Related papers: Entropic uncertainty relations and the stabilizer …
Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of R\'{e}nyi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach…
Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be…
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…
We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. The obtained equality indicates that the uncertainty relation can be expressed more accurately, and…
The uncertainty principle bounds our ability to simultaneously predict two incompatible observables of a quantum particle. Assisted by a quantum memory to store the particle, this uncertainty could be reduced and quantified by a new…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…
Fluctuation theorems are fundamental results in non-equilibrium thermodynamics. Considering the fluctuation theorem with respect to the entropy production and an observable, we derive a new thermodynamic uncertainty relation which also…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
Finite tight frames are interesting in various topics including questions of quantum information. Each complex tight frame leads to a resolution of the identity in the Hilbert space. Symmetric informationally complete measurements are a…
We use quantum estimation theory to derive a thermodynamic uncertainty relation in Markovian open quantum systems, which bounds the fluctuation of continuous measurements. The derived quantum thermodynamic uncertainty relation holds for…
Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the…
Uncertainty relations emerging from the Tsallis entropy are derived and discussed. In particular we found a positively defined function that saturates the so called entropic inequalities for entropies characterizing the physical states…
Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate…
We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…