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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…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays a vital role in quantum information processing. We study uncertainty relations based on metric-adjusted skew information for finite quantum…
Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…
We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems. The relevant uncertainty principle is…
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…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
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…
Uncertainty principle is the basis of quantum mechanics. It reflects the basic law of the movement of microscopic particles. Wigner-Yanase skew information, as a measure of quantum uncertainties, is used to characterize the intrinsic…
We discuss some applications of various versions of uncertainty relations for both discrete and continuous variables in the context of quantum information theory. The Heisenberg uncertainty relation enables demonstration of the EPR paradox.…
Quantum coherence and quantum correlations lie in the center of quantum information science, since they both are considered as fundamental reasons for significant features of quantum mechanics different from classical mechanics. We present…
The concept of wave-particle duality holds significant importance in the field of quantum mechanics, as it elucidates the dual nature encompassing both wave-like and particle-like properties exhibited by microscopic particles. In this…
We investigate quantitatively the wave-particle duality in a general Mach-Zehnder interferometer setup with an asymmetric beam splitter. The asymmetric beam splitter introduces additional a priori which-path knowledge, which is different…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…
The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand…
Information entropies provide powerful and flexible way to express restrictions imposed by the uncertainty principle. This approach seems to be very suitable in application to problems of quantum information theory. It is typical that…
Uncertainty relations lie at the very core of quantum mechanics, and form the cornerstone of essentially all quantum cryptographic applications. In particular, they play an important role in cryptographic protocols in the…
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
It is pointed out that the case for Shannon entropy and von Neumann entropy, as measures of uncertainty in quantum mechanics, is not as bleak as suggested in quant-ph/0006087. The main argument of the latter is based on one particular…
We study the entanglement between the two beams exiting a Mach-Zehnder interferometer fed by a couple of squeezed-coherent states with arbitrary squeezing parameter. The quantum correlations at the output are function of the internal…