Schmidt decomposition and analysis of statistical correlations

Bogdanov, Yu. I.; Богданова, Н. А.; Лукичев, В. Ф.; Fastovets, D. V.; Chernyavskii, A. Yu.

doi:10.1134/s1063739716050036

Cited by 4 publications

(4 citation statements)

References 3 publications

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“…Both kinds of vector are valid representations of quantum states in a Hilbert space. In the patent application, we used the Schmidt decomposition() to analyze the 24‐hour periodic structure of the signal and to extract its principal components, one of which served as a “signature,” and we defined a distance measure. Here, we use the singular value decomposition (SVD), which is equivalent to the Schmidt decomposition, together with the same distance measure.…”

Section: Methodsmentioning

confidence: 99%

Identification of the source of an interferer by comparison with known carriers using a single satellite

Glendinning

Nölle

Hausleitner³

et al. 2018

Satell Commun Network

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We describe a method for identifying the source of a satellite interferer using a single satellite.The technique relies on the fact that the strength of a carrier signal measured at the downlink station varies with time due to a number of factors, and we use a quantum-inspired algorithm to compute a ''signature'' for a signal, which captures part of the pattern of variation that is a characteristic of the uplink antenna. We define a distance measure to numerically quantify the degree of similarity between two signatures, and by computing the distances between the signature for an interfering carrier and the signatures of the known carriers being relayed by the same satellite at the same time, we can identify the antenna that the interferer originated from, if a known carrier is being relayed from it. As a proof of concept, we evaluate the performance of the technique using a simple statistical model applied to measured carrier data. KEYWORDSidentification, interferer, quantum inspired, single satellite, singular value decomposition INTRODUCTIONThe increasing demand for satellite communication links has led to an increasing number of satellite signals and to an increasing amount of uplink interference. The causes of this interference include the growth in the number of small ground terminals, low-quality equipment, poor installations and maintenance, uplink personnel mistakes (human error), faulty equipment, incorrectly pointed antennas, adjacent satellite interference, terrestrial service interference, and sometimes intentional jamming. 1,2 Satellite operators are therefore increasingly interested in solutions not only for detecting interference, which is the main task of a satellite monitoring system, but also to identify its source.The traditional approach is to geographically localize, or geolocate, the transmitting station of an interferer. However, most localization systems need to receive the interference signal via two adjacent satellites in order to perform geolocation, 3-7 and there are a number of limitations associated with this approach:• An adjacent satellite must be available that is equipped with transponder(s) receiving components of the interfering signal and a reference signal (same uplink frequency range and same polarization).• The interference and reference signals need to have enough crosstalk energy between the primary and adjacent satellites to achieve a sufficient level of correlation.• Accurate ephemeris data must be available for both satellites.• The reference signal needs to be received from both satellites via transponders operating with the same physical local oscillators (LOs) as the transponders retransmitting the interference signal.• If the system is installed at only one earth station, the downlink signals of both satellites need to be receivable at this earth station (downlink beams of both satellites need to cover the measurement site location). If this is not possible (beams pointing to different locations), the system needs to be installed at different locations inside the ...

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Section: Methodsmentioning

confidence: 99%

Identification of the source of an interferer by comparison with known carriers using a single satellite

Glendinning

Nölle

Hausleitner³

et al. 2018

Satell Commun Network

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“…The mathematical apparatus related to the Schmidt decomposition provides a convenient tool that allows us to analyze the entanglement of quantum states and correlations in classical distributions [20]. Assume is the quantum state of a bipartite system consisting of subsystems and Then, the Schmidt decomposition is given in the form [2]:…”

Section: Schmidt Decompositionmentioning

confidence: 99%

Schmidt Decomposition and Coherence of Interfering Alternatives

et al. 2021

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The Schmidt decomposition and the correlational analysis based on it make it possible to identify statistical dependences between various subsystems of a single physical system. The systems under consideration can be both quantum states and classical probability distributions. In this study, two different physical systems are considered: quantum Schrödinger cat states and double-slit interference of microparticles. It is shown that the considered systems have a single internal structure and can be described in general terms of interfering alternatives. An effective approach is developed that allows us to calculate optical characteristics of interference such as visibility and coherence. It is shown that the scalar product of the states of the environment of interfering alternatives acts as a natural generalization of the classical complex parameter of the coherence of light oscillations, which determines the visibility of the interference pattern. A simple quantitative relationship is obtained between the visibility of the interference pattern and the Schmidt number, which determines the level of connection between a quantum system and its environment. The developed approaches are generalized to the case of multidimensional Schrödinger cat states.

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“…To learn more about Schmidt decomposition and it relationship with correlation analysis please see article [9].…”

Section:   mentioning

confidence: 99%

“…Such correlated photon pairs are called biphotons. Schmidt correlations formalism allows us to analyze not only entanglement in quantum systems, but also classical correlations between subsystems in different probability distributions [8,9].…”

Section: Introductionmentioning

confidence: 99%

Schmidt decomposition and multivariate statistical analysis

Bogdanov¹,

Богданова

Fastovets³

et al. 2016

SPIE Proceedings

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The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical correlation analysis. Correlation of photons in the beam splitter output channels, when input photons statistics is given by compound Poisson distribution is examined. The developed formalism allows us to analyze multidimensional systems and we have obtained analytical formulas for Schmidt decomposition of multivariate Gaussian states. It is shown that mathematical tools of quantum mechanics can significantly improve the classical statistical analysis. The presented formalism is the natural approach for the analysis of both classical and quantum multivariate systems and can be applied in various tasks associated with research of dependences.

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Schmidt decomposition and analysis of statistical correlations

Cited by 4 publications

References 3 publications

Identification of the source of an interferer by comparison with known carriers using a single satellite

Identification of the source of an interferer by comparison with known carriers using a single satellite

Schmidt Decomposition and Coherence of Interfering Alternatives

Schmidt decomposition and multivariate statistical analysis

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