Related papers: Strong unitary uncertainty relations
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the B\"ottcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is…
Uncertainty and intrinsic measurement disturbance, two fundamental concepts in quantum measurement, have conventionally been viewed as distinct and studied separately. In this work, we establish a fundamental connection between them,…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
We study fine-grained uncertainty relations for several quantum measurements in a finite-dimensional Hilbert space. The proposed approach is based on exact calculation or estimation of the spectral norms of corresponding positive matrices.…
Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…
Uncertainty principle reveals the intrinsic differences between the classical and quantum worlds, which plays a significant role in quantum information theory. By using $\rho$-absolute variance, we introduce the uncertainty of quantum…
Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…
We elaborate on the recent proposal of employing unitary operators in Quantum Mechanics. The Bell and Mermin inequalities for entangled coherent states are scrutinized by making use of the unitary displacement operators. A violation of the…
The quantification of the "measurement uncertainty" aspect of Heisenberg's Uncertainty Principle---that is, the study of trade-offs between accuracy and disturbance, or between accuracies in an approximate joint measurement on two…
Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger…
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…
The new uncertainty relation is derived in the context of the canonical quantum theory with gravity for the case of the maximally symmetric space. This relation establishes a connection between fluctuations of the quantities which determine…
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…
New uncertainty relations for n observables are established. The relations take the invariant form of inequalities between the characteristic coefficients of order r, r = 1,2,...,n, of the uncertainty matrix and the matrix of mean…
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…
Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term for various trade-off relations in nature. In…
This chapter provides a principled introduction to uncertainty relations underlying sparse signal recovery. We start with the seminal work by Donoho and Stark, 1989, which defines uncertainty relations as upper bounds on the operator norm…
We study a possible improvement of uncertainty relations. The Heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables. The Schroedinger uncertainty…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…