Related papers: Uses of a Quantum Master Inequality
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in…
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates.…
The prevalent role of force in traditional quantum mechanics is outlined, with special reference to approximate calculations for stationary states. It will be explored how far this force concept can be made useful in the concerned area. The…
Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a…
We show that classical mechanics can be recovered as the high-entropy limit of quantum mechanics. That is, the high entropy masks quantum effects, and mixed states of high enough entropy can be approximated with classical distributions. The…
Classical Bayes' rule lays the foundation for the classical causal relation between cause (input) and effect (output). This causal relation is believed to be universally true for all physical processes. Here we show, on the contrary, that…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
In this paper, we inaugurate the field of quantum fair machine learning. We undertake a comparative analysis of differences and similarities between classical and quantum fair machine learning algorithms, specifying how the unique features…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes…
The standard uncertainty relations (UR) in quantum mechanics are typically used for unbounded operators (like the canonical pair). This implies the need for the control of the domain problems. On the other hand, the use of (possibly…
The role of the Equivalence Principle (EP) in classical and quantum mechanics is reviewed. It is shown that the weak EP has a counterpart in quantum theory, a Quantum Equivalence Principle (QEP). This implies that also in the quantum domain…
A consistent theory of quantum gravity will require a fully quantum formulation of the classical equivalence principle. Such a formulation has been recently proposed in terms of the equality of the rest, inertial and gravitational mass…
The conventional interpretation of quantum mechanics, though it permits a correspondence to classical physics, leaves the exact mechanism of transition unclear. Though this was only of philosophical importance throughout the twentieth…
Uncertainty relations capture the essence of the inevitable randomness associated with the outcomes of two incompatible quantum measurements. Recently, Berta et al. have shown that the lower bound on the uncertainties of the measurement…
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the…
The classical Penrose inequality specifies a lower bound on the total mass in terms of the area of certain trapped surfaces. This fails at the semiclassical level. We conjecture a Quantum Penrose Inequality: the mass at spatial infinity is…
Quantum uncertainty is a well-known property of quantum mechanics that states the impossibility of predicting measurement outcomes of multiple incompatible observables simultaneously. In contrast, the uncertainty in the classical domain…