arXiv subjects

Ghasem Asadi Cordshooli

Publications and source records attributed to Ghasem Asadi Cordshooli.

6 recordsLinked to original sources

arXiv2026

Coherent-State Kernels for Composite Quantum Operations

This paper develops a unified kernel-based method for computing exact matrix elements of composite quantum operations by inserting resolutions of the identity after individual operators or between successive factors of an operator chain. A single insertion gives an exact scalar identity, and nested insertions between the factors give multiple integral identities for chains of closed operators under explicit Bochner-integrability conditions. The procedure is carried through on polynomial and analytic functions of the ladder operators, on one- and two-mode Gaussian unitaries, and on three composite operations: a Kerr phase followed by squeezing or by a cubic phase gate, a two-mode squeezer followed by a beam splitter, and a heralded cat-state circuit with two beam splitters. At rational Kerr phases the Kerr-squeezed amplitudes reduce to finite sums of squeezed coherent-state amplitudes weighted by quadratic Gauss sums, with an explicit error bound at the remaining phases; the two-mode network gives a bivariate Hermite polynomial; and the heralded circuit gives closed forms for the amplitudes, the heralding probabilities and their extension to an arbitrary passive network fed by one squeezed source. The examples are set against the reach of four established techniques: operator ordering, the Berezin symbol calculus, Lie disentangling and the symplectic formalism. Each technique reaches a subset of the examples directly, while the insertion procedure reaches all of them under the same hypotheses. A comparison with direct Fock summation identifies the regime in which the finite Kerr sums are efficient, and the choice of resolution at each boundary of a chain follows a selection rule set by the action of the adjacent factor. Each closed form agrees with an independent numerical computation.

quant-ph↗

arXiv2026

Coherent-State Integrals Beyond the Domain of Operator Products

Inserting a resolution of the identity between two operators turns a matrix element of their product into a phase-space integral. For unbounded operators the product need not exist on the vector at hand, while the integral may still converge. We follow this gap through the chain $e^{μa^2}e^{λa^{\dagger2}}$ of two-photon exponentials, where it can be traced completely. Five regions of parameter space appear: where the Bochner conditions of the strong formulation hold, where the product exists as a vector, where it exists as a sesquilinear form, where the coherent-state integral converges, and where the Fock-space series converges. The first three are strictly nested inside the intersection of the last two, and these two overlap without either containing the other. A single Hermite-type function agrees with the matrix element where it exists and with the integral and the series wherever they converge, so the integral carries the analytic continuation of the matrix element beyond the domain of the product and beyond the convergence of its Fock series. On the real slice of parameter space, an iterated form of the integral also reaches every point where the series converges. The analysis rests on a weak composition lemma whose hypotheses concern only the bra, the ket and the resolving family. For bounded chains the same identity is unconditional, and worked examples of that kind are given in a companion paper.

math-ph↗

arXiv2026

Exact Fock Amplitudes of the Cubic-Phase Gate on Arbitrary Pure Gaussian States

The cubic phase gate is the only non-Gaussian element of universal continuous-variable quantum computation. Its Fock amplitudes are known in closed form only when the input is a Fock state. For a Gaussian input the usual route is to build the cubic quadrature in a truncated Fock space and exponentiate it, which alters the generator before the exponential is taken. A closed form is obtained here for every pure single-mode Gaussian input, with the squeezing along any quadrature axis and with arbitrary displacement and boost. It is a finite combination of the Airy function and its derivative, and the argument is shared by all Fock indices, so a whole Fock profile costs two Airy evaluations. A recurrence is also derived that builds each coefficient from the four preceding ones, together with the regime in which it is stable. Evaluating the closed form at the weak nonlinearities of current experiments requires care, since its terms grow large and alternate in sign. The precision this demands is quantified, and the truncated construction is benchmarked against the exact result, whose error at cutoffs in common use is found to be of the same size as the quantity being computed.

quant-ph↗

arXiv2026

The Resolution of the Identity as a Generator of Exact Integral Identities: A Coherent-State Approach

The resolution of the identity is typically utilized as a passive representation tool in standard quantum mechanics textbooks. In this paper, we reinterpret this traditional perspective by introducing the resolution of the identity associated with Glauber coherent states as a direct generator of exact complex Gaussian integral identities. By systematically projecting the continuous coherent-state completeness relation onto the discrete Fock basis, highly generalized Gaussian integral relations emerge naturally as a direct consequence of state preservation, rather than being introduced as independent mathematical postulates. We demonstrate that this overarching formal structure simultaneously dictates both discrete (Kronecker delta) and continuous (Dirac delta) localization kernels under appropriate basis projections, providing a sharp conceptual contrast between the structural features of overcomplete and strictly orthogonal representations. Crucially, we highlight an intriguing non-commuting behavior in the parameter limits of the master identity. Requiring only the elementary properties of coherent states and the Dirac formalism, this approach offers a transparent and visually intuitive illustration of how Hilbert-space completeness inherently encodes vast libraries of exact, solvable mathematical relations -- providing a unifying perspective suitable for advanced undergraduate and graduate instruction.

quant-ph↗

arXiv2020

Mean Field Theory for the Quantum Rabi Model, Inconsistency to the Rotating Wave Approximation

Considering well localized atom, the mean field theory (MFT) was applied to replace the operators by equivalent expectation values. The Rabi model was reduced to a fourth orders NDE describing atoms position. Solution by the harmonic balance method (HBM) showed good accuracy and consistency to the numerical results, which introduces it as a useful tool in the quantum dynamics studies.

quant-ph↗

arXiv2017

Quantum dynamics of ultra-cold atoms in the presence of virtual photons

A single trapped ion interacting with laser light in a radiofrequency trap is considered by diagonalization of full Hamiltonian of the system in a suitable basis. The energies, eigenvectors, probabilities of finding the atom in the ground state, density matrixes and its entanglement are computed. The study repeated for the Hamiltonian under the rotated wave approximation in the same basis. The results compared in general and in the Lamb-Dick regime for ultra-cold atoms to reveal essential changes in the results.

quant-ph↗