UPPER AND LOWER LIMITS FOR THE NUMBER OF BOUND STATES OF PHYSICAL SYSTEMS.

In this article, we define and build the criteria for the testing of hypotheses in the physical quantum systems.For each quantum state, we construct the measure in the space ( ),where U P is the space of the pure states of the quantum system, S is the Borel

Luciano Fonda, G. C. Ghirardi

F. Coester

Jacob D. Bekenstein

David Freund

Muzafarova Sevinch Muhammadovna

This paper investigates a critical challenge at the intersection of quantum optics and fundamental physics: the strict physical constraints governing Bell state measurement (BSM) efficiency within linear-optical frameworks. Without the integration of ancilla photons, conventional setups relying on standard linear-optical components are bounded by a fundamental efficiency threshold that cannot be exceeded. We conduct an analytical analysis of the physical roots of this barrier using Hong-Ou-Mandel photon interference phenomena and multi-photon state space geometry. Furthermore, this study models advanced physical techniques to break past this threshold, focusing on non-linear optical mediums—such as parametric down-conversion setups—and polarization-entangled ancilla flying qubits. These analytical insights deliver foundational physical parameters necessary for engineering fault-tolerant optical quantum computing networks and scalable quantum internet repeaters.