arXiv subjects

Vladimir A. Orlov

Publications and source records attributed to Vladimir A. Orlov.

3 recordsLinked to original sources

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 these platforms poses practical and theoretical challenges, as their formalisms assign different properties and physical interpretations to many shared notions. We construct a bridge between DV spin systems and restricted CV bosonic systems within corresponding sectors using the tomographic probability representation of quantum states and the Jordan--Schwinger and Holstein--Primakoff maps. Although these maps are well known at the operator level, their action on tomograms and other probability representations has not been addressed in the literature. To the best of our knowledge, we provide the first explicit demonstration of their action on tomographic probability distributions and Wigner functions, establishing direct correspondences between the measurement statistics of DV systems and the corresponding restricted CV bosonic representations. Our tomographic mapping transfers measurement data between quantum architectures through an intrinsic data compression kernel that selects the Hilbert space sector relevant to the target representation. It yields the tomogram of a target sector directly from experimental data in another representation, without reconstructing the density matrix. This provides a unified framework for transferring and comparing quantum information across different hardware platforms within the corresponding restricted sectors, with applications to hybrid protocols, device benchmarking, and the validation of error correction schemes based on mappings between finite-dimensional systems and sector restricted bosonic representations.

quant-ph↗

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.

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