Platonic Quantum Theory

James C. Emerson

The "hidden variables" or "guiding equation" explanation for the measurement of quantum nonlocality (entanglement) effects can be interpreted as instantiation of Platonic information. Because these Bohm-deBroglie principles are already external to the material objects that they theoretically affect, interpreting them as Platonic is feasible. Taking an approach partially suggested by Quantum Information Theory which views quantum phenomena as sometimes observable-measurable information, this thesis defines hidden variables/guiding equation as information. This approach enables us to bridge the divide between the abstract Platonic realm and the physical world. The unobservable quantum wavefunction collapse is interpreted as Platonic instantiation. At each interaction, the wave function for a quantum system collapses. Instantly, Platonic information is instantiated in the system.

Philip VAN LOOCKE

A cellular automaton that includes some principles from quantum theory is considered. The automaton generates forms of an aesthetic nature. At every time step, a form grows with a single cell. This cell is selected with a selection probability that is determined by an amplitude. If the algorithm is run with selection of the cell of maximal amplitude at every time step, a type of form results that is called'platonic'. Such forms typically have higher aesthetic complexity than their non-platonic counterparts. The case of selection probabilities determined by squares of amplitudes has a strong analogy with quantum theory. This analogy is elaborated by consideration of forms that have mutual correlations. These correlations can be of a classical nature, of a quantum mechanical type, or of a type that is termed'super-correlation'.

Martin Strauss

Károly F. Pál, Tamás Vértesi

In this paper we study the Platonic Bell inequalities for all possible dimensions. There are five Platonic solids in three dimensions, but there are also solids with Platonic properties (also known as regular polyhedra) in four and higher dimensions. The concept of Platonic Bell inequalities in the three-dimensional Euclidean space was introduced by Tavakoli and Gisin [Quantum 4, 293 (2020)]. For any three-dimensional Platonic solid, an arrangement of projective measurements is associated where the measurement directions point toward the vertices of the solids. For the higher dimensional regular polyhedra, we use the correspondence of the vertices to the measurements in the abstract Tsirelson space. We give a remarkably simple formula for the quantum violation of all the Platonic Bell inequalities, which we prove to attain the maximum possible quantum violation of the Bell inequalities, i.e. the Tsirelson bound. To construct Bell inequalities with a large number of settings, it is crucial to compute the local bound efficiently. In general, the computation time required to compute the local bound grows exponentially with the number of measurement settings. We find a method to compute the local bound exactly for any bipartite two-outcome Bell inequality, where the dependence becomes polynomial whose degree is the rank of the Bell matrix. To show that this algorithm can be used in practice, we compute the local bound of a 300-setting Platonic Bell inequality based on the halved dodecaplex. In addition, we use a diagonal modification of the original Platonic Bell matrix to increase the ratio of quantum to local bound. In this way, we obtain a four-dimensional 60-setting Platonic Bell inequality based on the halved tetraplex for which the quantum violation exceeds the 2 ratio.

Liyang Sui, Hong-Hao Song, Sainan Huai +13 more

The three-dimensional (3D) Ising model is a foundational model in statistical physics and critical phenomena, yet its analytical intractability has long impeded the precise determination of universal critical exponents. While high-precision estimates have been obtained through classical numerical methods and conformal bootstrap techniques, a direct quantum simulation of the 3D Ising criticality remains challenging, requiring nontrivial connectivity, sufficient system size, and high spectral resolution. In this work, assisted by the state-operator correspondence of conformal field theory, we perform a digital quantum simulation of the 3D Ising critical exponents using a multiply-connected 9-qubit superconducting quantum processor with a Platonic lattice geometry. Employing an extended variational quantum eigensolver equipped with a phase-based loss function, we variationally prepare the low-energy eigenstates of the transverse-field Ising model on a cubic Platonic lattice encoded in an 8-qubit register. The four lowest eigenenergies are extracted via Fourier-transform analysis and high-precision numerical fitting, agreeing with the exact diagonalization values up to +/- 0.001. The resulting scaling dimension Delta_epsilon = 1.5850 and critical exponent nu = 0.7067 match well with theory.