arXiv subjects

Szymon Łukaszyk

Publications and source records attributed to Szymon Łukaszyk.

5 recordsLinked to original sources

arXiv2026

On the quantum separability of qubit registers

We show that the bipartite separability of a pure qubit state hinges critically on the combinatorial structure of its computational-basis support. Using Boolean cube geometry, we introduce a taxonomy that distinguishes support-guaranteed separability from cases in which entanglement depends on probability amplitudes. We provide closed-form support counts, identify forbidden configurations that enforce multipartite entanglement, and show how these results can enable fast entanglement diagnostics in quantum circuits. The framework offers immediate utility in classical simulation, entanglement-aware circuit design, and quantum error-correcting code analysis. This establishes support geometry as a practical and scalable tool for understanding entanglement in quantum information processing.

physics.gen-ph↗

arXiv2023

Life as the Explanation of the Measurement Problem

This study argues that a biological cell, a dissipative structure, is the smallest agent capable of processing quantum information through its holographic triangulated $\textit{sphere of perception}$, where this mechanism has been extended by natural evolution to endo and exosemiosis in multicellular organisms and further to the language of $\textit{Homo sapiens}$. Thus, life explains the measurement problem of quantum theory within the framework of the holographic principle, emergent gravity, and emergent dimensionality. Each Planck triangle on a black hole surface was shown to correspond to a qubit in an equal superposition, attaining known bounds on the products of its energy and orthogonalization interval. Black holes generate entropy variation shells through the solid-angle correspondence. The entropic work introduced the bounds on the number of active Planck triangles dependent on the information capacity of the black hole generator and with at most one active triangle below the unit of black hole entropy. The velocity and dissipativity bounds and the bounds on the theoretical probabilities for active, energy-carrying Planck triangles were derived. In particular, this study shows that black holes, Turing machines, and viruses cannot assume the role of an observer. The entropy variation shells and black-body objects may hint at solutions to ball lightning and sonoluminescence unexplained physical spherical phenomena.

physics.gen-ph↗

arXiv2023

De Sitter Special Relativity as a Possible Reason for Conformal Symmetry and Confinement in QCD

Conformal symmetry and color confinement in the infrared regime of QCD are interpreted by means of a conjectured deSitter $dS_4$ geometry of the internal space-time of hadrons, an assumption inspired by the hypothesis on deSitter special relativity. Within such a scenario, the interactions involving the virtual gluon and constituent quark degrees of freedom of hadrons are deduced from the Green functions of Laplace operators on the $dS_4$ geodesics. Then the conformal symmetry of QCD emerges as a direct consequence of the conformal symmetry of the $dS_4$ space-time, while the color confinement, understood as colorlessness of hadrons, appears as a consequence of the inevitable charge neutrality of the unique closed space-like manifold, the three dimensional hyper-sphere $S^3$, on whose geodesics the hadron's constituents are conjectured to reside when near rest frame. Mesons are now modelled as quarkish color-anticolor dipoles, whose free quantum motions on the aforementioned $S^3$ geodesic are perturbed by a potential generated by a gluon--anti-gluon color dipole. The potential predicted presents itself as the color charge analogue to the "curved" Coulomb potential, i.e. to the electric potential that defines a consistent electrostatic theory on a hyper-spherical surface. The advantage of this method is that it allows to establish a direct relationship of the potential parameters to the fundamental constants of QCD. We apply the model to the description of the spectra of the $a_1$ and $f_1$ mesons, and the pion electric charge form factor, finding fair agreement with data.

physics.gen-ph↗

arXiv2022

A No-go Theorem for Superposed Actions (Making Schrödinger's Cat Quantum Nonlocal)

The Extended Wigner's Friend thought experiment, which involves a quantum system with an agent who draws conclusions based on the results of a measurement of a quantum state provided in two nonorthogonal versions by another agent, led its designers to the conclusion that quantum theory cannot consistently explain the use of itself. It has also been suggested that this thought experiment is equivalent to entangled state (Bell-type) experiments. This study indicates that the assumption of the first Wigner's friend's freedom of choice, regarding how to prepare a quantum state in one of the two available nonorthogonal versions, invalidates such equivalence. A no-go theorem for superposed actions is derived on this basis. It is also argued that modeling Wigner-type experiments under the principle of locality, i.e., using enclosed containers modeled as composite, many-body quantum states, is fundamentally wrong as it neglects quantum nonlocality.

quant-ph↗

arXiv2021

Four Cubes

A short survey on the properties of four graphs constructed in $\{0, 1\}^n$ Boolean space is presented. Flexible activation function of an artificial neuron in a sparse distributed memory model is defined on the basis of the Ugly duckling theorem. Cotan Laplacian on 2-face triangulation of $n$-cube has degenerate spectrum of eigenvalues corresponding to the Hamming distance distribution of $\{0, 1\}^n$ space. Degenerate spectrum of eigenvalues of the cotan Laplacian defined on the graph comprising $2^n$ 2-face triangulated $n$-cubes sharing common origin includes all integers from 0 to 3$n$, without the eigenvalue of 3$n$-1 (multiplicities of the same eigenvalues form A038717 OEIS sequence), while the multiplicities of the same eigenvalues $[-n\sqrt{2}, n\sqrt{2}]$ of the adjacency matrix of $2^n$-cube form trinomial triangle. The distance matrix of this graph, providing further OEIS sequences, as well as its relation with Buckminster Fuller vector equilibrium is also discussed.

math.GM↗