相关论文: Measurement and Its Mathematical Scale

Scales of the microworld are defined on the grounds of the hierarchy that can be set up within a well ordered finite or infinite countable set of well ordered sets. Indirect measurements in pure mathematical as well as physical meaning are…

Many attempts have been made to characterise and solve the infamous measurement problem of quantum mechanics by advocating, implicitly or explicitly, different realist perspectives. As a result, we are still uncertain where this problem and…

It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…

A formulation towards quantifying resource count used in a measurement, that is independent of the model of the measurement dynamics(Quantum/Classical), is considered. For any general measurement with $(M+1)$ discrete outcomes, it is found…

Several recent studies have been devoted to investigating the limitations that ordinary quantum mechanics and/or quantum gravity might impose on the measurability of space-time observables. These analyses are often confined to the…

Statistical analysis is often used to evaluate the evidence for or against scientific hypotheses, and various statistics (e.g., p-values, likelihood ratios, Bayes factors) are interpreted as measures of evidence strength. Here I consider…

The class of local invertible operations is defined and the invariance of entanglement under such operations is established. For the quantification of entanglement, universal entanglement measures are defined, which are invariant under…

Left on its own, a quantum state evolves deterministically under the Schr\"odinger Equation, forming superpositions. Upon measurement, however, a stochastic process governed by the Born rule collapses it to a single outcome. This dual…

We propose a general theoretical approach to quantum measurements based on the path (histories) summation technique. For a given dynamical variable A, the Schr\"odinger state of a system in a Hilbert space of arbitrary dimensionality is…

A new, realist interpretation of the quantum measurement processes is given. In this scenario a quantum measurement is a non-equilibrium phase transition in a ``resonant cavity'' formed by the entire physical universe including all its…

We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…

The framework of a new scale invariant analysis on a Cantor set $C\subset $ $% I=[0,1] $, presented originally in {\it S. Raut and D. P. Datta, Fractals, 17, 45-52, (2009)}, is clarified and extended further. For an arbitrarily small…

Quantum metrology can achieve far better precision than classical metrology, and is one of the most important applications of quantum technologies in the real world. To attain the highest precision promised by quantum metrology, all steps…

The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…

Recently, it was shown that most popular IR measures are not interval-scaled, implying that decades of experimental IR research used potentially improper methods, which may have produced questionable results. However, it was unclear if and…

Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a…

A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…

In a recent work, arXiv:2503.05884, we proposed a unified notion of nonclassicality that applies to arbitrary processes in quantum theory, including individual quantum states, measurements, channels, set of these, etc. This notion is…

This treaties aims to introduce a speculative framework to comprehend modern metrology. In a classical sense, measurement measures physically existing quantities, such as length, mass, and time. By contrast, modern measurement measures a…

While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…