Related papers: The Uncertainty Principle of Quantum Processes
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
The Born's rule introduces intrinsic randomness to the outcomes of a measurement performed on a quantum mechanical system. But, if the system is prepared in the eigenstate of an observable then the measurement outcome of that observable is…
Since their discovery in 1927, the Heisenberg Inequalities have become an icon of quantum mechanics. Often inappropriately referred to as the Uncertainty Principle, these inequalities relating the standard deviations of the position and…
We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is…
We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is…
The usual Heisenberg uncertainty relation for position and momentum may be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure states,…
We explore the different meanings of "quantum uncertainty" contained in Heisenberg's seminal paper from 1927, and also some of the precise definitions that were explored later. We recount the controversy about "Anschaulichkeit",…
The engine that powers quantum cryptography is the principle that there are no physical means for gathering information about the identity of a quantum system's state (when it is known to be prepared in one of a set of nonorthogonal states)…
Bohmian mechanics is a theory that provides a consistent explanation of quantum phenomena in terms of point particles whose motion is guided by the wave function. In this theory, the state of a system of particles is defined by the actual…
The derivation of the Heisenberg Uncertainty Principle (HUP) from the Uncertainty Theorem of Fourier Transform theory demonstrates that the HUP arises from the dependency of momentum on wave number that exists at the quantum level. It also…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
The finite and infinite square wells are potentials typically discussed in undergraduate quantum mechanics courses. In this paper, we discuss these potentials in the light of the recent studies of the modification of the Heisenberg…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
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…
Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown…
We present critical arguments against individual interpretation of Bohr's complementarity and Heisenberg's uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the…
Some predictions of quantum mechanics are in contrast with the macroscopic realm of everyday experience, in particular those originated by the Heisenberg uncertainty principle, encoded in the non-commutativity of some measurable operators.…
Is the dynamical evolution of physical systems objectively a manifestation of information processing by the universe? We find that an affirmative answer has important consequences for the measurement problem. In particular, we calculate the…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
The origin of the uncertainty inherent in quantum measurements has been discussed since quantum theory's inception, but to date the source of the indeterminacy of measurements performed at an angle with respect to a quantum state's…