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Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the…
We investigate the additivity properties for both bipartite and multipartite systems by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular,…
In this paper, we present a new entanglement monotone for bipartite quantum states. Its definition is inspired by the so-called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual…
In this paper, we show an interesting connection between a quantum sampling technique and quantum uncertainty. Namely, we use the quantum sampling technique, introduced by Bouman and Fehr, to derive a novel entropic uncertainty relation…
The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…
Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…
The entropic uncertainty relation with quantum side information (EUR-QSI) from [Berta et al., Nat. Phys. 6, 659 (2010)] is a unifying principle relating two distinctive features of quantum mechanics: quantum uncertainty due to measurement…
As the fundamental tool in quantum information science, the uncertainty principle is essential for manifesting nonclassical properties of quantum systems. Plenty of efforts on the uncertainty principle with two observables have been…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
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…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results…
Recently, Di\'osi et al. (Int. J. Quant. Inf. 4, 99 (2006)) introduced a simple, yet very interesting model for reservoirs, in order to study the relationship between thermodynamic entropy production of a system and the corresponding von…
The guesswork is an information-theoretic quantity which can be seen as an alternate security criterion to entropy. Recent work has established the theoretical framework for guesswork in the presence of quantum side information, which we…
Through the generalization of Khinchin's classical axiomatic foundation, a basis is developed for nonadditive information theory. The classical nonadditive conditional entropy indexed by the positive parameter q is introduced and then…
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…
It has been shown recently that the framework of quantum sampling, as introduced by Bouman and Fehr, can lead to new entropic uncertainty relations highly applicable to finite-key cryptographic analyses. Here we revisit these so-called…
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…
Recently, an entropic uncertainty relation for multiple measurements has been proposed by Liu et al. in [Phys. Rev. A 91, 042133 (2015)]. However, the lower bound of the relation is not always tight with respect to different measurements.…
Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such…