Related papers: Uses of a Quantum Master Inequality
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
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…
We apply the classical data processing inequality to quantum metrology to show that manipulating the classical information from a quantum measurement cannot aid in the estimation of parameters encoded in quantum states. We further derive a…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
In this work, we reveal a new type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any non-trivial threshold in a perfect or an unambiguous way. This…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
Quantum coherence is important in quantum mechanics, and its essence is from superposition principle. We study the coherence of any two pure states and that of their arbitrary superposition, and obtain the relationship between them. In the…
The basic Leggett inequalities, i.e. those inequalities in which the particular assumptions of Leggett's hidden-variable model (e.g. Malus law) were not yet introduced, are usually derived using hidden-variable distributions of…
It is now a well-known fact that the correlations arising from local dichotomic measurements on an entangled quantum state may exhibit intrinsically non-classical features. In this paper we delve into a comprehensive study of random…
The standard argument for the validity of Einstein's equivalence principle in a non-relativistic quantum context involves the application of a mass superselection rule. It is surprising that the consistency between such an important…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…
We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
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…
The concept of the Quantum Ratio was born out of the efforts to find a simple but universal criterion if the center of mass (CM) of an isolated (microscopic or macroscopic) body behaves quantum mechanically or classically, and under which…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…