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The uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The situation is different if one can build a…
The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
In [Berta 2014 Entanglement], uncertainty relations in the presence of quantum memory was formulated for mutually unbiased bases using conditional collision entropy. In this paper, we generalize their results to the mutually unbiased…
Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…
The problem of quantum state classification asks how accurately one can identify an unknown quantum state that is promised to be drawn from a known set of pure states. In this work, we introduce the notion of $k$-learnability, which…
Reality of quantum observables, a feature of long-standing interest within foundations of quantum mechanics, has recently been quantified and deeply studied by means of entropic measures [Phys. Rev. A 97, 022107 (2018)]. However, there is…
Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
Uncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, was…
The limitation on obtaining precise outcomes of measurements performed on two non-commuting observables of a particle as set by the uncertainty principle in its entropic form, can be reduced in the presence of quantum memory. We derive a…
We study universally valid uncertainty relations in general quantum systems described by general $\sigma$-finite von Neumann algebras to foster developing quantitative analysis in quantum systems with infinite degrees of freedom such as…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
We derive an exact uncertainty relation for arbitrary quantum states of finite-dimensional Hilbert spaces. For any given $k$-partition of a $d$-dimensional multipartite system, we introduce the total uncertainty as the sum of the…
Unentangled pure states on a bipartite system are exactly the coherent states with respect to the group of local transformations. What aspects of the study of entanglement are applicable to generalized coherent states? Conversely, what can…
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
Quantum entanglement and nonlocality are inequivalent notions: There exist entangled states that nevertheless admit local-realistic interpretations. This paper studies a special class of local-hidden-variable theories, in which the linear…
As a very fundamental principle in quantum physics, uncertainty principle has been studied intensively via various uncertainty inequalities. Based on the information measure introduced by Brukner and Zeilinger in [Phys. Rev. Lett. 83, 3354…
Fidelity is the standard measure for quantifying the similarity between two quantum states. It is equal to the square of the minimum Bhattacharyya coefficient between the probability distributions induced by quantum measurements on the two…