Related papers: Remarks on the Fact that the Uncertainty Principle…
The uncertainty principle and entanglement are two fundamental, but yet not well understood, features of quantum theory. The uncertainty relation reflects the capability limit in acquiring the knowledge of different physical properties of a…
The variance of an observable in a quantum state is usually used to describe Heisenberg uncertainty relation. For mixed states, the variance includes quantum uncertainty and classical uncertainty. By means of the skew information and the…
We study the special case of $n\times n$ 1D Gaussian Hermitian random band matrices, when the covariance of the elements is determined by the matrix $J=(-W^2\triangle+1)^{-1}$. Assuming that $n\ge CW\log W\gg 1$, we prove that the averaged…
Uncertainty principle is the basis of quantum mechanics. It reflects the basic law of the movement of microscopic particles. Wigner-Yanase skew information, as a measure of quantum uncertainties, is used to characterize the intrinsic…
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…
The celebrated Heisenberg Uncertainty Principle \Delta x \Delta p\ge \hbar/2 can allow measurement accuracies less than \Delta x or \Delta p. Classical analog of this is known as sub-Fourier sensitivity. We illustrate this phenomenon in a…
As a consequence of the place ascribed to measurements in the postulates of quantum mechanics, if two differently prepared systems are described with the same density operator \r{ho}, they are said to be in the same quantum state. For more…
The example of nonpositive trace-class Hermitian operator for which Robertson-Schroedinger uncertainty relation is fulfilled is presented. The partial scaling criterion of separability of multimode continuous variable system is discussed in…
By applying the supersymmetric approach we rigorously prove smoothness of the averaged density of states for a three dimensional random band matrix ensemble, in the limit of infinite volume and fixed band width. We also prove that the…
A state of a single particle can be represented by a quantum blob in the corresponding phase space, or by a cell in its 2-D subspace. Its area is frequently stated to be no less than one half of the Plank constant, implying that such a cell…
The Heisenberg uncertainty principle is one of the most famous features of quantum mechanics. However, the non-determinism implied by the Heisenberg uncertainty principle --- together with other prominent aspects of quantum mechanics such…
Some of the possible consequences of a generalized uncertainty principle (which emerges in the context of string theory and quantum gravity models as a consequence of fluctuations of the background metric) are analyzed considering the case…
We present an "uncertainty principle" for quantum channels, showing a relationship between the dimensions of the range of a channel and the range of its complement. We examine some interesting specific cases, and discuss consequences for…
Sir Rudolph Peierls, in a reply to John Bell's last critique of the state of our understanding of quantum mechanics, maintained that it is easy to give an acceptable account of the physical significance of the quantum theory. The key is to…
We examine some properties of the non-normalized (or canonical) density matrix in the coherent states representation, by two equivalent ways. On the one hand by its definition, and on the other hand as a solution to Bloch's canonical…
We use phase space distributions specifically, the Wigner distribution (WD) and Husimi distribution (HD) to investigate certain information-theoretic measures as descriptors for a given system. We extensively investigate and analyze…
The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays…
Realism about quantum theory naturally leads to realism about the quantum state of the universe. It leaves open whether it is a pure state represented by a wave function, or an impure (mixed) one represented by a density matrix. I…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
We point out an important hidden inconsistency in Fermi's probability of the quantum states that engendered inconsistent/inaccurate equations-of-state extensively used in the literature to model nonideal plasma systems. The importance of…