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Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
A general tool for description of open quantum systems is given by the formalism of quantum operations. Most important of them are trace-preserving maps also known as quantum channels. We discuss those conditions on quantum channels under…
In the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by…
In this paper the relation between quantum covariances and quantum Fisher informations are studied. This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information. The proof given…
Recently, a new interesting concept of reverse uncertainty relation is introduced. Different from the normal uncertainty relation, the reverse one indicates that one cannot only prepare quantum states with joint small uncertainty, but also…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
We consider a range of "theories" that violate the uncertainty relation for anti-commuting observables derived in [JMP, 49, 062105 (2008)]. We first show that Tsirelson's bound for the CHSH inequality can be derived from this uncertainty…
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
We show that the Euclidean Snyder non-commutative space implies infinitely many different physical predictions. The distinct frameworks are specified by generalized uncertainty relations underlying deformed Heisenberg algebras. Considering…
Bell nonlocality and uncertainty relations are distinct features of quantum theory from classical physics. Bell nonlocality concerns the correlation strength among local observables on different quantum particles, whereas the uncertainty…
Gaussian distribution of a quantum state with continuous spectrum is known to maximize the Shannon entropy at a fixed variance. Applying it to a pair of canonically conjugate quantum observables $\hat x$ and $\hat p$, quantum entropic…
Measurement error and disturbance, in the presence of conservation laws, are analysed in general operational terms. We provide novel quantitative bounds demonstrating necessary conditions under which accurate or non-disturbing measurements…
It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…
We investigate the product form uncertainty relations of variances for $n\,(n\geq 3)$ quantum observables. In particular, tight uncertainty relations satisfied by three observables has been derived, which is shown to be better than the ones…
The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved…
We address the following criterion for quantifying the quantum information resources: classically simulable {\it vs.} classically non-simulable information processing. This approach gives rise to existence of a deeper level of quantum…
We extend the Watanabe--Sagawa--Ueda (WSU) uncertainty relations for measurement errors to infinite-dimensional systems. The original WSU formulation provided a definition of measurement errors with a clear physical interpretation based on…
An issue which has attracted increasing attention in contemporary researches are Kirkwood--Dirac quasiprobabilities. List of their use includes many questions of quantum physics. Applications of complex tight frames in quantum information…