Related papers: Uncertainty relation on Wigner-Yanase-Dyson skew i…
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…
An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality.
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…
In this paper, we establish analogs of Miyachi, Cowling-Price, and Heisenberg-Pauli-Weyl uncertainty principles in the framework of the linear canonical Dunkl transform. We also obtain some weighted inequalities, such as Nash, Clarkson,…
We establish strict upper bounds on local quantum uncertainty (LQU) and skew information associated with state conversion via certain quantum channels. Specifically, we obtain a bound on the achievable LQU for bipartite channels whose Kraus…
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered…
The issue of interference and which-way information is addressed in the context of 3-slit interference experiments. A new path distinguishability ${\mathcal D_Q}$ is introduced, based on Unambiguous Quantum State Discrimination (UQSD). An…
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…
Traditional forms of quantum uncertainty relations are invariably based on the standard deviation. This can be understood in the historical context of simultaneous development of quantum theory and mathematical statistics. Here, we present…
We extend a class of recently derived thermodynamic uncertainty relations to vector-valued observables. In contrast to the scalar-valued observables examined previously, this multidimensional thermodynamic uncertainty relation provides a…
We prove a version of the data-processing inequality for the relative entropy for general von Neumann algebras with an explicit lower bound involving the measured relative entropy. The inequality, which generalizes previous work by Sutter…
We present a joint-measurement uncertainty relation for a pair of mean square deviations of canonical variables averaged over Gaussian distributed quantum optical states. Our Bayesian formulation is free from the unbiasedness assumption,…
A concise derivation of all uncertainty relations is given entirely within the context of phase-space quantization, without recourse to operator methods, to the direct use of Weyl's correspondence, or to marginal distributions of x and p.
A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and…
Nowadays, geometric tools are being used to treat a huge class of problems of quantum information science. By understanding the interplay between the geometry of the state space and information-theoretic quantities, it is possible to obtain…
Several variations of the Heisenberg uncertainty inequality are derived on the basis of "noise-resolution duality" recently proposed by the authors. The same approach leads to a related inequality that provides an upper limit for the…
When we extract information from a system by performing a quantum measurement, the state of the system is disturbed due to the backaction of the measurement. Numerous studies have been performed to quantitatively formulate tradeoff…
We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
A definition of quantum correlation is presented for an arbitrary bipartite quantum state based on the skew information. This definition not only inherits the good properties of skew information such as the contractivity and so on, but also…