Related papers: Entropy and the uncertainty principle
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…
For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from…
The uncertainty principle is deemed as one of cornerstones in quantum mechanics, and exploring its lower limit of uncertainty will be helpful to understand the principle's nature. In this study, we propose a generalized entropic uncertainty…
Uncertainty relations are among the unique fingerprints of quantum physics, being direct expression of non-commutativity and complementarity. Entropic uncertainty relations arise in quantum information theory as the most natural expression…
We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite…
A formulation of the density functional theory is constructed on the foundations of entropic inference. The theory is introduced as an application of maximum entropy for inhomogeneous fluids in thermal equilibrium. It is shown that entropic…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
Quantum physics, despite its observables being intrinsically of a probabilistic nature, does not have a quantum entropy assigned to them. We propose a quantum entropy that quantify the randomness of a pure quantum state via a conjugate pair…
In Coles-Piani's recent remarkable version of the entropic uncertainty principle, the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
We examine quantum gravity effects by applying the generalized uncertainty principle (GUP) to entropic uncertainty relation conditions on quantum entanglement. In particular, we study the GUP corrections to the Shannon entropic uncertainty…
Many important quantities in quantum information science, such as entropy and entanglement, are non-linear functions of the density matrix and cannot be expressed as operator observables. Standard open-system approaches evolve only a single…
The uncertainty principle, first introduced by Heisenberg in inertial frames, clearly distinguishes quantum theories from classical mechanics. In non-inertial frames, its information-theoretic expressions, namely entropic uncertainty…
A theory of thermodynamics has been recently formulated and derived on the basis of R\'enyi entropy and its relative versions. In this framework, we define the concepts of partition function, internal energy and free energy, and fundamental…
Entropic uncertainty relations are powerful tools, especially in quantum cryptography. They typically bound the amount of uncertainty a third-party adversary may hold on a measurement outcome as a result of the measurement overlap. However,…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy. For these we state conditions for equality, and we prove some new error bounds away from…
Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways…