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Keywords = schrödinger’s cat

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16 pages, 8172 KiB  
Article
A Comparative Analysis of a Nonlinear Phase Space Evolution of SU(2) and SU(1,1) Coherent States
by Rodrigo D. Aceves, Miguel Baltazar, Iván F. Valtierra and Andrei B. Klimov
Quantum Rep. 2025, 7(3), 31; https://doi.org/10.3390/quantum7030031 - 5 Jul 2025
Viewed by 256
Abstract
We carried out a comparative study of the phase space evolution of SU(2) and SU(1,1) coherent states generated by the same nonlinear two-mode Hamiltonian. We analyze the dynamics of the Wigner functions in the respective phase spaces and discuss the principal associated physical [...] Read more.
We carried out a comparative study of the phase space evolution of SU(2) and SU(1,1) coherent states generated by the same nonlinear two-mode Hamiltonian. We analyze the dynamics of the Wigner functions in the respective phase spaces and discuss the principal associated physical effects: the squeezing of the appropriate observables and the Schrödinger’s cat state generation characteristic of both the considered symmetry groups. Full article
(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)
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28 pages, 761 KiB  
Article
Counterintuitive Scenarios in Discrete Gravity Without Quantum Effects or Causality Violations
by Benjamin F. Dribus, Jesiah T. Darnell and Neil Goldsmith
Symmetry 2024, 16(12), 1609; https://doi.org/10.3390/sym16121609 - 4 Dec 2024
Viewed by 1150
Abstract
In certain established approaches to quantum gravity, such as causal set theory and causal dynamical triangulations, discrete spacetime structure is taken to be a primary feature, not a secondary effect of “quantizing” a pre-existing classical continuum-based theory, as is done in approaches such [...] Read more.
In certain established approaches to quantum gravity, such as causal set theory and causal dynamical triangulations, discrete spacetime structure is taken to be a primary feature, not a secondary effect of “quantizing” a pre-existing classical continuum-based theory, as is done in approaches such as string theory and loop quantum gravity. For a priori discrete models, the full quantum theory is often obtained via some version of Feynman’s sum-over-histories approach, in which each “history” is a discrete object viewed as a classical spacetime. Counterintuitive physical scenarios such as Schrödinger’s cat or the grandfather paradox are typically associated with either quantum effects or causality violations, but we demonstrate that equally bizarre scenarios can arise at a purely classical level in the discrete causal context due to symmetry considerations. In particular, the graph-theoretic phenomenon of pseudosimilarity leads to situations in which alternative events occurring at physically distinguishable locations in the universe can cause different parts of the universe to “swap identities” in a fugue-like manner alien to continuum-based theories. This phenomenon is perhaps best understood as an extension of the relativity principle, which we call relativity of identity. Full article
(This article belongs to the Special Issue Symmetries in Gravity Research: Classical and Quantum)
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25 pages, 859 KiB  
Article
Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity
by Diego J. Cirilo-Lombardo and Norma G. Sanchez
Symmetry 2024, 16(8), 1026; https://doi.org/10.3390/sym16081026 - 12 Aug 2024
Cited by 1 | Viewed by 1486
Abstract
A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented [...] Read more.
A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, nS and nT, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) Mp(n) representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the Mp(n) group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of Mp(2) are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition <t<). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for n), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological domains on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic Mp(n) group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it. Full article
(This article belongs to the Section Physics)
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49 pages, 468 KiB  
Article
In Our Mind’s Eye: Thinkable and Unthinkable, and Classical and Quantum in Fundamental Physics, with Schrödinger’s Cat Experiment
by Arkady Plotnitsky
Entropy 2024, 26(5), 418; https://doi.org/10.3390/e26050418 - 13 May 2024
Cited by 5 | Viewed by 2216
Abstract
This article reconsiders E. Schrödinger’s cat paradox experiment from a new perspective, grounded in the interpretation of quantum mechanics that belongs to the class of interpretations designated as “reality without realism” (RWR) interpretations. These interpretations assume that the reality ultimately responsible for quantum [...] Read more.
This article reconsiders E. Schrödinger’s cat paradox experiment from a new perspective, grounded in the interpretation of quantum mechanics that belongs to the class of interpretations designated as “reality without realism” (RWR) interpretations. These interpretations assume that the reality ultimately responsible for quantum phenomena is beyond conception, an assumption designated as the Heisenberg postulate. Accordingly, in these interpretations, quantum physics is understood in terms of the relationships between what is thinkable and what is unthinkable, with, physical, classical, and quantum, corresponding to thinkable and unthinkable, respectively. The role of classical physics becomes unavoidable in quantum physics, the circumstance designated as the Bohr postulate, which restores to classical physics its position as part of fundamental physics, a position commonly reserved for quantum physics and relativity. This view of quantum physics and relativity is maintained by this article as well but is argued to be sufficient for understanding fundamental physics. Establishing this role of classical physics is a distinctive contribution of the article, which allows it to reconsider Schrödinger’s cat experiment, but has a broader significance for understanding fundamental physics. RWR interpretations have not been previously applied to the cat experiment, including by N. Bohr, whose interpretation, in its ultimate form (he changed it a few times), was an RWR interpretation. The interpretation adopted in this article follows Bohr’s interpretation, based on the Heisenberg and Bohr postulates, but it adds the Dirac postulate, stating that the concept of a quantum object only applies at the time of observation and not independently. Full article
19 pages, 1160 KiB  
Article
Degeneracy and Photon Trapping in a Dissipationless Two-Mode Optomechanical Model
by Thiago Alonso Merici, Thiago Gomes De Mattos and José Geraldo Peixoto De Faria
Entropy 2024, 26(1), 87; https://doi.org/10.3390/e26010087 - 19 Jan 2024
Viewed by 1361
Abstract
In this work, we theoretically study a finite and undamped two-mode optomechanical model consisting of a high quality optical cavity containing a thin, elastic, and dielectric membrane. The main objective is to investigate the precursors of quantum phase transition in such a model [...] Read more.
In this work, we theoretically study a finite and undamped two-mode optomechanical model consisting of a high quality optical cavity containing a thin, elastic, and dielectric membrane. The main objective is to investigate the precursors of quantum phase transition in such a model by studying the behavior of some observables in the ground state. By controlling the coupling between membrane and modes, we find that the two lowest energy eigenstates become degenerate, as is indicated by the behavior of the mean value of some operators and by other quantifiers as a function of the coupling. Such degenerate states are characterized by a coherent superposition of eigenstates describing one of the two modes preferentially populated and the membrane dislocated from its equilibrium position due the radiation pressure (Schrödinger’s cat states). The delocalization of the compound system photons+membrane results in an increase in fluctuations as measured by Robertson-Schrödinger uncertainty relations. Full article
(This article belongs to the Section Non-equilibrium Phenomena)
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16 pages, 630 KiB  
Article
Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States
by Julio A. López-Saldívar, Olga V. Man’ko, Margarita A. Man’ko and Vladimir I. Man’ko
Entropy 2023, 25(12), 1628; https://doi.org/10.3390/e25121628 - 6 Dec 2023
Cited by 1 | Viewed by 2647
Abstract
The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator [...] Read more.
The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 su(2)-group states) and even and odd Schrödinger cat states related to the other representation of su(2)-algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan–Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the su(2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C2 and C3. Also, their use in quantum information and computing is mentioned. Full article
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11 pages, 337 KiB  
Article
Nuclear Motion Is Classical: Spectrum of a Magic Protonated Water Cluster
by Irmgard Frank
Molecules 2023, 28(18), 6454; https://doi.org/10.3390/molecules28186454 - 6 Sep 2023
Viewed by 1213
Abstract
The assumption that nuclear motion is classical explains many phenomena. The problems of Schrödinger’s cat and the EPR paradoxon do not exist in a perfectly deterministic theory. All it needs is to describe nuclear motion classically right from the beginning. To establish this [...] Read more.
The assumption that nuclear motion is classical explains many phenomena. The problems of Schrödinger’s cat and the EPR paradoxon do not exist in a perfectly deterministic theory. All it needs is to describe nuclear motion classically right from the beginning. To establish this simple idea, it must be tested for as many examples as possible. In the present paper, we use ab initio molecular dynamics to investigate the infrared spectrum of a ‘magic’ protonated water cluster H3O+(H2O)20 which exhibits some features that were believed to afford a quantum treatment of nuclear motion. The role of the temperature in contrast to a quantum mechanical description is discussed. Full article
(This article belongs to the Special Issue Advances in Computational and Theoretical Chemistry)
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18 pages, 1359 KiB  
Article
Transfer of Quantum States and Stationary Quantum Correlations in a Hybrid Optomechanical Network
by Hugo Molinares, Bing He and Vitalie Eremeev
Mathematics 2023, 11(13), 2790; https://doi.org/10.3390/math11132790 - 21 Jun 2023
Cited by 2 | Viewed by 1991
Abstract
We present a systematic study on the effects of dynamical transfer and steady-state synchronization of quantum states in a hybrid optomechanical network consisting of two cavities, which carry atoms inside and interact via a common moving mirror such as the mechanical oscillator. It [...] Read more.
We present a systematic study on the effects of dynamical transfer and steady-state synchronization of quantum states in a hybrid optomechanical network consisting of two cavities, which carry atoms inside and interact via a common moving mirror such as the mechanical oscillator. It is found that a high fidelity transfer of Schrödinger’s cat and squeezed states between two cavities modes is possible. On the other hand, we demonstrate the synchronization effect of the cavity modes in a steady squeezed state with its high fidelity realized by the mechanical oscillator that intermediates the generation, transfer and stabilization of the squeezing. In this framework, we also study the generation and evolution of bipartite and tripartite entanglement and find its connection to the effects of quantum state transfer and synchronization. Particularly, when the transfer occurs at the maximal fidelity, any entanglement is almost zero, so the different cavity modes are disentangled. However, these modes become entangled when the two bosonic modes are synchronized in a stationary squeezed state. The results provided by the current study may find applications in quantum information technologies, in addition to the setups for metrology, where squeezed states are essential. Full article
(This article belongs to the Special Issue Advances in Quantum Optics and Quantum Information)
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17 pages, 319 KiB  
Article
Dynamics of System States in the Probability Representation of Quantum Mechanics
by Vladimir N. Chernega and Olga V. Man’ko
Entropy 2023, 25(5), 785; https://doi.org/10.3390/e25050785 - 11 May 2023
Cited by 7 | Viewed by 1915
Abstract
A short description of the notion of states of quantum systems in terms of conventional probability distribution function is presented. The notion and the structure of entangled probability distributions are clarified. The evolution of even and odd Schrödinger cat states of the inverted [...] Read more.
A short description of the notion of states of quantum systems in terms of conventional probability distribution function is presented. The notion and the structure of entangled probability distributions are clarified. The evolution of even and odd Schrödinger cat states of the inverted oscillator is obtained in the center-of-mass tomographic probability description of the two-mode oscillator. Evolution equations describing the time dependence of probability distributions identified with quantum system states are discussed. The connection with the Schrödinger equation and the von Neumann equation is clarified. Full article
(This article belongs to the Special Issue Quantum Probability and Randomness IV)
14 pages, 4246 KiB  
Communication
Statistical Mixture of Kaleidoscope States Interacting with a Two-Level Atom: Entropy and Purification
by Jorge A. Anaya-Contreras, Arturo Zúñiga-Segundo and Héctor M. Moya-Cessa
Photonics 2023, 10(2), 150; https://doi.org/10.3390/photonics10020150 - 31 Jan 2023
Viewed by 1832
Abstract
We investigate some of the fundamental features of the interaction of a mixture of coherent states, namely, a Kaleidoscope states mixture, with two-level atoms in the Jaynes–Cummings model framework. We begin our analysis by calculating the von Neumann entropy of the field, which [...] Read more.
We investigate some of the fundamental features of the interaction of a mixture of coherent states, namely, a Kaleidoscope states mixture, with two-level atoms in the Jaynes–Cummings model framework. We begin our analysis by calculating the von Neumann entropy of the field, which is determined with the help of the virtual atom method. The oscillations appearing in the entropy indicate a state of purity greater than the initial state, i.e., a purification of the initial state due to a transfer of coherence from the atom to the field. In this oscillatory region, we obtain a negative Wigner function that hints at a (noisy) multiple Schrödinger cat. Full article
(This article belongs to the Special Issue Lasers and Dynamic of Systems)
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11 pages, 267 KiB  
Article
Schrödinger’s Cat Meets Occam’s Razor
by Richard D. Gill
Entropy 2022, 24(11), 1586; https://doi.org/10.3390/e24111586 - 1 Nov 2022
Cited by 3 | Viewed by 3438
Abstract
We discuss V.P. Belavkin’s approach to the Schrödinger cat problem and show its close relation to ideas based on superselection and interaction with the environment developed by N.P. Landsman. The purpose of the paper is to explain these ideas in the most simple [...] Read more.
We discuss V.P. Belavkin’s approach to the Schrödinger cat problem and show its close relation to ideas based on superselection and interaction with the environment developed by N.P. Landsman. The purpose of the paper is to explain these ideas in the most simple possible context, namely: discrete time and separable Hilbert spaces, in order to make them accessible to those coming from the philosophy of science and not too happy with idiosyncratic notation and terminology and sophisticated mathematical tools. Conventional elementary mathematical descriptions of quantum mechanics take “measurement” to be a primitive concept. Paradoxes arise when we choose to consider smaller or larger systems as measurement devices in their own right, by making different and apparently arbitrary choices of location of the “Heisenberg cut”. Various quantum interpretations have different resolutions of the paradox. In Belavkin’s approach, the classical world around us does really exist, and it evolves stochastically and dynamically in time according to probability laws following from successive applications of the Born law. It is a collapse theory. The quantum/classical distinction is determined by the arrow of time. The underlying unitary evolution of the wave-function of the universe enables the designation of a collection of beables which grows as time evolves, and which therefore can be assigned random, classical trajectories. In a slogan: the past is particles, the future is a wave. We, living in the now, are located on the cutting edge between past and future. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering)
10 pages, 1643 KiB  
Article
Generation of Schrödinger Cat States in a Hybrid Cavity Optomechanical System
by Xingwei An, Tonghui Deng, Lei Chen, Saiyun Ye and Zhirong Zhong
Entropy 2022, 24(11), 1554; https://doi.org/10.3390/e24111554 - 29 Oct 2022
Cited by 2 | Viewed by 2111
Abstract
We present an alternative scheme to achieve Schrödinger cat states in a strong coupling hybrid cavity optomechanical system. Under the single-photon strong-coupling regime, the interaction between the atom–cavity–oscillator system can induce the mesoscopic mechanical oscillator to Schrödinger cat states. Comparing to previous schemes, [...] Read more.
We present an alternative scheme to achieve Schrödinger cat states in a strong coupling hybrid cavity optomechanical system. Under the single-photon strong-coupling regime, the interaction between the atom–cavity–oscillator system can induce the mesoscopic mechanical oscillator to Schrödinger cat states. Comparing to previous schemes, the proposed proposal consider the second order approximation on the Lamb–Dicke parameter, which is more universal in the experiment. Numerical simulations confirm the validity of our derivation. Full article
(This article belongs to the Section Quantum Information)
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17 pages, 6665 KiB  
Review
Estrogens and the Schrödinger’s Cat in the Ovarian Tumor Microenvironment
by Marija Gjorgoska and Tea Lanišnik Rižner
Cancers 2021, 13(19), 5011; https://doi.org/10.3390/cancers13195011 - 6 Oct 2021
Cited by 5 | Viewed by 4955
Abstract
Ovarian cancer is a heterogeneous disease affecting the aging ovary, in concert with a complex network of cells and signals, together representing the ovarian tumor microenvironment. As in the “Schrödinger’s cat” thought experiment, the context-dependent constituents of the—by the time of diagnosis—well-established tumor [...] Read more.
Ovarian cancer is a heterogeneous disease affecting the aging ovary, in concert with a complex network of cells and signals, together representing the ovarian tumor microenvironment. As in the “Schrödinger’s cat” thought experiment, the context-dependent constituents of the—by the time of diagnosis—well-established tumor microenvironment may display a tumor-protective and -destructive role. Systemic and locally synthesized estrogens contribute to the formation of a pro-tumoral microenvironment that enables the sustained tumor growth, invasion and metastasis. Here we focus on the estrogen biosynthetic and metabolic pathways in ovarian cancer and elaborate their actions on phenotypically plastic, estrogen-responsive, aging immune cells of the tumor microenvironment, altogether highlighting the multicomponent-connectedness and complexity of cancer, and contributing to a broader understanding of the ovarian cancer biology. Full article
(This article belongs to the Special Issue Immune Microenviroment in Gynecologic Malignancies)
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17 pages, 923 KiB  
Article
Theory of Photon Subtraction for Two-Mode Entangled Light Beams
by Oscar Rosas-Ortiz and Kevin Zelaya
Quantum Rep. 2021, 3(3), 500-516; https://doi.org/10.3390/quantum3030033 - 3 Sep 2021
Cited by 2 | Viewed by 3595
Abstract
Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical cats on demand. However, it lacks theoretical formulation enabling precise predictions [...] Read more.
Photon subtraction is useful to produce nonclassical states of light addressed to applications in photonic quantum technologies. After a very accelerated development, this technique makes possible obtaining either single photons or optical cats on demand. However, it lacks theoretical formulation enabling precise predictions for the produced fields. Based on the representation generated by the two-mode SU(2) coherent states, we introduce a model of entangled light beams leading to the subtraction of photons in one of the modes, conditioned to the detection of any photon in the other mode. We show that photon subtraction does not produce nonclassical fields from classical fields. It is also derived a compact expression for the output field from which the calculation of conditional probabilities is straightforward for any input state. Examples include the analysis of squeezed-vacuum and odd-squeezed states. We also show that injecting optical cats into a beam splitter gives rise to entangled states in the Bell representation. Full article
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11 pages, 5664 KiB  
Case Report
Traumatic Intralenticular Neovascularization in a HLA B27+ Pediatric Patient
by Călin Petru Tătaru, Cătălina Ioana Tătaru, Maria Dudău, Alexandra Moșu, Lăcrămioara Luca, Bosa Maria, Alice Bancu and Paul Filip Curcă
Diagnostics 2021, 11(8), 1493; https://doi.org/10.3390/diagnostics11081493 - 18 Aug 2021
Viewed by 2325
Abstract
(1) Background: Intralenticular tumors are an entity akin to Schrodinger’s cat since, although the human crystalline cells themselves are not known to malignly proliferate, various entities can take the appearance and clinical presentation of a tumor originating in the lens. We present the [...] Read more.
(1) Background: Intralenticular tumors are an entity akin to Schrodinger’s cat since, although the human crystalline cells themselves are not known to malignly proliferate, various entities can take the appearance and clinical presentation of a tumor originating in the lens. We present the peculiar case of an 11-year-old male patient of African descent, HLA B27+, with a previous history of minor ocular trauma and unilateral anterior uveitis a year before which was admitted to our department with total opacification of the crystalline lens in the right eye and lens neovascularization. During surgery, a vascular, white fibrotic mass measuring 0.1–0.2 cm was discovered inside the lens bag and was excised. (2) Methods: Retrospective case review. (3) Results: The histopathological exam of the excised mass revealed an abundant infiltrate consisting of CD68+ foamy macrophages and lymphoplasmacytic elements. CD68 is a pan-macrophage marker associated with an active inflammatory mechanism soliciting macrophages, and tissue activated macrophages are correlated to increased stromal and serum levels of vascular endothelial growth factor, providing an explanation for lens angiogenesis. (4) Conclusions: The diagnosis is of a “masquerade tumor” resulted from an abnormal inflammatory process in connection with previous ocular trauma and possibly the patient’s HLA B27+ status. Full article
(This article belongs to the Special Issue New Frontiers in Diagnostics for Cataract Surgery)
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