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Measurements of Quantum Systems disturb their states. To quantify this non-classical characteristic, Zurek and Ollivier introduced the quantum discord, a quantum correlation which can be nonzero even when entanglement in the system is zero.…
Fluctuations are intrinsic to microscopic systems and impose fundamental limits on nonequilibrium precision, as captured by the thermodynamic uncertainty relation (TUR), which links current fluctuations to entropy production. While feedback…
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the…
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…
Theoretical understanding of the scaling of entropies and the mutual information has led to significant advances in the research of correlated states of matter, quantum field theory, and gravity. Measuring von Neumann entropy in quantum…
In quantum thermodynamics, entropy production is usually defined in terms of the quantum relative entropy between two states. We derive a lower bound for the quantum entropy production in terms of the mean and variance of quantum…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
To find the essential nature of quantum theory has been an important problem for not only theoretical interest but also applications to quantum technologies. In those studies on quantum foundations, the notion of uncertainty plays a primary…
We derive the uncertainty relation for a quantum open system comprised of a Brownian particle interacting with a bath of quantum oscillators at finite temperature. We examine how the quantum and thermal fluctuations of the environment…
Quantum memory systems are vital in quantum information processing for dependable storage and retrieval of quantum states. Inspired by classical reliability theories that synthesize reliable computing systems from unreliable components, we…
Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate…
We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…
We approach the physical implications of the non-commutative nature of Complementary Observable Algebras (COA) from an information theoretic perspective. In particular, we derive a general \textit{entropic certainty principle} stating that…
Entanglement and uncertainty relation are two focuses of quantum theory. We relate entanglement sharing to the entropic uncertainty relation in a $(d\times d)$-dimensional system via weak measurements with different pointers. We consider…
We investigate the uncertainty principle for two successive projective measurements in terms of R\'enyi entropy based on a single quantum system. Our results cover a large family of the entropy (including the Shannon entropy) uncertainty…
Nonlocality, which is the key feature of quantum theory, has been linked with the uncertainty principle by fine-grained uncertainty relations, by considering combinations of outcomes for different measurements. However, this approach…
We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental…
There is a renewed interest in the uncertainty principle, reformulated from the information theoretic point of view, called the entropic uncertainty relations. They have been studied for various integrable systems as a function of their…
Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the…