arXiv subjects

Vladimir A. Orlov

Publications and source records attributed to Vladimir A. Orlov.

3 recordsLinked to original sources

arXiv2026

Spin-Boson Mappings in the Formalism of $f$-Deformations

We develop a unified algebraic approach to spin-boson transformations based on the formalism of $f$-deformed oscillators. In the single-mode case, we show that the Holstein-Primakoff and Dyson-Maleev transformations, together with the interpolating $α$-family, arise as different factorizations of the same algebraically determined object. The standard spin-boson mappings can thus be interpreted as realizations of a common structure, which makes it possible to clearly separate the exact algebraic content on the physical subspace from effects associated with non-Hermiticity, the choice of metric, and extensions beyond the physical subspace. In the two-mode case, the same approach yields both deformed versions of the Jordan-Schwinger transformation and new exact two-mode realizations. Our results provide a unified description of known spin-boson transformations and naturally lead to new bosonic representations.

quant-ph↗

arXiv2026

Optimal Nonparametric Estimation of Phase-Space Representations for Non-Gaussian Continuous Variable Quantum States

We further develop Kernel Quantum State Estimation (KQSE), a fully data-driven nonparametric method for continuous variable quantum state reconstruction and characterization, introduced in our recent work and rooted in nonparametric kernel density estimation (KDE). Unlike approaches relying on finite-dimensional basis truncations, parametric ansätze, or prior models, KQSE combines a new kernel estimator of the characteristic function of the tomographic quadrature distribution with suitable kernel integral transformations. The characteristic function is estimated directly from experimental homodyne or heterodyne data and subsequently transformed to estimate quantum state representations and characteristics, including the Wigner function and the density matrix kernel. Observing that several other physically relevant representations and characteristics admit transformations of a closely related form, we derive convergence rates for the corresponding broad class of KQSE-based estimators. The resulting framework covers all phase-space representations, the photon-number tomogram, trace products of quantum states, and purity. We derive mean squared error convergence rates for these kernel transformed estimators and show that the corresponding KQSE applications inherit the near optimal rate O(T^{-1}), where $T$ is the total number of measurements. The proposed theory applies equally to Gaussian and non-Gaussian continuous variable quantum states without imposing a Fock space cutoff. Numerical experiments on simulated Gaussian and non-Gaussian states and real homodyne data demonstrate the advantages of KQSE over state-of-the-art methods, establishing it as a statistically consistent and computationally modest framework for continuous variable quantum state estimation and characterization, particularly in the non-Gaussian regime.

quant-ph↗

arXiv2026

From Discrete to Continuous-Variable Systems via Jordan-Schwinger Tomographic Transformation

Hybrid quantum systems that combine discrete-variable (DV) and continuous-variable (CV) architectures represent a promising direction in quantum information science. However, transferring concepts, information and states between such fundamentally different platforms entails both practical and theoretical challenges. The formalisms of these two universes differ significantly, and many notions, although sharing the same names, possess distinct properties and physical interpretations. In this work, we construct a bridge between DV and CV systems by means of the tomographic probability representation of quantum states complemented by the Jordan--Schwinger and Holstein--Primakoff maps. While both maps are well known at the operator level, their action on the classical counterparts of quantum states, namely tomograms and other probability representations, has not been addressed in the literature. To the best of our knowledge, this work provides the first explicit demonstration of how the Jordan--Schwinger and Holstein--Primakoff maps act on tomographic probability distributions and Wigner functions, thereby establishing a direct correspondence between the classical measurement statistical descriptions of CV and DV quantum systems. Our tomographic mapping enables a direct transfer of measurement data between different quantum architectures by acting as an intrinsic data-compression kernel. It allows one to obtain the tomogram of a target representation directly from experimentally acquired data in another, without reconstructing the density matrix. This provides a unified framework for transferring and comparing quantum information across heterogeneous quantum hardware platforms, facilitating hybrid protocols, device benchmarking, and the validation of error-correction schemes that rely on mappings between finite- and infinite-dimensional systems.

quant-ph↗