Related papers: Entropic uncertainty relations for SIC-POVMs and M…
Strong subadditivity goes beyond the tensored subsystem and commuting operator models. As previously noted by Petz and later by Araki and Moriya, two subalgebras of observables satisfy a generalized SSA-like inequality if they form a…
The uncertainty relation is a fundamental limit in quantum mechanics and is of great importance to quantum information processing as it relates to quantum precision measurement. Due to interactions with the surrounding environment, a…
Uncertainty relation is not only of fundamental importance to quantum mechanics, but also crucial to the quantum information technology. Recently, majorization formulation of uncertainty relations (MURs) have been widely studied, ranging…
The principal aim of this Comment is to correct those entropic uncertainty relations that are presented in a paper by Massar [arXiv:quant-ph/0703036v2 (current version)], concerning two approaches to a study of the noise produced by POVM's.…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
Entropic uncertainty relations are quantitative characterizations of Heisenberg's uncertainty principle, which make use of an entropy measure to quantify uncertainty. In quantum cryptography, they are often used as convenient tools in…
We consider a family of prior probability distributions of particular interest, all being defined on the three-dimensional convex set of two-level quantum systems. Each distribution is, following recent work of Petz and Sudar, taken to be…
The concepts of `conditional entropy' and `information' retain their validity for quantum systems, but their properties differ somewhat from those of their classical counterparts; specifically, some equalities and inequalities of classical…
Uncertainty quantification is a key aspect in many tasks such as model selection/regularization, or quantifying prediction uncertainties to perform active learning or OOD detection. Within credal approaches that consider modeling…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…
New inequalities for symplectic tomograms of quantum states and their connection with entropic uncertainty relations are discussed within the framework of the probability representation of quantum mechanics.
A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the…
Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…
A way to pose the entropic uncertainty principle for trace-preserving super-operators is presented. It is based on the notion of extremal unraveling of a super-operator. For given input state, different effects of each unraveling result in…
In this work, we consider a probability representation of quantum dynamics for finite-dimensional quantum systems with the use of pseudostochastic maps acting on true probability distributions. These probability distributions are obtained…
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.…
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…
In this work we establish rigorously a measurement uncertainty relation (MUR) for three unbiased qubit observables, which was previously shown to hold true under some presumptions. The triplet MUR states that the uncertainty, which is…
Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…