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Degradation of Grover＇s search under collective phase flips in queries to the oracle

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Frontiers of physics 2018年第5期13卷 271-279页

作者： alexey E. Rastegin Department of Theoretical Physics Irkutsk State University Irkutsk Russia

We address the case in which querying the oracle in Grover＇s algorithm is exposed to noise including phase distortions. The oracle-box wires can be altered by an opposing party that tries to prevent reception of correct data from the oracle. This situation reflects an experienced truth that any access to prophetic knowledge cannot be common and direct. To study this problem, we introduce a simple model of collective phase distortions on the basis of a phase-damping channel. In the model, the probability of success is not altered via the oracle-box wires per se. Phase distortions of the considered type can hardly be detected via any one-time query to the oracle. However, the probability of success is significantly changed when such errors are introduced as an intermediate step in the Grover iteration. We investigate the probability of success with respect to variations of the parameter that characterizes the amount of phase errors. It turns out that the probability of success decreases significantly even if the error is not very high. Moreover, this probability quickly reduces to the value of one half, which corresponds to the completely mixed state. We also study trade-off relations between quantum coherence and the probability of success in the presence of noise of the considered type.

关键词： Grover's algorithm phase noise relative entropy of coherence

Nonlinearity of Quantum Mechanics and Solution of the Problem of Wave Function Collapse

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Communications in Theoretical Physics 2015年第7期64卷 47-53页

作者： alexey V.Melkikh Ural Federal University

The problem of the wave function collapse(a problem of measurement in quantum mechanics) is *** is shown that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The particle creation and annihilation processes, which are described based on quantum field theory, play a key role in the measurement processes. Superposition principle is not valid for the system of equations of quantum field theory for particles and fields, because this system is a non-linear. As a result of the creation(annihilation) of a particle,an additional uncertainty arises, which "smears" the interference pattern. The imposition of such a large number of uncertainties in the repetitive measurements leads to the classical behavior of particles. The decoherence theory also implies the creation and annihilation of particles, and this processes are the consequence of non-linearity of quantum mechanics. In this case, the term "collapse of the wave function" becomes a consequence of the other statements of quantum mechanics instead of a separate postulate of quantum mechanics.

关键词： creation and annihilation of particles decoherence

Pricing strategies in inelastic energy markets： can we use less if we can＇t extract more？

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Frontiers of Earth Science 2014年第1期8卷 3-17页

作者： alexey Voinov Tatiana Filatova International Institute for Geo-lnformation Science and Earth Observation University of Twente Enschede 7522EA The Netherlands Centre for Studies in Technology and Sustainable Development University of Twente Enschede 7522EA The Netherlands

Limited supply of nonrenewable energy resources under growing energy demand creates a situation when a marginal change in the quantity supplied or demanded causes non-marginal swings in price levels. The situation is worsened by the fact that we are currently running out of cheap energy resources at the global scale while adaptation to climate change requires extra energy costs. It is often argued that technology and alternative energy will be a solution. However, alternative energy infrastructure also requires additional energy investments, which can further increase the gap between energy demand and supply. This paper presents an explorative model that demonstrates that a smooth transition from an oil-based economy to alternative energy sources is possible only if it is started well in advance while fossil resources are still abundant. Later the transition looks much more dramatic and it becomes risky to rely entirely on technological solutions. It becomes increasingly likely that in addition to technological solutions that can increase supply we will need to find ways to decrease demand and consumption. We further argue that market mechanisms can be just as powerful tools to curb demand as they have traditionally been for stimulating consumption. We observe that individuals who consume more energy resources benefit at the expense of those who consume less, effectively imposing price externalities on the latters. We suggest two transparent and flexible methods of pricing that attempt to eliminate price externalities on energy resources. Such pricing schemes stimulate less consumption and can smooth the transition to renewable energy.

关键词： peak oil price externality alternative energy resources EROEI

Generalized Logan’s Problem for Entire Functions of Exponential Type and Optimal Argument in Jackson’s Inequality in L2（R3）

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Acta Mathematica Sinica,English Series 2018年第10期34卷 1563-1577页

作者： Valerii IVANOV alexey IVANOV Department of Applied Mathematics and Computer Science Tula State University

We study Jackson＇s inequality between the best approximation of a function f∈ L2（R^3） by entire functions of exponential spherical type and its generalized modulus of continuity. We prove Jackson＇s inequality with the exact constant and the optimal argument in the modulus of continuity. In particular, Jackson＇s inequality with the optimal parameters is obtained for classical modulus of continuity of order r and Thue-Morse modulus of continuity of order r∈ N. These results are based on the solution of the generalized Logan problem for entire functions of exponential type. For it we construct a new quadrature formulas for entire functions of exponential type.

关键词： Best approximation generalized modulus of continuity Jackson's inequality optimal argument Logan's problem quadrature formula

Uncertainty and Certainty Relations for Successive Projective Measurements of a Qubit in Terms of Tsallis' Entropies

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Communications in Theoretical Physics 2015年第6期63卷 687-694页

作者： alexey E.Rastegin Department of Theoretical Physics Irkutsk State University

We study uncertainty and certainty relations for two successive measurements of two-dimensional observables. Uncertainties in successive measurement are considered within the following two scenarios. In the first scenario, the second measurement is performed on the quantum state generated affer the first measurement with completely erased information. In the second scenario, the second measurement is performed on the post-first- tioned on the actual measurement outcome. Induced entropies. For two successive projective t state condiquantum uncertainties are characterized by means of the Tsallis t of a qubit, we obtain minimal and maximal values of related entropic measures of induced uncertainties. Some conclusions found in the second scenario are extended to arbitrary finite dimensionality. In particular, a connection with mutual unbiasedness is emphasized.

关键词： successive measurements Tsallis entropy uncertainty principle purity

Uncertainty and Certainty Relations for Pauli Observables in Terms of R′enyi Entropies of Order α ∈(0;1]

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Communications in Theoretical Physics 2014年第3期61卷 293-298页

作者： alexey E.Rastegin Department of Theoretical Physics Irkutsk State University

We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Renyi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Renyi a-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.

关键词： Pauli observables Renyi entropy quantum measurement uncertainty principle

Digital Earth surface maps for radar ground clutter simulation

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Journal of Systems Engineering and Electronics 2022年第2期33卷 340-344页

作者： ORESHKINA Margarita STEPANOV Maksim KISELEV alexey Novosibirsk State Technical University Novosibirsk 630073Russia

This paper dwells upon optimizing the azimuth samp-ling interval of digital surface maps used to model radar ground *** resulting equations can be used to find the digital map sampling interval for the required calculation error and modeled power of the simulated signal,which determines the resulting distribution of backscatter *** paper further showcases how the sampling interval could be increased by pre-processing the map.

关键词： ground clutter mathematical modelling radar simulation

Generalized Conditional Entropies of Partitions on Quantum Logic

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Communications in Theoretical Physics 2012年第12期58卷 819-822页

作者： alexey E. Rastegin Department of Theoretical Physics Irkutsk State University

For partitions on quantum logic, the Rdnyi and Tsallis conditional entropies are introduced. Several relations between the conditional entropies of such partitions are derived.

关键词： quantum logic Renyi entropy Tsallis entropy

Function fitting for modeling seasonal normalized difference vegetation index time series and early forecasting of soybean yield

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The Crop Journal 2022年第5期10卷 1452-1459页

作者： alexey Stepanov Konstantin Dubrovin Aleksei Sorokin Far Eastern Agriculture Research Institute Vostochnoe680521 KhabarovskRussia Computing Center of the Far Eastern Branch of the Russian Academy of Sciences 680000 KhabarovskRussia

Forecasting crop yields based on remote sensing data is one of the most important tasks in *** is the main crop in the Russian Far *** is desirable to forecast soybean yield as early as possible while maintaining high *** study aimed to investigate seasonal time series of the normalized difference vegetation index(NDVI) to achieve early forecasting of soybean *** research used data from the Moderate Resolution Image Spectroradiometer(MODIS),an arable-land mask obtained from the VEGA-Science web service,and soybean yield data for 2008-2017 for the Jewish Autonomous Region(JAR) *** approximating functions were fitted to model the NDVI time series:Gaussian,double logistic(DL),and quadratic and cubic *** the period from calendar weeks 22-42(end of May to mid-October),averaged over two districts,the model using the DL function showed the highest accuracy(mean absolute percentage error-4.0%,root mean square error(RMSE)-0.029,P <0.01).The yield forecast accuracy of prediction in the period of weeks 25-30 in JAR municipalities using the parameters of the Gaussian function was higher(P <0.05) than that using the other *** mean forecast error for the Gaussian function was 14.9% in week 25(RMSE was0.21 t ha) and 5.1%-12.9% in weeks 26-30(RMSE varied from 0.06 to 0.15 t ha) according to the2013-2017 *** weeks 31-32,the error was 5.0%-5.4%(RMSE was 0.07 t ha) using the Gaussian parameters and 7.4%-7.7%(RMSE was 0.09-0.11 t ha) for the DL *** the method was applied to municipal districts of other soy-producing regions of the Russian Far *** was0.14-0.32 t hain weeks 25-26 and did not exceed 0.20 t hain subsequent weeks.

关键词： NDVI Function fitting Early prediction Yield Soybean