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Medical imaging is essential in modern healthcare because it assists physicians in the diagnosis of cancer. Various tissues and features in medical imaging can be recognized using image segmentation algorithms. This feature makes it possible to pinpoint and define particular areas, which makes it easier to precisely locate and characterize anomalities or lesions for cancer diagnosis. Among cancers affecting women, breast cancer is particularly prevalent, underscoring the urgent need to improve the accuracy of image segmentation for breast cancer in order to assist medical practitioners. Multi-threshold image segmentation is widely acknowledged for its direct and effective characteristics. In this context, this paper suggests a refined whale optimization algorithm to improve the segmentation accuracy of breast cancer data. This algorithm optimizes performance by combining a quantum phase interference mechanism and an enhanced solution quality strategy. This work compares the method with classical, homogeneous, state-of-the-art algorithms and runs experiments on the IEEE CEC2017 benchmark to validate its practical optimization performance. Furthermore, a multi-threshold image segmentation algorithm-based image segmentation technique is presented in this study. The Berkeley segmentation dataset and the breast invasive ductal carcinomas segmentation dataset are segmented using the approach using a non-local means two-dimensional histogram and Renyi's entropy. Experimental results demonstrate the excellent performance of this segmentation method in image segmentation applications across both low and high threshold levels. As a result, it emerges as a valuable image segmentation technique with practical applications. [ABSTRACT FROM AUTHOR]

In ultracold Fermi gases, by adjusting the strength of spin orbit coupling to match Fermi energy, many novel quantum effec ts can be genera ted. In the pas t few decades, scholars have conducted extensive theoretical and experimental research on Fermi gases induced by one-dimensional spin orbit coupling. Compared with high-dimensional spin orbit coupling, one-dimensional spin orbit coupling, although relatively simple, is the most reliable and feasible tool for exploring basic quantum physical phenomena in experiments. This paper systematically summarizes the interesting physical phenomena of Fermi gas under one-dimensional spin orbit coupling in theoretical work. Including theoretical research on dynamic oscillation and soliton effect, topological superfluid, Majorana edge state, ferromagnetic phase transit ion, and quantum phase. How to achieve spin orbi t coupling and observe singular phenomena in exp erime nts is a hot and difficult research topic. We summarize several common experimentai schemes and detection met hods. Finally, we look forward to the research on Fermi gas induced by onedimensional spin orbit coupling. One dimensional spin orbit coupling can provide reference for abecedarians and contribute to the study of multi body system regulated by spin orbit coupling. This paper aims to provide a reference for abecedarians in cold atomic physics to gain a deeper understanding of the physical mechanisms of multi-body systems under spin orbit coupling. [ABSTRACT FROM AUTHOR]

We consider a simple harmonic oscillator subject to a time-dependent, spatially homogeneous perturbation and show that it is canonically equivalent to a non-perturbed oscillator. The canonical transformation that relates both systems can be implemented as a unitary transformation mapping the perturbed system and the non-perturbed systems onto each other. This unitary transformation allows us to explicitly compute the time dependence of the states of the perturbed system, and in particular to compute the phase that affects all states. The phase turns out to be a classical action along the classical trajectory of the origin (in phase space), along its motion under the action of perturbation. In this simple system, the transition probabilities due to the perturbation can also be computed explicitly. Our approach is independent of the magnitude of the perturbation, and does not require an adiabaticity assumption. [ABSTRACT FROM AUTHOR]

Understanding phases of matter is of both fundamental and practical importance. Prior to the widespread appreciation and acceptance of topological order, the paradigm of spontaneous symmetry breaking, formulated along the Landau–Ginzburg–Wilson (LGW) dogma, is central to understanding phases associated with order parameters of distinct symmetries and transitions between phases. This work proposes to identify ground-state phases of the quantum many-body system in terms of time order, which is operationally defined by the appearance of the non-trivial temporal structure in the two-time auto-correlation function of a symmetry operator (order parameter) while the system approaches thermodynamic limit. As a special case, the (symmetry protected) time crystalline order phase detects continuous time crystal (CTC). We originally discover the physical meaning of CTC’s characteristic period and amplitude. Time order phase diagrams for spin-1 atomic Bose–Einstein condensate (BEC) and quantum Rabi model are fully worked out. In addition to time-crystalline order, the intriguing phase of time-functional order is discussed in two non-Hermitian interacting spin models.

The paper describes an algorithm for semantic representation of behavioral contexts relative to a dichotomic decision alternative. The contexts are represented as quantum qubit states in two-dimensional Hilbert space visualized as points on the Bloch sphere. The azimuthal coordinate of this sphere functions as a one-dimensional semantic space in which the contexts are accommodated according to their subjective relevance to the considered uncertainty. The contexts are processed in triples defined by knowledge of a subject about a binary situational factor. The obtained triads of context representations function as stable cognitive structure at the same time allowing a subject to model probabilistically-variative behavior. The developed algorithm illustrates an approach for quantitative subjectively-semantic modeling of behavior based on conceptual and mathematical apparatus of quantum theory. [ABSTRACT FROM AUTHOR]

The semi-classical QFT is a transformation in which a specific bit in the calculation circuit is measured and the next bit is controlled by classical information processing according to the measurement result. This paper proposed the t-bit semi-classical quantum phase estimation algorithm by the idea of semi-classical quantum Fourier transform, and it had been implemented on the IBM Q Experience quantum cloud platform, the IBM qiskit quantum simulator and the quantum simulator of the domestic source-Wuyuan cloud platform. The experiment shows that this method improves the estimation accuracy while reducing the need of the algorithm on the circuit scale and the two-bit controlled gate. [ABSTRACT FROM AUTHOR]

The phase in quantum states is an essential information carrier for quantum telecommunications, signal processing, and computation. Quantum phase estimation is therefore a fundamental operation to extract and control useful information at the quantum level. Here, we analyze various approaches to quantum phase estimation, when a phase parameter characterizing a quantum process gets imprinted in a relative phase attached to a quantum state serving as a probe signal. The estimation approaches are based on standard concepts of signal processing (Fourier transform, maximum likelihood), yet operated in the quantum realm. We also exploit the Fisher information, both in its classical and its quantum forms, in order to assess the performance of each approach to quantum phase estimation. We demonstrate a possibility of enhanced estimation performance, inaccessible classically, which is obtained via optimized quantum entanglement. Beyond their significance to quantum phase estimation, the results illustrate how standard concepts of signal processing can contribute to the ongoing developments in quantum information and quantum technologies. [ABSTRACT FROM AUTHOR]

The ground states of spin-1 Bose–Einstein condensate under helicoidal spin–orbit-coupling are investigated, by solving the corresponding Gross–Pitaevskii equations, and via the time-splitting Fourier pseudospectral method. Taking into account the ferromagnetic interaction as well as the antiferromagnetic case, we identify some novel structures on the ground states, including the spot phase, particle-like supersolid phase, hole-like supersolid phase, particle-hole-like supersolid phase, and wave-shaped stripe phase. With the variance of helicoidal gauge potential, the system would undergo abundant quantum phases. • We consider a helicoidal gauge potential on the spin-1 Bose-Einstein condensate. • We figure out the spot phase featuring two horizontal or vertical bright spots. • We identify the particle-like, hole-like, and particle-hole-like supersolid phases. [ABSTRACT FROM AUTHOR]

Quantum approach to human cognition and behavior suffers from a so-called phase problem—lack of means to determine the phase parameter of quantum models before the experiment, which deprives them of predictive power and most of their potential practical impact. We report an empirically supported hypothesis which can help to resolve the issue. According to the hypothesis, the quantum phase between unresolved cognitive alternatives in a family of similar decision making situations is nearly constant across national, linguistic, and cultural backgrounds of subjects. If confirmed, the quantum phase stability phenomenon supplements the quantum model of decision making endowing it with predictive power. This possibility is demonstrated in the testing experiment where irrational behavior within previously unexplored social group could be probabilistically predicted with high accuracy.

Quantum approach to human cognition and behavior suffers from a so-called phase problem—lack of means to determine the phase parameter of quantum models before the experiment, which deprives them of predictive power and most of their potential practical impact. We report an empirically supported hypothesis which can help to resolve the issue. According to the hypothesis, the quantum phase between unresolved cognitive alternatives in a family of similar decision making situations is nearly constant across national, linguistic, and cultural backgrounds of subjects. If confirmed, the quantum phase stability phenomenon supplements the quantum model of decision making endowing it with predictive power. This possibility is demonstrated in the testing experiment where irrational behavior within previously unexplored social group could be probabilistically predicted with high accuracy. [ABSTRACT FROM AUTHOR]

Abstract We derive and discuss a quasidistribution for phases in line of earlier investigations of quasidistributions in quantum optics and their sampling. We illustrate it for classical and quantum fields as well as at the quantum–classical border generated by nonlinear optical processes, such as optical parametric process and Raman scattering. A new nonclassical property of optical fields related to their phases is derived. [ABSTRACT FROM AUTHOR]

Phase is a basic ingredient for quantum states since quantum mechanics uses complex numbers to describe quantum states. In this work, we introduce a rigorous framework to quantify the phase of quantum states. To do so, we regard phase as a quantum resource, and specify the free states and free operations. We determine the conditions a phase measure should satisfy and provide some phase measures. We also propose the notion of intrinsic phase for quantum states. • We introduce a rigorous framework to quantify the phase of quantum states. • We determine the conditions a phase measure should satisfy and provide some phase measures. • We propose the notion of intrinsic phase for quantum states. [ABSTRACT FROM AUTHOR]

We derive suitable uncertainty relations for characteristics functions of phase and number of a single-mode field obtained from the Weyl form of commutation relations. Some contradictions between the product and sums of characteristic functions are noted. [ABSTRACT FROM AUTHOR]

In this paper, we study the time evolution of the geometric phase and nonlocal correlations for a three-level atom interacting with the quantum field emerged in a nonlinear Kerr medium. We discuss the dependence of the physical quantifiers on the phase damping effect. We examine the effects of the initial state and different system parameters on the evolution of the nonlocal correlation and geometric phase with and without the phase damping effect. Furthermore, we explore the link between the geometric phase and the nonlocal correlation during the time evolution. Finally, we show that the model proposed will be very useful to avoid the phase damping effect by a proper choice of the physical parameters in the field for both cases of the initial pure and mixed states of the three-level atom. [ABSTRACT FROM AUTHOR]

We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin–Klauder approaches. One method pertains to Weyl–Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of “weight” functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line. [ABSTRACT FROM AUTHOR]

The Robertson–Schrödinger, Heisenberg–Robertson and Trifonov uncertainty relations for arbitrary two functions f 1 and f 2 depending on the quantum phase and the number of photons respectively, are given. Intelligent states and states which minimize locally the product of uncertainties ( Δ f 1 ) 2 ⋅ ( Δ f 2 ) 2 or the sum ( Δ f 1 ) 2 + ( Δ f 2 ) 2 are investigated for the cases f 1 = ϕ , exp ( i ϕ ) , exp ( − i ϕ ) , cos ϕ , sin ϕ and f 2 = n . [ABSTRACT FROM AUTHOR]

We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric multipole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations, we obtain quantum phases of the electric multipole moment both on a noncommutative space and a noncommutative phase space. We demonstrate that these phase are geometric and dispersive. [ABSTRACT FROM AUTHOR]

Bohmian mechanics, a hydrodynamic formulation of the quantum theory, constitutes a useful tool to understand the role of the phase as the mechanism responsible for the dynamical evolution displayed by quantum systems. This role is analyzed and discussed here in the context of quantum interference, considering to this end two well-known scenarios, namely Young's two-slit experiment and Wheeler's delayed choice experiment. A numerical implementation of the first scenario is used to show how interference in a coherent superposition of two counter-propagating wave packets can be seen and explained in terms of an effective model consisting of a single wave packet scattered off an attractive hard wall. The outcomes from this model are then applied to the analysis of Wheeler's delayed choice experiment, also recreated by means of a reliable realistic simulation. Both examples illustrate quite well how the Bohmian formulation helps to explain in a natural way (and therefore to demystify) aspects of the quantum theory typically regarded as paradoxical. In other words, they show that a proper understanding of quantum phase dynamics immediately removes any trace of unnecessary artificial wave-particle arguments. [ABSTRACT FROM AUTHOR]

Although any quantum system subject to disturbances tends to approach a classical behaviour because of decoherence, such decoherence may be largely quenched when the perturbations are characterized by high-frequency oscillations. This is related to a simple property of Fourier transforms: if, as usually happens, the time dependence of the process is smooth, this implies a rapid decrease of the omega-dependent quantities at high frequencies. As a consequence, in the case of scattering of a particle with a solid (surface or bulk) the contribution of high-frequency vibrations to the Debye-Waller factor is small. But the effect is much more general: it is shown that, whenever a particle interacts with a large system, high-frequency oscillations of the latter contribute little to decoherence, both in the absence (elastic case) and in the presence of energy exchange (thus, if such high-frequency oscillations are the only relevant perturbation, the process maintains quantum- mechanical features). [ABSTRACT FROM AUTHOR]

A generalized Weyl quantization formalism for a particle on the circle is shown to supply an effective method for defining the number–phase Wigner function in quantum optics. A Wigner function for the state ϱ ˆ and the kernel K for a particle on the circle is defined and its properties are analysed. Then it is shown how this Wigner function can be easily modified to give the number–phase Wigner function in quantum optics. Some examples of such number–phase Wigner functions are considered. [ABSTRACT FROM AUTHOR]

We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric qaudrupole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field, we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations both on a noncommutative space and a noncommutative phase space, we obtain quantum phases of the electric quadrupole moment, respectively. We demonstrate that these phases are geometric and dispersive. [ABSTRACT FROM AUTHOR]

The phase fluctuation of Laguerre-Gaussian (LG) vortex beams induced by atmospheric turbulence affects the quantum phase associated with azimuth coordinates and affects the orbital angular momentum of the vortex beams. The measurement of orbital angular momentum is affected by the change in the classical phase and the quantum phase in the Hilbert space. This paper analyzes the additional random complex phase of the vortex beam generated by the atmospheric turbulence and discusses the effect of atmospheric turbulence on the orbital angular momentum of an LG vortex beam using the photon state-vector function. The distributions of the classical phase of vortex beams affected by turbulence of different strengths are calculated and compared with the case for LG vortex beams transmitted through free space. Results show that the atmospheric turbulence affects the phase value of LG vortex beams transmitted in the external field and significantly affects the beam phase structure in the near field. However, the effect of turbulence on the phase of vortex beams is insignificant for a transmission range z > 2000 m while the phase values vary slowly and gradually become constant. [ABSTRACT FROM AUTHOR]

Abstract: Generalized Weyl quantization formalism for the cylindrical phase space is developed. It is shown that the quantum observables relevant to the phase of the linear harmonic oscillator or electromagnetic field can be represented within this formalism by the self-adjoint operators on the Hilbert space . [Copyright &y& Elsevier]

We investigate the strongly interacting lattice Bose gases on a lattice with two-body interaction of nearest neighbors characterized by pair tunneling. The excitation spectrum and the depletion of the condensate of lattice Bose gases are investigated using the Bogoliubov transformation method and the results show that there is a pair condensate as well as a single particle condensate. The various possible quantum phases, such as the Mott-insulator phase (MI), the superfluid phase (SF) of an individual atom, the charge density wave phase (CDW), the supersolid phase (SS), the pair-superfluid (PSF) phase, and the pair-supersolid phase (PSS) are discussed in different parametric regions within our extended Bose-Hubbard model using perturbation theory. [ABSTRACT FROM AUTHOR]

A new method based on Synge's world function is developed for determining within the WKB approximation the gravitationally induced quantum phase shift of a particle propagating in a stationary spacetime. This method avoids any calculation of geodesics. A detailed treatment is given for relativistic particles within the weak field, linear approximation of any metric theory. The method is applied to the calculation of the oscillation terms governing the interference of neutrinos considered as the superposition of two eigenstates having different masses. It is shown that the neutrino oscillations are not sensitive to the gravitomagnetic components of the metric as long as the spin contributions can be ignored. Explicit calculations are performed when the source of the field is a spherical, homogeneous body. A comparison is made with previous results obtained in Schwarzschild spacetime. [ABSTRACT FROM AUTHOR]

Abstract: A comparative analysis of four different approaches to the notion of phase in quantum optics is carried out in the framework of the Ramsey interferometer scheme, where phase correlation between two spatially separated quantum electromagnetic modes emerges as a consequence of resonant two-level atoms traversing the modes. The measure of correlation is expressed through the dispersion of the inter-mode phase difference cosine. A simple law obtained within a semiclassical approach is used to verify the quantum phase approaches. Somewhat unexpectedly, the definite advantage of the superoperator method by M.Ban is revealed. [Copyright &y& Elsevier]

Abstract: The quantum decision theory is examined in its simplest form of two-condition two-choice setting. A set of inequalities to be satisfied by any quantum conditional probability describing the decision process is derived. Experimental data indicating the breakdown of classical explanations are critically examined with quantum theory using the full set of quantum phases. [ABSTRACT FROM AUTHOR]

Abstract: A recent method of constructing quantum mechanics in noncommutative coordinates, alternative to implying noncommutativity by means of star product is discussed. Within this approach we study Hall effect as well as quantum phases in noncommutative coordinates. The θ-deformed phases which we obtain are velocity independent. [ABSTRACT FROM AUTHOR]

Based on the concept of classical phase, we formulate a new explanation for the quantum phase from the quantum mechanical point of view. The quantum phase is the canonically conjugate variable of an angular momentum operator, which corresponds to the angular position φ in an actual physical space with a classical reference frame, but it takes a complex exponential form eiφ≡cosφ+i sinφ in the abstract Hilbert space of a quantum reference frame. This formulation is simply the famous Euler formula in a complex number field. In particular, when φ = π/2, the correlative quantum phase is a unitary pure imaginary number eiπ/2≡cos(π/2)+i sin(π/2) ≡ i. By using a photon state-vector function that is the general solution of photon Schrödinger equation and can completely describe a photon’s behavior, we discuss the relationship between the angular momentum of a photon and the phase of the photon; we also analyze the intrinsic relationship between the macroscopic light wave phase and the microscopic photon phase. [ABSTRACT FROM AUTHOR]

This paper extends the index theory originally valid only for classical nonlinear systems to quantum mechanical systems. Based on the Hamilton quantum mechanics, probabilistic behavior described by a wavefunction ψ(x) can be represented equivalently by nonlinear, complex-valued Hamilton equations of motion, from which we can identify fixed points, evaluate their indices and derive quantum index theory. Three quantum indices are discovered for quantum systems. The momentum index np counting the net change of the momentum phase is the counterpart of the classical index and is an indication of whether a quantum trajectory is closed. The wavefunction index nΨ counting the net change of the wavefunction phase, called Berry's geometrical phase, is responsible for the Aharonov-Bohm effect and for the Wilson-Sommerfeld quantization law. The combined index nψ¹ = np + nψ counts the net phase change of the wavefunction derivative ψ¹. Apart from their geometric meanings, it is pointed out here that the three indices, np, nψ and nψ, act as quantum numbers to represent quantization levels, respectively, for the kinetic energy E&#;955, the quantum potential energy Q and the combined energy Eλ + Q. [ABSTRACT FROM AUTHOR]

Abstract: Recently we have shown that the reduction of the Carruthers–Nieto symmetric quantum phase fluctuation parameter (U) with respect to its coherent state value corresponds to an antibunched state, but the converse is not true. Consequently reduction of U is a stronger criterion of nonclassicality than the lowest order antibunching. Here we have studied the possibilities of reduction of U in intermediate states by using the Barnett–Pegg formalism. We have shown that the reduction of phase fluctuation parameter U can be seen in different intermediate states, such as binomial state, generalized binomial state, hypergeometric state, negative binomial state, and photon added coherent state. It is also shown that the depth of nonclassicality can be controlled by various parameters related to intermediate states. Further, we have provided specific examples of antibunched states, for which U is greater than its Poissonian state value. [Copyright &y& Elsevier]

We study quantum phases of ultracold bosonic atoms in a two-dimensional optical superlattice. The extended Bose–Hubbard model derived from the system of ultracold bosonic atoms in an optical superlattice is solved numerically with the Gutzwiller approach. We find that the modulated superfluid (MS), Mott-insulator (MI) and density-wave (DW) phases appear in some regimes of parameters. The experimental detection of the first-order correlations and the second-order correlations of different quantum phases with time-of-flight and noise-correlation techniques is proposed. [ABSTRACT FROM AUTHOR]

We consider the issue of whether complex numbers are necessary in the formulation of quantum theory. We argue that their introduction is not forced on us by the dynamics, but it is absolutely necessary in order to incorporate the observable properties of the geometric phases that appear in interference experiments. This remark provides the motivation for the construction of a histories-based axiomatic scheme for quantum theory, in which phases are considered as primitive elements, on equal footing with probabilities. This scheme reduces to standard quantum theory for systems characterised by a background causal structure–however it may lead to a different description in the domain of quantum gravity. [ABSTRACT FROM AUTHOR]