demonstrate quantum superposition of these massive particles by measuring interference fringes in a new 2-m-long Talbot–Lau interferometer that permits access to a wide range of particle masses with a large variety of internal states. The molecules in our study have de Broglie wavelengths down to 53 fm, five orders of magnitude smaller than the diameter of the molecules themselves. Our results show excellent agreement with quantum theory and cannot be explained classically. The interference fringes reach more than 90% of the expected visibility and the resulting macroscopicity value of 14.1 represents an order of magnitude increase over previous experiments2.

One of the hallmarks of quantum physics is the generation of non-classical quantum states and superpositions, which has been demonstrated in several quantum systems, including ions, solid-state qubits and photons. However, only indirect demonstrations of non-classical states have been achieved in mechanical systems, despite the scientific appeal and technical utility of such a capability 1 , 2 , including in quantum sensing, computation and communication applications. This is due in part to the highly linear response of most mechanical systems, which makes quantum operations difficult, as well as their characteristically low frequencies, which hinder access to the quantum ground state 3 – 7 . Here we demonstrate full quantum control of the mechanical state of a macroscale mechanical resonator. We strongly couple a surface acoustic-wave 8 resonator to a superconducting qubit, using the qubit to control and measure quantum states in the mechanical resonator. We generate a non-classical superposition of the zero- and one-phonon Fock states and map this and other states using Wigner tomography 9 – 14 . Such precise, programmable quantum control is essential to a range of applications of surface acoustic waves in the quantum limit, including the coupling of disparate quantum systems 15 , 16 . A non-classical superposition of zero- and one-phonon mechanical Fock states is generated and measured by strongly coupling a surface acoustic-wave resonator to a superconducting qubit.

In contrast to a single quantum bit, an oscillator can store multiple excitations and coherences provided one has the ability to generate and manipulate complex multiphoton states. We demonstrate multiphoton control by using a superconducting transmon qubit coupled to a waveguide cavity resonator with a highly ideal off-resonant coupling. This dispersive interaction is much greater than decoherence rates and higher-order nonlinearities to allow simultaneous manipulation of hundreds of photons. With a tool set of conditional qubit-photon logic, we mapped an arbitrary qubit state to a superposition of coherent states, known as a \"cat state.\" We created cat states as large as 111 photons and extended this protocol to create superpositions of up to four coherent states. This control creates a powerful interface between discrete and continuous variable quantum computation and could enable applications in metrology and quantum information processing.

In this paper, the linear superposition principle and Hirota bilinear equations are simultaneously employed to handle two new (3+1)-dimensional Jimbo–Miwa equations. The corresponding resonant multi-soliton solutions and the related wave numbers are formally established, which are totally different from the previously reported ones. Moreover, the extracted N -soliton waves and dispersion relations have distinct physical structures compared to solutions obtained by Wazwaz. Finally, five graphical representations are portrayed by taking definite values to free parameters which demonstrates various versions of traveling solitary waves. The results show the proposed approach provides enough freedom to construct multi-soliton waves that may be related to a large variety of real physical phenomena and, moreover, enriches the solution structure.

Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that—when supplemented with a limited version of predictability (captured in the textbook accounts by the repeatability postulate)—these core postulates can account for all the symptoms of classicality. In particular, both objective classical reality and elusive information about reality arise, via quantum Darwinism, from the quantum substrate. This approach shares with the Relative State Interpretation of Everett the view that collapse of the wavepacket reflects perception of the state of the rest of the Universe relative to the state of observer’s records. However, our “let quantum be quantum” approach poses questions absent in Bohr’s Copenhagen Interpretation that relied on the preexisting classical domain. Thus, one is now forced to seek preferred, predictable, hence effectively classical but ultimately quantum states that allow observers keep reliable records. Without such (i) preferred basis relative states are simply “too relative”, and the ensuing basis ambiguity makes it difficult to identify events (e.g., measurement outcomes). Moreover, universal validity of quantum theory raises the issue of (ii) the origin of Born’s rule, pk=|ψk|2, relating probabilities and amplitudes (that is simply postulated in textbooks). Last not least, even preferred pointer states (defined by einselection—environment—induced superselection)—are still quantum. Therefore, unlike classical states that exist objectively, quantum states of an individual system cannot be found out by an initially ignorant observer through direct measurement without being disrupted. So, to complete the ‘quantum theory of the classical’ one must identify (iii) quantum origin of objective existence and explain how the information about objectively existing states can appear to be essentially inconsequential for them (as it does for states in Newtonian physics) and yet matter in other settings (e.g., thermodynamics). I show how the mathematical structure of quantum theory supplemented by the only uncontroversial measurement postulate (that demands immediate repeatability—hence, predictability) leads to preferred states. These (i) pointer states correspond to measurement outcomes. Their stability is a prerequisite for objective existence of effectively classical states and for events such as quantum jumps. Events at hand, one can now enquire about their probability—the probability of a pointer state (or of a measurement record). I show that the symmetry of entangled states—(ii) entanglement—assisted invariance or envariance—implies Born’s rule. Envariance also accounts for the loss of phase coherence between pointer states. Thus, decoherence can be traced to symmetries of entanglement and understood without its usual tool—reduced density matrices. A simple and manifestly noncircular derivation of pk=|ψk|2 follows. Monitoring of the system by its environment in course of decoherence typically leaves behind multiple copies of its pointer states in the environment. Only pointer states can survive decoherence and can spawn such plentiful information-theoretic progeny. This (iii) quantum Darwinism allows observers to use environment as a witness—to find out pointer states indirectly, leaving systems of interest untouched. Quantum Darwinism shows how epistemic and ontic (coexisting in epiontic quantum state) separate into robust objective existence of pointer states and detached information about them, giving rise to extantons—composite objects with system of interest in the core and multiple records of its pointer states in the halo comprising of environment subsystems (e.g., photons) which disseminates that information throughout the Universe.