Quanta最新文献

{"title":"Tunneling Probability of Quantum Wavepacket in Time-Dependent Potential Well","authors":"Aarouj Ahmed","doi":"10.12743/quanta.v13i1.246","DOIUrl":"https://doi.org/10.12743/quanta.v13i1.246","url":null,"abstract":"Quantum tunneling of particles plays an important role in many chemical reactions. Studying quantum tunneling in time-dependent potential wells is tricky since most of the available solutions of time-dependent potential wells are coupled to specific properties of the Hamiltonian. Here, we investigate the tunneling probability of a quantum wavepacket in time-dependent potential well by using the split operator method. This numerical method can give us an overview of the tunneling probability of a quantum wavepacket for any temporal change in the shape of the potential well. We study a time-dependent potential well model evolving from symmetric to asymmetric quartic double well since quartic potential wells resemble certain practically available potential well models.Quanta 2024; 13: 11–19.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141014882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Enigmas of Fluctuations of the Universal Quantum Fields","authors":"Mani L. Bhaumik","doi":"10.12743/quanta.v12i1.250","DOIUrl":"https://doi.org/10.12743/quanta.v12i1.250","url":null,"abstract":"The primary ingredients of reality are the universal quantum fields, which fluctuate persistently, spontaneously, and randomly. The general perception of the scientific community is that these quantum fluctuations are due to the uncertainty principle. Here, we present cogent arguments to show that the uncertainty principle is a consequence of the quantum fluctuations, but not their cause. This poses a conspicuous enigma as to how the universal fields remain immutable with an expectation value so accurate that it leads to experimental results, which are precise to one part in a trillion. We discuss some reasonable possibilities in the absence of a satisfactory solution to this enigma.Quanta 2023; 12: 190–201.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138584846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Weak Values and Feynman's Blind Alley","authors":"Dmitri Sokolovski","doi":"10.12743/quanta.v12i1.249","DOIUrl":"https://doi.org/10.12743/quanta.v12i1.249","url":null,"abstract":"Feynman famously recommended accepting the basic principles of quantum mechanics without trying to guess the machinery behind the law. One of the corollaries of the Uncertainty Principle is that the knowledge of probability amplitudes does not allow one to make meaningful statements about the past of an unobserved quantum system. A particular type of reasoning, based on weak values, appears to do just that. Has Feynman been proven wrong by the more recent developments? Most likely not.Quanta 2023; 12: 180–189.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139260259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum Mechanics with Real Numbers: Entanglement, Superselection Rules and Gauges","authors":"Vlatko Vedral","doi":"10.12743/quanta.v12i1.241","DOIUrl":"https://doi.org/10.12743/quanta.v12i1.241","url":null,"abstract":"We show how imaginary numbers in quantum physics can be eliminated by enlarging the Hilbert space followed by an imposition of—what effectively amounts to—a superselection rule. We illustrate this procedure with a qubit and apply it to the Mach–Zehnder interferometer. The procedure is somewhat reminiscent of the constrained quantization of the electromagnetic field, where, in order to manifestly comply with relativity, one enlarges the Hilbert Space by quantizing the longitudinal and scalar modes, only to subsequently introduce a constraint to make sure that they are actually not directly observable.Quanta 2023; 12: 164–170.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135924159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shor's Factoring Algorithm and Modular Exponentiation Operators","authors":"Robert L. Singleton Jr","doi":"10.12743/quanta.v12i1.235","DOIUrl":"https://doi.org/10.12743/quanta.v12i1.235","url":null,"abstract":"We provide a pedagogical presentation of Shor's factoring algorithm, which is a quantum algorithm for factoring very large numbers (of order of hundreds to thousands of bits) in polynomial time. In contrast, all known classical algorithms for the factoring problem take an exponential time to factor such large numbers. Shor's algorithm therefore has profound implication for public-key encryption such as RSA and Diffie–Hellman key exchange. We assume no prior knowledge of Shor's algorithm beyond a basic familiarity with the circuit model of quantum computing. Shor's algorithm contains a number of moving parts, and can be rather daunting at first. The literature is replete with derivations and expositions of Shor's algorithm, but most of them seem to be lacking in essential details, and none of them provide a pedagogical presentation. They require a thicket of appendices and assume a knowledge of quantum algorithms and classical mathematics with which the reader might not be familiar. We therefore start with first principle derivations of the quantum Fourier transform (QFT) and quantum phase estimation (QPE), which are the essential building blocks of Shor's algorithm. We then go on to develop the theory of modular exponentiation (ME) operators, one of the fundamental components of Shor's algorithm, and the place where most of the quantum resources are deployed. We also delve into the number theory that establishes the link between factorization and the period of the modular exponential function. We then apply the QPE algorithm to obtain Shor's factoring algorithm. We also discuss the post-quantum processing and the method of continued fractions, which is used to extract the exact period of the modular exponential function from the approximately measured phase angles of the ME operator. The manuscript then moves on to a series of examples. We first verify the formalism by factoring N=15, the smallest number accessible to Shor's algorithm. We then proceed to factor larger integers, developing a systematic procedure that will find the ME operators for any semi-prime N=p×q (where q and p are prime). Finally, we factor the composite numbers N=21, 33, 35, 143, 247 using the Qiskit simulator. It is observed that the ME operators are somewhat forgiving, and truncated approximate forms are able to extract factors just as well as the exact operators. This is because the method of continued fractions only requires an approximate phase value for its input, which suggests that implementing Shor's algorithm might not be as difficult as first suspected.Quanta 2023; 12: 41–130.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135395508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Monte Carlo Simulation for the Frequency Comb Spectrum of an Atom Laser","authors":"A. Schelle","doi":"10.12743/quanta.v12i1.243","DOIUrl":"https://doi.org/10.12743/quanta.v12i1.243","url":null,"abstract":"A theoretical particle-number conserving quantum field theory based on the concept of imaginary time is presented and applied to the scenario of a coherent atomic laser field at ultra-cold temperatures. The proposed theoretical model describes the analytical derivation of the frequency comb spectrum for an atomic laser realized from modeling a coherent atomic beam of condensate and non-condensate quantum field components released from a trapped Bose–Einstein condensate at a given repetition phase and frequency. The condensate part of the atomic vapor is assumed to be subjected to thermal noise induced by the temperature of the surrounding thermal atomic cloud. This new quantum approach uses time periodicity and an orthogonal decomposition of the quantum field in a complex-valued quantum field representation to derive and model the quantum field's forward- and backward-propagating components as a standing wave field in the same unique time and temperature domain without quantitative singularities at finite temperatures. The complex-valued atom laser field, the resulting frequency comb, and the repetition frequency distribution with the varying shape of envelopes are numerically monitored within a Monte Carlo sampling method, as a function of temperature and trap frequency of the external confinement.Quanta 2023; 12: 171–179.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139372374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Theory of Quantum Instruments","authors":"S. Gudder","doi":"10.12743/quanta.v12i1.233","DOIUrl":"https://doi.org/10.12743/quanta.v12i1.233","url":null,"abstract":"Until recently, a quantum instrument was defined to be a completely positive operation-valued measure from the set of states on a Hilbert space to itself. In the last few years, this definition has been generalized to such measures between sets of states from different Hilbert spaces called the input and output Hilbert spaces. This article presents a theory of such instruments. Ways that instruments can be combined such as convex combinations, post-processing, sequential products, tensor products and conditioning are studied. We also consider marginal, reduced instruments and how these are used to define coexistence (compatibility) of instruments. Finally, we present a brief introduction to quantum measurement models where the generalization of instruments is essential. Many of the concepts of the theory are illustrated by examples. In particular, we discuss Holevo and Kraus instruments.Quanta 2023; 12: 27–40.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43435509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluation of the Feynman Propagator by Means of the Quantum Hamilton-Jacobi Equation","authors":"M. Fusco Girard","doi":"10.12743/quanta.v12i1.223","DOIUrl":"https://doi.org/10.12743/quanta.v12i1.223","url":null,"abstract":"It is shown that the complex phase of the Feynman propagator is a solution of the quantum Hamilton–Jacobi equation, namely, it is the quantum Hamilton's principal function (or quantum action). Therefore, the Feynman propagator can be computed either by means of the path integration, or by the way of the Hamilton–Jacobi equation. This is analogous to what happens in classical mechanics, where the Hamilton's principal function can be computed either by integrating the Lagrangian along the extremal paths, or as a solution of partial differential equation, namely the classical Hamilton–Jacobi equation. If the path is decomposed in the classical one and quantum fluctuations, the contribution of these quantum fluctuations satisfies a non-linear partial differential equation, whose coefficients depend on the classical action. When the contribution of the quantum fluctuations depend only on the time, it can be computed by means of a simple integration. The final results for the propagators in this case are equal to the Van Vleck–Pauli–Morette expressions, even though the two derivations are quite different.Quanta 2023; 12: 22–26.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43165373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Can Decoherence Solve the Measurement Problem?","authors":"M. Bhaumik","doi":"10.12743/quanta.v11i1.208","DOIUrl":"https://doi.org/10.12743/quanta.v11i1.208","url":null,"abstract":"The quantum decoherence program has become more attractive in providing an acceptable solution for the long-standing quantum measurement problem. Decoherence by quantum entanglement happens very quickly to entangle the quantum system with the environment including the detector. But in the final stage of measurement, acquiring the unentangled pointer states poses some problems. Recent experimental observations of the effect of the ubiquitous quantum vacuum fluctuations in destroying quantum entanglement appears to provide a solution.Quanta 2022; 11: 115–123.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43294307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Physical Meaning of the Holographic Principle","authors":"C. Fields, J. Glazebrook, A. Marcianò","doi":"10.12743/quanta.v11i1.206","DOIUrl":"https://doi.org/10.12743/quanta.v11i1.206","url":null,"abstract":"We show in this pedagogical review that far from being an apparent law of physics that stands by itself, the holographic principle is a straightforward consequence of the quantum information theory of separable systems. It provides a basis for the theories of measurement, time, and scattering. Utilizing the notion of holographic screens, which are information encoding boundaries between physical subsystems, we demonstrate that the physical interaction is an information exchange during which information is strictly conserved. Then we use generalized holographic principle in order to flesh out a fully-general quantum theory of measurement in which the measurement produces finite-resolution, classical outcomes. Further, we show that the measurements are given meaning by quantum reference frames and sequential measurements induce topological quantum field theories. Finally, we discuss principles equivalent to the holographic principle, including Markov blankets and the free-energy principle in biology, multiple realizability and virtual machines in computer science, and active inference and interface theories in cognitive science. This appearance in multiple disciplines suggests that the holographic principle is not just a fundamental principle of physics, but of all of science.Quanta 2022; 11: 72–96.","PeriodicalId":37613,"journal":{"name":"Quanta","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43798615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}