Predictions Of Quantum Mechanics Research Articles

Evaluation of acrylamide-based molecularly imprinted polymer thin-sheets for specific protein capture—a myoglobin model

We evaluate a series of thin-sheet hydrogel molecularly imprinted polymers (MIPs), using a family of acrylamide-based monomers, selective for the target protein myoglobin (Mb). The simple production of the thin-sheet MIP offers an alternative biorecognition surface that is robust, stable and uniform, and has the potential to be adapted for biosensor applications. The MIP containing the functional monomer N-hydroxymethylacrylamide (NHMAm), produced optimal specific rebinding of the target protein (Mb) with 84.9% (± 0.7) rebinding and imprinting and selectivity factors of 1.41 and 1.55, respectively. The least optimal performing MIP contained the functional monomer N,N-dimethylacrylamide (DMAm) with 67.5% (± 0.7) rebinding and imprinting and selectivity factors of 1.11 and 1.32, respectively. Hydrogen bonding effects, within a protein-MIP complex, were investigated using computational methods and Fourier transform infrared (FTIR) spectroscopy. The quantum mechanical calculations predictions of a red shift of the monomer carbonyl peak is borne-out within FTIR spectra, with three of the MIPs, acrylamide, N-(hydroxymethyl) acrylamide, and N-(hydroxyethyl) acrylamide, showing peak downshifts of 4, 11, and 8 cm−1, respectively.

Theoretical investigation of impact sensitivity of nitrogen rich energetic salts

The higher impact sensitivity of many energetic materials has become one of the major obstacles which diminishes its wide range of applications in various fields. Salt formation is an effective approach that enhances the stability of the molecules towards impact. In this study quantum mechanical calculations have been employed in order to predict the impact sensitivity trends for the series of nitrogen rich energetic salts: 3-Amino-1,2,4(4H)-oxadiazol-5-one (AOD) and 4-Nitramino-1,2,4-Triazole (NRTZ). Quantum mechanically derived criteria, namely, HOMO-LUMO energy gap, ratio of the bond dissociation energy to molecular total energy, the electrostatic potential at bond mid-point, bond topological parameters were computed, and the quality of results are assessed against experimental BAM fall hammer test results. Several sets of DFT functionals and basis sets were tested to identify the best level of theory for the selected nitrogenous salts. The results demonstrated an excellent qualitative prediction of the impact sensitivity by using CAMB3LYP/6-31G(d)/IEFPCM = water level of theory. Hence, quantum mechanical predictions are an ideal preliminary approach to design advanced energetic salts based on AOD and NRTZ with enhanced stability prior to the synthesis, which facilitates reducing the great cost and risk to safety.

Spacetime quantum actions

We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum generalization of the corresponding classical action. The diagonalization of such quantum actions enables us to recover the predictions of conventional quantum mechanics and reveals an extended unitary equivalence between all physical theories. Quantum correlations and coherent effects across time and between distinct theories acquire a rigorous meaning, which is encoded in the rich temporal structure of physical states. Connections with modern relativistic schemes and the path integral formulation also emerge.

The View from a Wigner Bubble

In a recent no-go theorem [Bong et al, Nature Physics (2020)], we proved that the predictions of unitary quantum mechanics for an extended Wigner's friend scenario are incompatible with any theory satisfying three metaphysical assumptions, the conjunction of which we call "Local Friendliness": Absoluteness of Observed Events, Locality and No-Superdeterminism. In this paper (based on an invited talk for the QBism jubilee at the 2019 Vaxjo conference) I discuss the implications of this theorem for QBism, as seen from the perspective of experimental metaphysics. I argue that the key distinction between QBism and realist interpretations of quantum mechanics is best understood in terms of their adherence to different theories of truth: the pragmatist versus the correspondence theories. I argue that a productive pathway to resolve the measurement problem within a pragmatist view involves taking seriously the perspective of quantum betting agents, even those in what I call a "Wigner bubble". The notion of reality afforded by QBism, I propose, will correspond to the invariant elements of any theory that has pragmatic value to all rational agents -- that is, the elements that are invariant upon changes of agent perspectives. The classical notion of `event' is not among those invariants, even when those events are observed by some agent. Neither are quantum states. Nevertheless, I argue that far from solipsism, a personalist view of quantum states is an expression of its precise opposite: Copernicanism.

Simulation of the Bell inequality violation based on quantum steering concept

Violation of Bell’s inequality in experiments shows that predictions of local realistic models disagree with those of quantum mechanics. However, despite the quantum mechanics formalism, there are debates on how does it happen in nature. In this paper by use of a model of polarizers that obeys the Malus’ law and quantum steering concept, i.e. superluminal influence of the states of entangled pairs to each other, simulation of phenomena is presented. The given model, as it is intended to be, is extremely simple without using mathematical formalism of quantum mechanics. However, the result completely agrees with prediction of quantum mechanics. Although it may seem trivial, this model can be applied to simulate the behavior of other not easy to analytically evaluate effects, such as deficiency of detectors and polarizers, different value of photons in each run and so on. For example, it is demonstrated, when detector efficiency is 83% the S factor of CHSH inequality will be 2, which completely agrees with famous detector efficiency limit calculated analytically. Also, it is shown in one-channel polarizers the polarization of absorbed photons, should change to the perpendicular of polarizer angle, at very end, to have perfect violation of the Bell inequality (2 sqrt 2 ) otherwise maximum violation will be limited to (1.5 sqrt{2}).

A local-realistic quantum mechanical model of spin and spin entanglement

This paper aims at reproducing quantum mechanical (QM) spin and spin entanglement results using a realist, stochastic, and local approach, without the standard QM mathematical formulation. The concrete model proposed includes the description of Stern–Gerlach apparatuses and of Bell test experiments. Single particle trajectories are explicitly evaluated as a function of a few stochastic variables that they assumedly carry on. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. Notably, it is shown that the proposed model, despite being both local and realist, is able to violate the Bell–CHSH inequalities by exploiting the coincidence loophole and thus intrinsically renouncing to one of the Bell’s assumptions.

Density Functional Theory (DFT)-Aided Structure Elucidation of Linear Diterpenes from the Irish Brown Seaweed Bifurcaria bifurcata.

Brown alga Bifurcaria bifurcata is an extraordinarily rich source of linear (acylic) diterpenes with enormous structural diversity. As part of our interest into secondary metabolites of the Irish seaweeds, here we report four new acyclic diterpenes (1–4) and seven known terpenoids (5–11) from the CHCl3 extract of B. bifurcata. The planar structures of the new metabolites were elucidated by means of 1D and 2D NMR, HRMS, and FT-IR spectroscopy. Since linear diterpenes are highly flexible compounds, the assignment of their stereochemistry by conventional methods, e.g., NOESY NMR, is difficult. Therefore, we employed extensive quantum-mechanical prediction of NMR chemical shifts and optical rotation analyses to identify the relative and absolute configurations of the new compounds 1–4. Several compounds moderately inhibited the human breast cancer cell line (MDA-MB-231) with IC50 values ranging from 10.0 to 33.5 μg/mL. This study not only demonstrates the vast capacity of the Irish B. bifurcata to produce highly oxygenated linear diterpenoids, but also highlights the potential of new methodologies for assignment of their stereogenic centers.

Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers.

This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.

Real-time prediction of 1H and 13C chemical shifts with DFT accuracy using a 3D graph neural network.

Nuclear magnetic resonance (NMR) is one of the primary techniques used to elucidate the chemical structure, bonding, stereochemistry, and conformation of organic compounds. The distinct chemical shifts in an NMR spectrum depend upon each atom's local chemical environment and are influenced by both through-bond and through-space interactions with other atoms and functional groups. The in silico prediction of NMR chemical shifts using quantum mechanical (QM) calculations is now commonplace in aiding organic structural assignment since spectra can be computed for several candidate structures and then compared with experimental values to find the best possible match. However, the computational demands of calculating multiple structural- and stereo-isomers, each of which may typically exist as an ensemble of rapidly-interconverting conformations, are expensive. Additionally, the QM predictions themselves may lack sufficient accuracy to identify a correct structure. In this work, we address both of these shortcomings by developing a rapid machine learning (ML) protocol to predict 1H and 13C chemical shifts through an efficient graph neural network (GNN) using 3D structures as input. Transfer learning with experimental data is used to improve the final prediction accuracy of a model trained using QM calculations. When tested on the CHESHIRE dataset, the proposed model predicts observed 13C chemical shifts with comparable accuracy to the best-performing DFT functionals (1.5 ppm) in around 1/6000 of the CPU time. An automated prediction webserver and graphical interface are accessible online at http://nova.chem.colostate.edu/cascade/. We further demonstrate the model in three applications: first, we use the model to decide the correct organic structure from candidates through experimental spectra, including complex stereoisomers; second, we automatically detect and revise incorrect chemical shift assignments in a popular NMR database, the NMRShiftDB; and third, we use NMR chemical shifts as descriptors for determination of the sites of electrophilic aromatic substitution.

The Quantum Mechanics <i>Needs</i> the Principle of Wave-Function Collapse—But This Principle Shouldn’t Be <i>Misunderstood</i>

The postulate of the collapse of the wave-function stands between the microscopic, quantum world, and the macroscopic world. Because of this intermediate position, the collapse process cannot be examined with the formalism of the quantum mechanics (QM), neither with that of classical mechanics. This fact makes some physicists propose interpretations of QM, which avoid this postulate. However, the common procedure used in that is making assumptions incompatible with the QM formalism. The present work discusses the most popular interpretations. It is shown that because of such assumptions those interpretations fail, i.e. predict for some experiments results which differ from the QM predictions. Despite that, special attention is called to a proposal of S. Gao, the only one which addresses and tries to solve an obvious and major contradiction. A couple of theorems are proved for showing that the collapse postulate is necessary in the QM. Although non-explainable with the quantum formalism, this postulate cannot be denied, otherwise one comes to conclusions which disagree with the QM. It is also proved here that the idea of “collapse at a distance” is problematic especially in relativistic cases, and is a misunderstanding. Namely, in an entanglement of two quantum systems, assuming that the measurement of one of the systems (accompanied by collapse of that system on one of its states) collapses the other systems, too without the second system being measured, which leads to a contradiction.

Computational biomedicine. Part 1: molecular medicine

Computational biomedicine. Part 1: molecular medicine

Absolute Configuration and Conformation of (-)-R-t-Butylphenylphosphinoamidate: Chiroptical Spectroscopy and X-ray Analysis.

The absolute configuration and conformations of (−)-tert-butylphenylphosphinoamidate were determined using three different chiroptical spectroscopic methods, namely vibrational circular dichroism (VCD), electronic circular dichroism (ECD), and optical rotatory dispersion (ORD). In each of the spectroscopic methods used, experimental data for the (−)-enantiomer of tert-butylphenylphosphinoamidate were measured in the solution phase. Using the concentration-dependent experimental infrared spectra, the existence of dimers in the solution was investigated, and the monomer–dimer equilibrium constant was determined. Concomitant quantum mechanical predictions of the VCD, ECD, and ORD for monomeric tert-butylphenylphosphinoamidate were carried out using density functional theory (DFT) calculations using the B3LYP functional and the 6-31G(d), 6-311G(2d,2p) and aug-cc-pVDZ basis sets. Similar predictions for dimeric tert-butylphenylphosphinoamidate were also obtained using the B3LYP/6-31G(d) method. A comparison of theoretically predicted data with the corresponding experimental data led to the elucidation of the absolute configuration as (−)-(R)-tert-butylphenylphosphinoamidate with one predominant conformation in the solution. This conclusion was independently supported by X-ray analysis of the complex with (+)-R-2,2′-dihydroxy-1,1′-binaphthol ((+)-R- BINOL).

Bell, Bohm, and qubit: EPR remixed

This article reviews the predictions of quantum mechanics (QM) for one- and two-particle Stern–Gerlach experiments and then frames Bell's results, which rule out hidden-variable alternatives to QM, as attempts by a skeptical Eve to fool Alice and Bob with (first example) classical probability mixtures of non-entangled quantum states and (second example) a classical hidden-variable theory. With hidden variables, Eve can succeed when Alice and Bob limit themselves to two Stern–Gerlach directions, but always fails for some choices of three directions. For three random directions, hidden-variable theories are impossible (we show) exactly 2/3 of the time. All the calculations in this article are available in Mathematica and Python files in the supplementary material, allowing readers to experiment with their own variants.

Are models of local hidden variables for the singlet polarization state necessarily constrained by the Bell inequality?

The Bell inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these states, it purportedly allows distinguishing in an experimentally testable way the predictions of quantum mechanics from those of models of local hidden variables and, ultimately, ruling the latter out. In this paper, we show, however, that the models of local hidden variables constrained by the Bell inequality all share a subtle, though crucial, feature that is not required by fundamental physical principles and, hence, it might not be fulfilled in the actual experimental setup that tests the inequality. Indeed, the disputed feature neither can be properly implemented within the standard framework of quantum mechanics and it is even at odds with the fundamental principle of relativity. Namely, the proof of the inequality requires the existence of a preferred absolute frame of reference (supposedly provided by the lab) with respect to which the hidden properties of the entangled particles and the orientations of each one of the measurement devices that test them can be independently defined through a long sequence of realizations of the experiment. We notice, however, that while the relative orientation between the two measurement devices is a properly defined physical magnitude in every single realization of the experiment, their global rigid orientation with respect to a lab frame is a spurious gauge degree of freedom. Following this observation, we were able to explicitly build a model of local hidden variables that does not share the disputed feature and, hence, it is able to reproduce the predictions of quantum mechanics for the entangled states of two qubits.

Proof of the Peres Conjecture for Contextuality.

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics cannot be reconciled with classical models that are noncontextual for ideal measurements. The first explicit derivation by Kochen and Specker was rather complex, but considerable simplifications have been achieved thereafter. We propose a systematic approach to find minimal Hardy-type and Greenberger-Horne-Zeilinger-type (GHZ-type) proofs of the Kochen-Specker theorem, these are characterized by the fact that the predictions of classical models are opposite to the predictions of quantum mechanics. Based on our results, we show that the Kochen-Specker set with 18 vectors from Cabello etal. [Phys. Lett. A 212, 183 (1996)PYLAAG0375-960110.1016/0375-9601(96)00134-X] is the minimal set for any dimension, verifying a longstanding conjecture by Peres. Our results allow to identify minimal contextuality scenarios and to study their usefulness for information processing.

Computer simulation of Mermin's quantum device

Quantum entanglement is a phenomenon that has no classical counterpart; it is not only difficult to learn but also difficult to teach. It is often an omitted or underrepresented topic in the syllabus of an introductory quantum mechanics or modern physics course. Nearly 40 years ago Mermin published a thought experiment to analyze a device consisting of a transmitter and two receivers. The receivers each had a three-position switch and two lights, one red and one green. Analysis of the operation of the device follows the predictions of quantum mechanics but only simple mathematics is employed to demonstrate the peculiar nature of quantum entanglement. A few years later he reintroduced his quantum device to a more general audience in a Physics Today article and provided another interesting interpretation. In the current paper, we make use of the recently published work in quantum information theory by Candela to have students write code to simulate the operation of the device in that article. Analysis of the device has significant pedagogical value—a fact recognized by Feynman—and simulation of its operation provides students a unique window into quantum mechanics without prior knowledge of the theory.

The Bell Theorem Revisited: Geometric Phases in Gauge Theories

The Bell theorem stands as an insuperable roadblock in the path to a very desired intuitive solution of the EPR paradox and, hence, it lies at the core of the current lack of a clear interpretation of the quantum formalism. The theorem states through an experimentally testable inequality that the predictions of quantum mechanics for the Bell polarization states of two entangled particles cannot be reproduced by any statistical model of hidden variables that shares certain intuitive features. In this paper, we show, however, that the proof of the Bell theorem involves a subtle, though crucial, assumption that is not required by fundamental physical principles and, hence, it is not necessarily fulfilled in the experimental setup that tests the inequality. Indeed, this assumption can neither be properly implemented within the standard framework of quantum mechanics. Namely, the proof of the theorem assumes that there exists a preferred absolute frame of reference, supposedly provided by the lab, which enables to compare the orientation of the polarization measurement devices for successive realizations of the experiment and, hence, to define jointly their response functions over the space of hypothetical hidden configurations for all their possible alternative settings. We notice, however, that only the relative orientation between the two measurement devices in every single realization of the experiment is a properly defined physical degree of freedom, while their global rigid orientation is a spurious gauge degree of freedom. Hence, the preferred frame of reference required by the proof of the Bell theorem does not necessarily exist. Following this observation, we build an explicitly local model of hidden variables that reproduces the predictions of quantum mechanics for the Bell states.

Heat transport in carbon nanotubes: Length dependence of phononic conductivity from the Boltzmann transport equation and molecular dynamics

In this article, we address lattice heat transport in single-walled carbon nanotubes (CNTs) by a quantum mechanical calculation of three-phonon scattering rates in the framework of the Boltzmann transport equation (BTE) and classical molecular dynamics (MD) simulation. Under a consistent choice of an empirical, realistic atomic interaction potential, we compare the tube length dependence of the lattice thermal conductivity (TC) at room temperature determined from an iterative solution of the BTE and from a nonequilibrium MD (NEMD) approach. Qualitatively similar trends are found in the limit of short tubes, where an extensive regime of ballistic heat transport prevailing in CNTs of lengths $L\lesssim 1\,\rm{\mu m}$ is independently confirmed. In the limit of long tubes, the BTE approach suggests a saturation of TC with tube length, whereas direct NEMD simulations of tubes extending up to $L=10\,\rm{\mu m}$ are demonstrated to be insufficient to settle the question of whether a fully diffusive heat transport regime and an intrinsic value of TC exist for CNTs. Noting that acoustic phonon lifetimes lie at the heart of a saturation of TC with tube length as per the BTE framework, we complement the quantum mechanical prediction of acoustic phonon lifetimes with an analysis of phonon modes in the framework of equilibrium MD (EMD). A normal mode analysis (NMA) with an emphasis on long wavelength acoustic modes corroborates the BTE prediction that heat transport in CNTs in the long tube limit is governed by the low attenuation rates of longitudinal and twisting phonons.

Classical dynamics of three-body systems in the Efimov potential

We investigate the classical nonrelativistic dynamics of three bodies in Efimov's $\ensuremath{-}1/{R}^{2}$ potential in three spatial dimensions, with a view towards semiclassical quantization and insight into the geometry of Efimov states. Without the short-distance cutoff, these dynamics are superintegrable, which allows an exact integration of the equations of motion for arbitrary initial conditions. We show that periodic orbits necessarily lead to exactly vanishing binding energy of the bound states, in disagreement with Efimov's quantum-mechanical results. A scaling anomaly demands that the quantum dynamics of three bodies in this potential be augmented by additional boundary conditions affecting all three particles at the short-distance cutoff point, i.e., near the triple collision. We discuss the inherent difficulties in the definition of appropriate three-body boundary conditions in three spatial dimensions and briefly discuss their consequences for (quasi)periodic orbits. Consequently, the classical orbits corresponding to Efimov states cannot be exactly periodic, but must have a finite timescale (lifetime), associated with the time it takes the system's hyperradius to fall to zero, or to the cutoff value, which is typically much longer than the (quasi)period of the hyperangular motion. The scaling properties of the lifetime are in agreement with the quantum-mechanical predictions of the half-life (width) of Efimov states surrounded by an ultracold gas. Detailed spatiotemporal evolution of the system is generally unpredictable beyond the three-body collision point, even though global conservation laws ensure that the system's hyperradius must be periodic.

Tracking the Dynamics of an Ideal Quantum Measurement.

The existence of ideal quantum measurements is one of the fundamental predictions of quantum mechanics. In theory, an ideal measurement projects a quantum state onto the eigenbasis of the measurement observable, while preserving coherences between eigenstates that have the same eigenvalue. The question arises whether there are processes in nature that correspond to such ideal quantum measurements and how such processes are dynamically implemented in nature. Here we address this question and present experimental results monitoring the dynamics of a naturally occurring measurement process: the coupling of a trapped ion qutrit to the photon environment. By taking tomographic snapshots during the detection process, we show that the process develops in agreement with the model of an ideal quantum measurement with an average fidelity of 94%.