Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · quant-ph/9704006

Measurement processes in quantum physics: a new theory of measurements in terms of statistical ensembles

W. A. Hofer
View original source ↗Read source document ↗Export metadata ↓

Abstract

Considering the recently established arbitrariness the Schroedinger equation has to be interpreted as an equation of motion for a statistical ensemble of particles. The statistical qualities of individual particles derive from the unknown intrinsic energy components, they depend on the physical environment by way of external potentials. Due to these statistical qualities and wave function normalization, non-locality is inherent to the fundamental relations of Planck, de Broglie and Schroedinger. A local formulation of these statements is introduced and briefly assessed, the modified and local Schroedinger equation is non-linear. Quantum measurements are analyzed in detail, the exact interplay between causal and statistical reasons in a measurement process can be accounted for. Examples of individual measurement effects in quantum theory are given, the treatment of diffraction experiments, neutron interferences, quantum erasers, the quantum Zeno effect, and interaction-free measurements can be described consistent with the suggested framework. The paper additionally provides a strictly local and deterministic calculation of interactions in a magnetic field. The results suggest that quantum theory is a statistical formalism which derives its validity in measurements from considering every possible measurement of a given system. It can equally be established, that the framework of quantum physics is theoretically incomplete, because a justification of ensemble qualities is not provided.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

W. A. Hofer. 1997-06-23. Measurement processes in quantum physics: a new theory of measurements in terms of statistical ensembles. https://arxiv.org/abs/quant-ph/9704006

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Iteratively decoded magic state distillation

We present numerical simulation results for the 7-to-1 and 15-to-1 state distillation circuits, constructed using transversal CNOTs acting on multiple surface code patches. The distillation circuits are decoded iteratively using the method outlined in [arXiv:2407.20976]. We show that, with a re-configurable qubit architecture, we can perform fast magic state distillation in $\sim\mathcal{O}(1)$ code cycles. We confirm that both circuits suppress an injected input logical error rate $p$ to $\mathcal{O}(p^3)$ in the presence of additional circuit-level noise. This is done with two types of stabiliser proxies, distilling logical $|-\rangle$ and $|Y\rangle$ states, the latter is the intended state of the 7-to-1 circuit while a stabiliser-proxy for the 15-to-1 circuit. We then also provide numerical evidences for actual $|T\rangle$ state distillation using the 15-to-1 circuit with a faulty-$T$ measurement, leveraging recent near-Clifford simulation tools. Finally, we outline how ZX-calculus and Pauli webs can be used to benchmark stabiliser proxies for these distillation circuits.

quant-ph↗
arXiv2026

Enhanced measurements on quantum computers via the simultaneous probing of non-commuting Pauli operators

Measuring the state of quantum computers is a highly non-trivial task, with implications for virtually all quantum algorithms. A promising avenue is multi-copy schemes, where identical copies of a quantum state are measured jointly so that all Pauli operators within the considered observable can be simultaneously assessed. Here, we present a first implementation of such a two-copy scheme in a measurement protocol. Based on Bayesian statistics, it accurately estimates not only the average of the desired observable but also the error en route. This enables an adaptive shot-allocation algorithm that preferentially samples the most uncertain Pauli terms. In regimes with many non-commuting Pauli operators, this ``double'' scheme can outperform the state-of-the-art measurement protocol in minimizing total shots for a given precision. We also numerically confirm the finding in previous theoretical works that the two-copy scheme incurs an overhead due to the square-root relationship between the variance of measured quantities and the number of measurement shots.

quant-ph↗
arXiv2026

Thermodynamics of a phaseonium-driven optomechanical Otto engine

We study an optomechanical Otto engine whose working medium is a single-mode cavity driven by beams of coherently prepared three-level phaseonium atoms. The atoms are not thermal reservoirs in the Gibbs sense; rather, their populations and ground-state coherence set the detailed-balance ratio of the cavity collision map, so that the field relaxes to a Gibbs state at an operational apparent temperature. We combine the finite-time collision-model dynamics with radiation-pressure work extraction and compare three reservoir preparations: a thermal reference at the same apparent temperatures, an incoherent atomic beam with the same populations, and the coherent phaseonium beam. We show that the phaseonium isochore charges the cavity passively: the cavity ergotropy and energy-basis coherence remain zero up to numerical precision, while the state converges to the Gibbs fixed point selected by the apparent detailed balance. We further estimate lower bounds on the cost of preparing the atomic populations and coherence, showing that the relevant advantage of phaseonium is a resource-preparation tradeoff rather than a cost-free enhancement over a thermal bath at the same temperature. Finally, we assess the finite-time performance of a two-cavity cascade with additive mechanical work accounting. Over the investigated coherence-phase range, the cascade produces approximately $47\%$--$52\%$ more power than the single-cavity engine while requiring only $65\%$--$68\%$ of the hot and cold phaseonium atoms needed by two independent engines, resulting in a $9\%$--$15\%$ enhancement of power per injected atom over a complete cycle.

quant-ph↗