Paper: arXiv 2511.01471

Authors: Mikhail Gennadievich Belov, Victor Victorovich Dubov, Vadim Konstantinovich Ivanov, Alexander Yurievich Maslov, Olga Vladimirovna Proshina, Vladislav Gennadievich Malyshkin

Abstract

In this work, we demonstrate experimentally that the execution flow, $I = dV/dt$, is the fundamental driving force of market dynamics. We develop a numerical framework to calculate execution flow from sampled moments using the Radon-Nikodym derivative. A notable feature of this approach is its ability to automatically determine thresholds that can serve as actionable triggers. The technique also determines the characteristic time scale directly from the corresponding eigenproblem. The methodology has been validated on actual market data to support these findings. Additionally, we introduce a framework based on the Christoffel function spectrum, which is invariant under arbitrary non-degenerate linear transformations of input attributes and offers an alternative to traditional principal component analysis (PCA), which is limited to unitary invariance.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematics, including Radon-Nikodym derivatives, eigenproblems, and Christoffel function spectra, indicating high complexity. It is validated on actual high-frequency market data with a computational framework and software release, demonstrating strong empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Identify Fundamental Driver of Market Dynamics"] --> B["Methodology: Numerical Framework"]
  B --> C{"Input: Sampled Market Moments"}
  C --> D["Compute Execution Flow I = dV/dt<br>via Radon-Nikodym Derivative"]
  D --> E["Christoffel Function Spectrum<br>Invariant to Linear Transformations"]
  E --> F["Derive Characteristic Time Scale<br>Solve Eigenproblem"]
  F --> G["Validation on Market Data"]
  G --> H["Key Outcomes<br>Execution Flow is Fundamental Driver<br>Actionable Triggers Identified<br>Alternative to PCA"]

Cited References (323)

  1. International Winter School on Physics of Semiconductors, Zelenogorsk (“27~” # feb # “~2009”)
  2. The code for polynomials calculation (2014) — link
  3. Long/short market dynamics: trading strategies for today’s markets (2007)
  4. Dynamics of markets: The new financial economics (2009)
  5. Information and Trading Targets in a Dynamic Market Equilibrium (2015) — link
  6. Mathematical Foundations of Realtime Equity Trading. Liquidity Deficit and Market Dynamics. Automated Trading Machines (2015) — link
  7. The Misbehavior of Markets: A fractal view of financial turbulence (2014) — link
  8. NASDAQ TotalView-ITCH 4.1 (2014) — link
and 315 more
  1. Daily TAQ Client Spec v4.2 (2025) — link
  2. SEC chair to Congress: ‘The markets are not rigged’ (“29~” # apr # “~2014”) — link
  3. Limit Order Flow, Market Impact and Optimal Order Sizes: Evidence from NASDAQ TotalView-ITCH Data (2011) — link
  4. Orthogonal polynomials: computation and approximation (2004) — link
  5. Optimal and Adaptive Methods of Hydroacoustic Signal Processing. Vol 1. Optimal methods. (Оптимальные и адаптивные методы обработки гидроакустических сигналов. Т. 1. Оптимальные методы) (2009) — link
  6. Market impact and trading profile of large trading orders in stock markets (“03~” # aug # “~2009”) — link
  7. Orthogonal Polynomials (“11~” # nov # “~2005”) — link
  8. Elements of the Theory of Functions and Functional Analysis (“8~” # may # “~2012”)
  9. Szeg\H o ’s Theorem and Its Descendants (2011) — link
  10. Orthogonal Polynomials (1939)
  11. G' e za Freud, Orthogonal Polynomials. Christoffel Functions. A Case Study (1986) — link
  12. LAPACK Version 3.5.0 (2013) — link
  13. A note on the polynomials of Hermite and Laguerre (1938) — link
  14. Table of Integrals, Series, and Products (1963)
  15. Handbook of mathematical functions (1972)
  16. The product of several Hermite or Laguerre polynomials (1962) — link
  17. Integrals and Series. Volume 2 (2003)
  18. Chebyshev polynomials in numerical analysis (1968)
  19. Polynomials With Respect to a General Basis. II. Applications (1979) — link
  20. Fast inversion of Hessenberg-quasiseparable-Vandermonde matrices and resulting recurrence relations and characterizations (2006) — link
  21. The black swan:: The impact of the highly improbable fragility (2010)
  22. Silent risk: Lectures on fat tails,(anti) fragility, and asymmetric exposures (2014) — link
  23. Mean, Median, and Skew: Correcting a textbook rule (2005) — link
  24. Nodes and Weights of Quadratures formulas: 16-digits tables (in Russian) (1964)
  25. Calculation of Gauss-Kronrod quadrature rules (1997) — link
  26. On a class of Gauss-like quadrature rules (1994) — link
  27. Learning theory for distribution regression (2014) — link
  28. Orthogonal Polynomials. (1979)
  29. Mathematical Foundations of Image Processing and Analysis (2014)
  30. Radon-Nikodym Approximation in Application to Image Reconstruction (2015) — link
  31. On the numerical condition of polynomial bases: estimates for the condition number of Vandermonde, Krylov and Hankel matrices (1996) — link
  32. Computation of Gaussian quadrature rules from modified moments (1979) — link
  33. Review of multi-instance learning and its applications (2005) — link
  34. Moment functions in image analysis: theory and applications (1998)
  35. Image analysis by Tchebichef moments (2001) — link
  36. Image reconstruction from a complete set of geometric and complex moments (2014)
  37. Image analysis with Legendre moment descriptors (2014)
  38. Multi-Instance Learning: A Survey (2004) — link
  39. Multiple–Instance Learning: Christoffel Function Approach to Distribution Regression Problem (2015) — link
  40. Solving the multiple instance problem with axis-parallel rectangles (1997) — link
  41. Robust statistics (2011)
  42. A Massive Local Rules Search Approach to the Classification Problem (2001) — link
  43. Multiple-Instance Learning: Radon-Nikodym Approach to Distribution Regression Problem (2015) — link
  44. Data Mining: Practical machine learning tools and techniques
  45. Solutions of ill-posed problems (1977)
  46. Model Platonism: Neoclassical economic thought in critical light (2012) — link
  47. Economic philosophy (1962)
  48. The intrinsic limits of modern economic theory: the emperor has no clothes (1989) — link
  49. Microeconomics in Context (2009)
  50. Market impact and trading profile of hidden orders in stock markets (2009) — link
  51. A fully consistent, minimal model for non-linear market impact (2014) — link
  52. Dynamical models of market impact and algorithms for order execution (2013) — link
  53. Market impact (2016) — link
  54. Adam Smith (2017) — link
  55. An Inquiry into the Nature and Causes of the Wealth of Nations (1827) — link
  56. Electricity market (2017) — link
  57. Velocity of money (2017) — link
  58. Quantile regression (2016) — link
  59. Bra–ket notation (2016) — link
  60. Straddle (2016) — link
  61. Lenna Image (2016) — link
  62. Goodhart’s law (2016) — link
  63. Norm-Free Radon-Nikodym Approach to Machine Learning (2015) — link
  64. Elements of pure economics (2013) — link
  65. From Walras’ auctioneer to continuous time double auctions: A general dynamic theory of supply and demand (2015) — link
  66. Market Dynamics. On Supply and Demand Concepts (2016) — link
  67. Market Dynamics. On A Muse Of Cash Flow And Liquidity Deficit (2017) — link
  68. Market Dynamics vs. Statistics: Limit Order Book Example (2016) — link
  69. The Deal/Book Split Analysis: A New Method to Disentangle the Contribution to Market and Limit Orders in Any Price Change (2014) — link
  70. Limit Order Book and its modelling in terms of Gibbs Grand-Canonical Ensemble (2016) — link
  71. The price impact of order book events: market orders, limit orders and cancellations (2012) — link
  72. Studies of the limit order book around large price changes (2009) — link
  73. The precautionary principle: fragility and black swans from policy actions (2014) — link
  74. How markets slowly digest changes in supply and demand (2008) — link
  75. Buy low, sell high: A high frequency trading perspective (2014) — link
  76. On Intelligence (2007)
  77. Features in the speckle correlations of light scattered from volume-disordered dielectric media (1999) — link
  78. Evaluation of economic risks related to LiIon batteries for autonomous solar power plant applications (2016) — link
  79. Generalized Radon–Nikodym Approach to Direct Estimation of Degradation Rate Distribution. (Деградация Li-ion накопителей энергии. Применение обобщенного подхода Радона–Никодима к оценке распределения скоростей деградации.) (2018) — link
  80. LG Chem. 18650HG2 datasheet. — link
  81. Thermopower of Neutron Transmutation-Doped Ge: Ga in the Hopping Region (1998)
  82. Generalized Radon–Nikodym Spectral Approach. Application to Relaxation Dynamics Study. (2016) — link
  83. Random-matrix theories in quantum physics: common concepts (1998) — link
  84. Machine learning: a Bayesian and optimization perspective (2015)
  85. Dynamical Approach to Random Matrix Theory (“12~” # Aug # “~2016”) — link
  86. Continuous wavelet transform and exactly solvable model of nonstationary signals (2012) — link
  87. Power Market and Trading (2006) — link
  88. Electricity production and spot prices in Germany. March 2018. (2018) — link
  89. Evaluation of the Annual Electric Energy Output of an a-Si:H Solar Cell in Various Regions of the CIS Countries (2014) — link
  90. Simulation of capacity fade in lithium-ion batteries (2003) — link
  91. Lithium-ion batteries hazard and use assessment (2012) — link
  92. Standards for electric vehicle batteries and associated testing procedures (2015) — link
  93. IEC 61960–3:2017 (2017) — link
  94. Toshiba. The 2.9Ah SCiB. — link
  95. Panasonic NCR18650B. Specification. — link
  96. A123. Nanophosphate High Power Lithium Ion Cell ANR26650. — link
  97. Samsung SDI. Introduction of ICR18650-22F. — link
  98. EnerDel. CE175-360 and CE160-365 cells — link
  99. The Spectral approach to timeserie bursts analysis (Спектральный подход к анализу всплесков временной последовательности) (2018) — link
  100. The Sources of Alternative Energy Development (Источники Развития Альтернативной Энергетики) (2017) — link
  101. Field-effect transistors with high mobility and small hysteresis of transfer characteristics based on CH 3 NH 3 PbBr 3 films (2017) — link
  102. A new type of solar cell is coming to market (2018) — link
  103. Spectral Approach to Li–ion Batteries Degradation Rate Estimation (2018) — link
  104. Chebfun guide (2014) — link
  105. Carnap and the logic of inductive inference (2011) — link
  106. Logical foundations of probability (1962) — link
  107. A treatise on probability (2013) — link
  108. The Elgar companion to post Keynesian economics (2003)
  109. Классические и квантовые вычисления. Учебное пособие (2013) — link
  110. Sum rules for Jacobi matrices and their applications to spectral theory (2003) — link
  111. On Lebesgue Integral Quadrature (2018) — link
  112. On Numerical Estimation of Joint Probability Distribution from Lebesgue Integral Quadratures (2018) — link
  113. The comparative efficiency of classical and fast projection algorithms in the resolution of weak hydroacoustic signals (Сравнительная эффективность классических и быстрых проекционных алгоритмов при разрешении слабых гидроакустических сигналов) (2017) — link
  114. Some modified matrix eigenvalue problems (1973) — link
  115. Market Dynamics: On Directional Information Derived From (Time, Execution Price, Shares Traded) Transaction Sequences (2019) — link
  116. Applied Bayesian and classical inference: the case of the Federalist papers (1984) — link
  117. Cancer diagnosis via linear programming (1990) — link
  118. Perturbations of Christoffel–Darboux Kernels: Detection of Outliers (2020) — link
  119. The empirical Christoffel function with applications in data analysis (2019) — link
  120. Data analysis from empirical moments and the Christoffel function (2020) — link
  121. Reducible polynomials in more than one variable (1982) — link
  122. A FORTRAN routine to estimate a function of two variables from its autocorrelation (1993) — link
  123. On The Radon-Nikodym Spectral Approach With Optimal Clustering (2019) — link
  124. Moments, positive polynomials and their applications (2009) — link
  125. Tractable semi-algebraic approximation using Christoffel-Darboux kernel (2019) — link
  126. A Random multivalued uniform boundedness principle (2005) — link
  127. Gr "o bner bases: Computational Approach to Commutative Algebra (1993) — link
  128. Hedonic housing prices and the demand for clean air (1978) — link
  129. Robust recovery of subspace structures by low-rank representation (2012) — link
  130. Statistical Methods for Design of Extremal Experiments (1968) — link
  131. Theory of Experiment (Теория эксперимента) (1971)
  132. A New Approach to Linear Filtering and Prediction Problems (1960) — link
  133. Computing a logarithm of a unitary matrix with general spectrum (2014) — link
  134. Evolution laws taking pure states to mixed states in quantum field theory (1995) — link
  135. Quantum field theory in curved spacetime and black hole thermodynamics (1994) — link
  136. On the interpretation of measurement in quantum theory (1970) — link
  137. States, Effects, and Operations: Fundamental Notions of Quantum Theory (1983) — link
  138. Quadratic forms with linear constraints (1943) — link
  139. On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere (2013) — link
  140. Maximization of sums of quotients of quadratic forms and some generalizations (1995) — link
  141. Optimization On The Euclidian Unit Sphere (2021) — link
  142. Nondifferentiable optimization and polynomial problems (2013) — link
  143. Autretech LLC — link
  144. Autretech LLC — link
  145. Autretech LLC — link
  146. Market Directional Information Derived From (Time, Execution Price, Shares Traded) Sequence of Transactions. On The Impact From The Future (2022) — link
  147. On The Radon–Nikodym Machine Learning Parallelization (2020) — link
  148. On Machine Learning Knowledge Representation In The Form Of Partially Unitary Operator. Knowledge Generalizing Operator (2022) — link
  149. On the inverse relaxation approach to supercapacitors characterization (2021) — link
  150. On supercapacitors time–domain spectroscopy. C/R characteristic slope (2024) — link
  151. SymPy: symbolic computing in Python (2017) — link
  152. Mutual fund performance (1966) — link
  153. A disintegration of the Christoffel function (2022) — link
  154. Derivatives of the matrix exponential and their computation (1995) — link
  155. QuTiP: An open-source Python framework for the dynamics of open quantum systems (2012) — link
  156. On Quadratic Form Optimization Problem With Multiple Constraints of the Quadratic Form Type (2021) — link
  157. Partially Unitary Learning (2024) — link
  158. Partially unitary learning (2024) — link
  159. Decoherence and the appearance of a classical world in quantum theory (2013) — link
  160. Completely positive linear maps on complex matrices (1975) — link
  161. A Radon-Nikodym theorem for completely positive maps (1986) — link
  162. Quantum Channel Learning (2024) — link
  163. Quantum channel learning (2025) — link
  164. Ija Pavlovna Ipatova (2004) — link
  165. Efficient training of unitary optical neural networks (2023) — link
  166. A modified Cayley transform for SU(3) (2024) — link
  167. Linear transformations which preserve trace and positive semidefiniteness of operators (1972) — link
  168. Quantum process tomography with unsupervised learning and tensor networks (2023) — link
  169. Singular Lagrangians and the Dirac–Bergmann algorithm in classical mechanics (2023) — link
  170. Superstate Quantum Mechanics (2025) — link
  171. Trade Execution Flow as the Underlying Source of Market Dynamics — → 2511.01471
  172. Financial data (2025) — link
  173. Semidefinite Programming for Quantum Channel Learning (2026) — link
  174. Aristotle discovers the economy (1957) — link
  175. Aristotle and Economicanalysis (2013) — link
  176. Aristotle’s theory of price revisited (1998) — link
  177. Crossover from linear to square-root market impact (2019) — link
  178. The Penn-Lehman automated trading project (2003) — link
  179. Agent-based computational finance (2006) — link
  180. A Q-learning agent for automated trading in equity stock markets (2021) — link
  181. From Walras’ auctioneer to continuous time double auctions: A general dynamic theory of supply and demand (2016) — link
  182. Elements of pure economics: Or the theory of social wealth (2013) — link
  183. Anomalous Impact in Reaction-Diffusion Financial Models (2014) — link
  184. May’s instability in large economies (2019) — link
  185. Equation-based model for the stock market (2017) — link
  186. A case study competition among methods for analyzing large spatial data (2019)
  187. The ELPA library: scalable parallel eigenvalue solutions for electronic structure theory and computational science (2014)
  188. LAPACK Users’ Guide (1999) — link
  189. The nature of statistical learning theory (2013) — link
  190. Representation learning: A review and new perspectives (2013) — link
  191. Data mining: practical machine learning tools and techniques with Java implementations (2002) — link
  192. The method of ordered risk minimization, I (1974) — link
  193. On the method of ordered risk minimization, II (1974) — link
  194. On generation of inductive hypotheses (1977) — link
  195. The perceptron, a perceiving and recognizing automaton Project Para (1957)
  196. The perceptron: a probabilistic model for information storage and organization in the brain. (1958) — link
  197. Developing algorithms and software for the parallel solution of the symmetric eigenvalue problem (2011) — link
  198. ELPA: A parallel solver for the generalized eigenvalue problem (2020) — link
  199. Solving large-scale eigenvalue problems on vector parallel processors (1998) — link
  200. ARPACK users’ guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods (1998)
  201. Fuzzy sets (1965) — link
  202. Fuzzy logic and arithmetical hierarchy (1995) — link
  203. Exponential contraction of switching jump diffusions with a hidden Markov chain (2021) — link
  204. Asynchronous fault detection filtering for piecewise homogenous Markov jump linear systems via a dual hidden Markov model (2021) — link
  205. Asynchronous control for discrete-time hidden Markov jump power systems (2021) — link
  206. Asynchronous mean stabilization of positive jump systems with piecewise-homogeneous Markov chain (2021) — link
  207. Detection and identification of changes of hidden Markov chains: asymptotic theory (2022) — link
  208. A review of Hidden Markov models and Recurrent Neural Networks for event detection and localization in biomedical signals (2021) — link
  209. Detrending moving average algorithm for multifractals (2010) — link
  210. Moving average quality control: principles, practical application and future perspectives (2019) — link
  211. Prediction of the COVID-19 pandemic for the top 15 affected countries: Advanced autoregressive integrated moving average (ARIMA) model (2020) — link
  212. Generally weighted moving average monitoring schemes: Overview and perspectives (2021) — link
  213. Least-squares estimation for uncertain moving average model (2021) — link
  214. Use of the autoregressive integrated moving average (ARIMA) model to forecast near-term regional temperature and precipitation (2020) — link
  215. DC series arc detection algorithm based on adaptive moving average technique (2021) — link
  216. The impracticality of homogeneously weighted moving average and progressive mean control chart approaches (2021) — link
  217. Overview of model-based online state-of-charge estimation using Kalman filter family for lithium-ion batteries (2019) — link
  218. Analysis of adaptive image retrieval by transition Kalman filter approach based on intensity parameter (2021) — link
  219. Probabilistic Kalman filter for moving object tracking (2020) — link
  220. A localization based on unscented Kalman filter and particle filter localization algorithms (2019) — link
  221. Differentiating exponentials of Hamiltonians (2020) — link
  222. Learning unitary matrices (2020) — link
  223. Introducing the quadratically-constrained quadratic programming framework in HPIPM (2022) — link
  224. Unitary evolution recurrent neural networks (2016) — link
  225. Learning unitaries by gradient descent (2020) — link
  226. Optimal quantum learning of a unitary transformation (2010) — link
  227. projUNN: efficient method for training deep networks with unitary matrices (2022) — link
  228. Learning unitary operators with help from u(n) (2017) — link
  229. An introduction to inverse problems in physics (2020) — link
  230. Efficient implementation of unitary transformations (2019) — link
  231. Machine learning algorithms in quantum computing: A survey (2020) — link
  232. Saddle-free Hessian-free optimization (2015) — link
  233. In defense of the unitary scalarization for deep multi-task learning (2022) — link
  234. Multi-task learning using uncertainty to weigh losses for scene geometry and semantics (2018) — link
  235. Multi-task learning as multi-objective optimization (2018) — link
  236. Quantum computation and quantum information (2010) — link
  237. From classical to quantum Shannon theory (2011) — link
  238. Learning Unitary Transformation by Quantum Machine Learning Model. (2021) — link
  239. Quantum artificial intelligence: learning unitary transformations (2020) — link
  240. Matrix optimization on universal unitary photonic devices (2019) — link
  241. Optimal quantum dataset for learning a unitary transformation (2023) — link
  242. Learning with density matrices and random features (2022) — link
  243. Solving the quantum many-body problem with artificial neural networks (2017) — link
  244. Exploring the many-body localization transition in two dimensions (2016) — link
  245. Equilibration dynamics of strongly interacting bosons in 2D lattices with disorder (2017) — link
  246. Probing slow relaxation and many-body localization in two-dimensional quasiperiodic systems (2017) — link
  247. Dynamics of disordered states in the Bose-Hubbard model with confinement (2017) — link
  248. Fast linear algebra is stable (2007) — link
  249. Variational Quantum Circuit Decoupling (2024) — link
  250. Variational Quantum Circuit Decoupling (2024) — link
  251. Optimal quantum channels (2021) — link
  252. A Schur method for the square root of a matrix (1983) — link
  253. Numerical methods for least squares problems (2024) — link
  254. Newton’s method for the matrix square root (1986) — link
  255. A fully parallel algorithm for the symmetric eigenvalue problem (1987) — link
  256. An efficient implementation of parallel eigenvalue computation for massively parallel processing (2001) — link
  257. P_ARPACK: An efficient portable large scale eigenvalue package for distributed memory parallel architectures (1996) — link
  258. Hamiltonian variational ansatz without barren plateaus (2024) — link
  259. Variational quantum algorithms (2021) — link
  260. Recoverability of quantum channels via hypothesis testing (2024) — link
  261. Conditional entropy and information in quantum systems (1999) — link
  262. R 'e nyi divergence and Kullback-Leibler divergence (2014) — link
  263. Sufficiency of R 'e nyi divergences (2024) — link
  264. Catalysis in quantum information theory (2024) — link
  265. Derivation of the Schr "o dinger equation from QED (2024) — link
  266. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer (1999) — link
  267. On the mixed-unitary rank of quantum channels (2022) — link
  268. Detecting mixed-unitary quantum channels is NP-hard (2020) — link
  269. Gradient-descent quantum process tomography by learning Kraus operators (2023) — link
  270. Finding the Kraus decomposition from a master equation and vice versa (2007) — link
  271. Reliable quantum state tomography (2012) — link
  272. Quantum Tomography (2003) — link
  273. Continuous-variable optical quantum-state tomography (2009) — link
  274. Quantisierung als eigenwertproblem (1926) — link
  275. Zur quantenmechanik. II. (1926) — link
  276. Snapshotting quantum dynamics at multiple time points (2024) — link
  277. Introduction to quantum mechanics (2019) — link
  278. Adiabatic quantum computation (2018) — link
  279. Adiabatic quantum computation is equivalent to standard quantum computation (2008) — link
  280. Quantum gates and circuits (1998) — link
  281. Classical and quantum information (2011) — link
  282. A feasible method for optimization with orthogonality constraints (2013) — link
  283. Nonlinear programming: theory and algorithms (2006) — link
  284. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers (1974) — link
  285. Structure of a quantized vortex in boson systems (1961) — link
  286. Vortex lines in an imperfect Bose gas (1961) — link
  287. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type (1947) — link
  288. Solving the time-dependent Schr "o dinger equation numerically (1994) — link
  289. Quantum distinguishability measures: Projectors versus state maximization (2024) — link
  290. Properties of the quantum channel (2012) — link
  291. Hamiltonian tomography via quantum quench (2020) — link
  292. Learning a local Hamiltonian from local measurements (2019) — link
  293. Scalable reconstruction of unitary processes and Hamiltonians (2015) — link
  294. Theoretical framework for quantum networks (2009) — link
  295. Higher-Order Quantum Operations (2025) — link
  296. Hamiltonian learning via shadow tomography of pseudo-choi states (2025) — link
  297. Efficient and robust estimation of many-qubit Hamiltonians (2024) — link
  298. Foundations of classical and quantum electrodynamics (2013) — link
  299. Quantum process tomography of unitary and near-unitary maps (2014) — link
  300. Gaussian quantum information (2012) — link
  301. Theoretical framework for higher-order quantum theory (2019) — link
  302. Transforming quantum operations: Quantum supermaps (2008) — link
  303. Higher-order quantum transformations of Hamiltonian dynamics (2024) — link
  304. Recoverability for Holevo’s just-as-good fidelity (2018) — link
  305. An introduction to polynomial and semi-algebraic optimization (2015) — link
  306. Handbook on semidefinite, conic and polynomial optimization (2011) — link
  307. Quantum gate fidelity in terms of Choi matrices (2011) — link
  308. Semidefinite programming (1996) — link
  309. Handbook of semidefinite programming: theory, algorithms, and applications (2012) — link
  310. Convex optimization (2004) — link
  311. A high-performance software package for semidefinite programs: SDPA 7 (2010) — link
  312. CVXPY : A P ython-embedded modeling language for convex optimization (2016) — link
  313. CVXOPT : P ython software for convex optimization (2015) — link
  314. Semidefinite programming in quantum information science (2023) — link
  315. Semidefinite programming relaxations for quantum correlations (2024) — link

1 of 323 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.