States In Quantum Theory Research Articles

Uncovering the Hidden Defects of the Basic Equations of Quantum Mechanics on the Basis of Scientific Philosophy

From the very beginning of his development, Einstein was very critical of the main results of quantum mechanics. That is why in 1925, when the main papers on matrix mechanics were published, he wrote to his friend Besso [1] as follows: "The most interesting theoretical achievement of recent times is the Heisenberg-Born-Jordan theory of quantum states. A real witchcraft calculus in which infinite determinants (matrices) appear instead of Cartesian coordinates. It is highly witty and, due to its complexity, is insured against proving erroneous." In this connection I wish to say the following. A lot of time has passed since this thought was made. Therefore it makes sense to try to prove that the results of matrix mechanics actually contain defects. In the paper an attempt is made to prove that it is really so.

Optimal quantum reservoir computing for the noisy intermediate-scale quantum era.

Universal fault-tolerant quantum computers require millions of qubits with low error rates. Since this technology is years ahead, noisy intermediate-scale quantum (NISQ) computation is receiving tremendous interest. In this setup, quantum reservoir computing is a relevant machine learning algorithm. Its simplicity of training and implementation allows to perform challenging computations on today's available machines. In this Letter, we provide a criterion to select optimal quantum reservoirs, requiring few and simple gates. Our findings demonstrate that they render better results than other commonly used models with significantly less gates and also provide insight on the theoretical gap between quantum reservoir computing and the theory of quantum states' complexity.

Thermal expansion of FeNi Invar and zinc-blende CdTe from the view point of local structure

Thermal expansion of FeNi Invar and zinc-blende CdTe was investigated from the view point of local structure using the extended x-ray absorption fine structure (EXAFS) spectroscopic data and the path-integral effective classical potential (PIECP) Monte Carlo computational simulations. In this Review article, first the quantum statistical perturbation theory is intuitively described to see different character concerning thermal expansion between the quantum and classical theories. The diatomic Br2 molecule is employed as a simple example. Second, the PIECP theory is briefly described to note advantages and disadvantages of this simulation technique. Historical background is also discussed for the EXAFS investigation of thermal expansion based on the quantum statistical theories. The results of the FeNi Invar alloy are then summarized. The origin of zero thermal expansion in the FeNi alloy is ascribed to the so-called Invar effect that implies the variation of the electronic structure of Fe atoms depending on temperature. Zero thermal expansion at low temperature is however found to originate from the vibrational quantum effect. It is also noted that the interatomic distances of Fe-Fe, Fe-Ni, and Ni-Ni pairs are slightly but meaningfully different from each other, although the alloy exhibit a simple fcc crystal. Such a pair- dependent difference is also true for thermal expansion and we will discuss thermal expansion from the local point of view, which is interestingly different from the lattice thermal expansion significantly. Finally, the results of the zinc blende (or diamond) structure are presented. Although the origin of negative thermal expansion in these tetrahedral crystals is known as a result of classical vibrational anomaly within the Newton dynamics theory, the quantum statistical simulation is found to be essential to reproduce the negative thermal expansion of CdTe. It is emphasized that the vibrational quantum effect and classical anharmonicity are of great importance for the understanding of low-temperature thermal expansion as well as the elastic constants.

Quantum theory of photonic vortices and quantum statistics of twisted photons

The topological charge of a photonic vortex is an essential quantity in singular optics and the critical parameter to characterize the vorticity of twisted light. However, the definition of the photonic topological charge remains elusive. Here we put forth a theoretical formalism to provide a comprehensive treatment of photonic vortices. We introduce quantum operators for the photon current density and helicity current density based on the continuity equations from the paraxial Helmholtz equation. Our formalism allows us to introduce flow velocity and circulation for photonic currents in parallel to their counterparts in superfluids. The quantized circulation of the photonic currents is conserved during propagation and it gives an explicit definition of the photonic topological charge as the winding number of a photonic vortex. In particular, we predict helicity current generated pure-helicity vortices, in which the photon current vanishes. Finally, we show an interesting effect that the quantum statistics of twisted photon pairs are essentially determined by their spin states.

Topological Quantum Statistical Mechanics and Topological Quantum Field Theories

The Ising model describes a many-body interacting spin (or particle) system, which can be utilized to imitate the fundamental forces of nature. Although it is the simplest many-body interacting system of spins (or particles) with Z2 symmetry, the phenomena revealed in Ising systems may afford us lessons for other types of interactions in nature. In this work, we first focus on the mathematical structure of the three-dimensional (3D) Ising model. In the Clifford algebraic representation, many internal factors exist in the transfer matrices of the 3D Ising model, which are ascribed to the topology of the 3D space and the many-body interactions of spins. They result in the nonlocality, the nontrivial topological structure, as well as the long-range entanglement between spins in the 3D Ising model. We review briefly the exact solution of the ferromagnetic 3D Ising model at the zero magnetic field, which was derived in our previous work. Then, the framework of topological quantum statistical mechanics is established, with respect to the mathematical aspects (topology, algebra, and geometry) and physical features (the contribution of topology to physics, Jordan–von Neumann–Wigner framework, time average, ensemble average, and quantum mechanical average). This is accomplished by generalizations of our findings and observations in the 3D Ising models. Finally, the results are generalized to topological quantum field theories, in consideration of relationships between quantum statistical mechanics and quantum field theories. It is found that these theories must be set up within the Jordan–von Neumann–Wigner framework, and the ergodic hypothesis is violated at the finite temperature. It is necessary to account the time average of the ensemble average and the quantum mechanical average in the topological quantum statistical mechanics and to introduce the parameter space of complex time (and complex temperature) in the topological quantum field theories. We find that a topological phase transition occurs near the infinite temperature (or the zero temperature) in models in the topological quantum statistical mechanics and the topological quantum field theories, which visualizes a symmetrical breaking of time inverse symmetry.

The impact of distinct loss mechanisms on multi-photon states

Quantum optics plays an important role in many contemporary applications of quantum information processing and quantum metrology. Experimental implementations of these protocols, however, inevitably exhibit loss. This loss has two distinct forms, stochastic loss and deterministic loss, which impact quantum mechanical systems in distinct ways. In this exposition, we offer a straightforward experimental illustration of the impact of both forms of loss on multi-photon states. Specifically, we show that heralding statistics for two-photon states decrease in the obvious way under stochastic loss, and yet are unchanged in the presence of deterministic loss. This demonstration offers an intuitive clarification of loss for multi-photon systems for the student familiar with elementary quantum mechanics, and emphasizes the difference between pure and mixed states in quantum theory more generally. This presentation is targeted towards advanced undergraduate students familiar with quantum optics.

Reductive Explanation and the Construction of Quantum Theories

I argue that philosophical issues concerning reductive explanations help constrain the construction of quantum theories with appropriate state spaces. I illustrate this general proposal with two examples of restricting attention to physical states in quantum theories: regular states and symmetry-invariant states.

Mechanistic insights into efficient reversible hydrogen storage in ferrotitanium

Although FeTi is a well-known hydrogen storage material, producing FeTi on a commercial scale is quite challenging, and generally, one ends up with a multi-phase system consisting of Fe2Ti and FeTi. As Fe2Ti is inert towards hydrogen, it lowers the hydrogen storage efficacy of FeTi. However, there are some reports, which propose that the presence Fe2Ti in FeTi, primarily on the surface is inevitable and it helps in activation of FeTi. Here, we report results of targeted experiments together with first-principles density functional theory (DFT) based calculations to investigate the hydrogen storage properties of FeTi vis-à-vis origin of inertness of Fe2Ti towards hydrogen storage. The formation enthalpies, calculated using density functional theory, of FeTi–H system were found to be very close to the experimental values (−28.1 and −33.72 kJ/mol H2 for FeTiH and FeTiH2 respectively), and that of Fe2Ti–H systems was positive, indicating the inability to form stable intermetallic-hydrides. This corroborates well with the experimental observations, that the pure phase of Fe2Ti cannot store hydrogen. Further, the Gibbs free energy for FeTiH and FeTiH2 were evaluated at 298 K using first-principles quantum mechanics and statistical thermodynamics theories. The vibrational and electronic entropies were calculated using Debye theory of heat capacities. Gibbs free energy at 298 K for FeTiH and FeTiH2 were found to be −5.01 and −3.52 kJ/mol of H2, respectively. Our present study concludes that proper care must be taken to avoid or minimize the formation of Fe2Ti during the production of FeTi.

Generalised versions of separable decompositions applicable to bipartite entangled quantum states

The investigation of separable states in quantum theory has been driven by the notion that they are highly classical, in that they do not demonstrate nonlocality, and are in some contexts unable to support non-classical computation. The converse question, the extent to which entangled states do or do not support non-classical information processing, is less well understood. Motivated by this question we extend the notion of quantum separability into the entangled quantum states, by constructing separable decompositions that describe them with the ‘smallest’ possible sets of non-physical local operators. We consider a few ways to define the word ‘smallest’ and present techniques for obtaining them. The methods involve calculating certain forms of cross norm. The results generalise significantly the results obtained in our previous work on this topic (2015 New J. Phys. 17 093047), and can be be used to construct classical simulation methods and local hidden variable models for subsets of local measurements on entangled quantum states.

Thickness-driven first-order phase transitions in manganite ultrathin films

We report thickness dependent inhomogeneous antiferromagnetic (AFM) to ferromagnetic (FM) phase transitions in ultrathin $\mathrm{L}{\mathrm{a}}_{0.7}\mathrm{S}{\mathrm{r}}_{0.3}\mathrm{Mn}{\mathrm{O}}_{3}$ (LSMO) films grown on the $\mathrm{SrTi}{\mathrm{O}}_{3}$ substrate. When the films are 4--7 unit cells (UCs) thick, FM domains appear as isolated nanodisks in the AFM matrix that together floats on top of the three AFM base UCs, leading a superparamagnetic blocking behavior. Our first principles calculations unravel the rather counterintuitive physical origin of this mixed phase state; the formation of FM/AFM domain boundaries is energetically favorable. At 8 UCs, an abrupt shear strain relief occurs in the LSMO thin film and twinning patterns with two unit cell periodicity form along the [010] and [100] directions. Our studies reveal the complexity of the magnetic phase transition at the nanometer scale and open a door for the development of quantum devices and statistical theories.

Generalized entropies in quantum and classical statistical theories

We study a version of the generalized (h, {\phi})-entropies, introduced by Salicr\'u et al, for a wide family of probabilistic models that includes quantum and classical statistical theories as particular cases. We extend previous works by exploring how to define (h, {\phi})-entropies in infinite dimensional models.

Beams of photons with nonzero projections of orbital angular momenta: new results

Solving Maxwell’s equations in cylindrical coordinates yields states in quantum theory with definite values of energy ℏω, longitudinal momentum ℏkz, and total angular momentum projection ℏm on the z-axis (where ℏ is the Planck constant). Experimentally, values of up to ℏm Ȉ 104 ℏ have been obtained for the last quantity. The wave front of such states is like a meat grinder screw, with the lines of force of the Poynting vector representing the screw line. Such states differ from plane waves by the nonzero orbital angular momentum projection on the direction of motion, and from spherical waves, by the definite direction of motion. For brevity, these states are referred to as ‘twisted photons’. In this paper, recent experimental and theoretical results on twisted photons are reviewed, to which the present authors actively contributed. Detailed discussion is given to recent experiments on the production of high-intensity beams of terahertz (wavelength: 140 μm) twisted photons performed on the Novosibirsk free electron laser at the Budker Institute of Nuclear Physics, SB RAS. Recent theoretical work on the interaction of twisted photons with atoms is summarized. Due to their extra degree of freedom — the projection of the total angular momentum on the direction of motion — twisted photons represent a novel research tool of potentially wide application in physics.

On the Choice of Algebra for Quantization

In this article, I examine the relationship between physical quantities and physical states in quantum theories. I argue against the claim made by Arageorgis that the approach to interpreting quantum theories known as Algebraic Imperialism allows for “too many states.” I prove a result establishing that the Algebraic Imperialist has very general resources that she can employ to change her abstract algebra of quantities in order to rule out unphysical states.

Quantum stability of nonlinear wave type solutions with intrinsic mass parameter in QCD

The problem of existence of a stable vacuum field in a pure quantum chromodynamics (QCD) is revised. Our approach is based on using classical stationary non-linear wave type solutions with intrinsic mass scale parameter. Such solutions can be treated as quantum mechanical wave functions describing massive spinless states in quantum theory. We verify whether non-linear wave type solutions can form a stable vacuum field background within the framework of effective action formalism. We demonstrate that there is a special class of stationary generalized Wu-Yang monopole solutions which are stable against quantum gluon fluctuations.

Markovian statistics on evolving systems

A novel framework for the analysis of observation statistics on time discrete linear evolutions in Banach space is presented. The model differs from traditional models for stochastic processes and, in particular, clearly distinguishes between the deterministic evolution of a system and the stochastic nature of observations on the evolving system. General Markov chains are defined in this context and it is shown how typical traditional models of classical or quantum random walks and Markov processes fit into the framework and how a theory of quantum statistics (sensu Barndorff-Nielsen, Gill and Jupp) may be developed from it. The framework permits a general theory of joint observability of two or more observation variables which may be viewed as an extension of the Heisenberg uncertainty principle and, in particular, offers a novel mathematical perspective on the violation of Bell’s inequalities in quantum models. Main results include a general sampling theorem relative to Riesz evolution operators in the spirit of von Neumann’s mean ergodic theorem for normal operators in Hilbert space.

Experimental test of environment-assisted invariance

Envariance, or environment-assisted invariance, is a recently identified symmetry for maximally entangled states in quantum theory with important ramifications for quantum measurement, specifically for understanding Born's rule. We benchmark the degree to which nature respects this symmetry by using entangled photon pairs. Our results show quantum states can be $(99.66\ifmmode\pm\else\textpm\fi{}0.04)%$ envariant as measured using the quantum fidelity, and $(99.963\ifmmode\pm\else\textpm\fi{}0.005)%$ as measured using a modified Bhattacharya coefficient, as compared with a perfectly envariant system which would be 100% in either measure. The deviations can be understood by the less-than-maximal entanglement in our photon pairs.

Low temperature heat capacity of water clusters

Geometry optimization and vibrational frequency calculation are carried out at the MP2/6-31G(d,p) level for 35 low-energy isomers of (H2O)n clusters in the size range n=6–21. The heat capacities of the clusters are calculated using quantum statistical theories based on the harmonic approximation. The specific heat capacity increases with the cluster size but the difference diminishes gradually with increasing size. The heat capacities divided by the number of intermolecular vibrational modes are very close for all the clusters. The overall picture of the heat capacity of the clusters is bulk-like and it agrees well with the experimental results of size-selected clusters.

Unstable states in quantum theory

Various approaches to the problem of describing unstable particles are reviewed. Fundamental problems that arise in quantum field description of these particles and the ways of their solution are considered. Among them, there is an approach related to the notion of the smeared (continuous) mass, which originates from the finite lifetime of unstable particles. The quantum field model of unstable particles with smeared mass, which is built upon two basic axiomatic elements, is considered in detail. The basic processes with unstable particles (decay and scattering) are considered within the framework of the model and the formalism for describing physical characteristics of those processes is developed. The model is successfully applied to describing the processes of pair and triple boson production at the linear collider, top quark pair production, and certain hadronic decays. Based on this model, the factorization method is developed, which allows a description of complicated and multistep scattering and decay processes with unstable particles to be considerably simplified.

Anomalies and renormalization of mixed states in quantum theories

In a Hamiltonian approach to anomalies, parity and time-reversal symmetries can be restored by introducing suitable impure (or mixed) states. However, the expectation values of observables such as the Hamiltonian diverges in such impure states. Here, we show that such divergent expectation values can be treated within a renormalization group (RG) framework, leading to a set of β-functions in the moduli space of the operators representing the observables. This leads to well-defined expectation values of the Hamiltonian in a phase where the impure state restores the P and T symmetry. We also show that this RG procedure leads to a mass gap in the spectrum. Such a framework may be relevant for long wavelength descriptions of condensed matter systems such as the quantum spin Hall (QSH) effect.

Gravity-Related Wave Function Collapse

The gravity-related model of spontaneous wave function collapse, a longtime hypothesis, damps the massive Schrödinger Cat states in quantum theory. We extend the hypothesis and assume that spontaneous wave function collapses are responsible for the emergence of Newton interaction. Superfluid helium would then show significant and testable gravitational anomalies.