Related papers: Two imaginarity monotones induced by unified $(\al…
Complex numbers are widely used in both classical and quantum physics, and are indispensable components for describing quantum systems and their dynamical behavior. Recently, the resource theory of imaginarity has been introduced, allowing…
In this paper, we introduce two measures for the resource theory of imaginarity. One is induced by $\alpha$--$z$--R\'enyi relative entropy and the other, defined for positive definite density matrices, is induced by Tsallis relative…
Complex numbers are widely used in quantum physics and are indispensable components for describing quantum systems and their dynamical behavior. The resource theory of imaginarity has been built recently, enabling a systematic research of…
Complex numbers are indispensable in quantum mechanics and the resource theory of imaginarity has been developed recently. In this paper, we propose a method to construct imaginary measures by real part states. Specifically, we propose an…
Complex numbers are theoretically proved and experimentally confirmed as necessary in quantum mechanics and quantum information, and a resource theory of imaginarity of quantum states has been established. In this work, we establish a…
Complex numbers are widely used in both classical and quantum physics, and play an important role in describing quantum systems and their dynamical behavior. In this paper we study several measures of imaginarity of quantum states in the…
In this paper, we introduce and study unified $(r,s)$-relative entropy and quantum unified $(r,s)$-relative entropy, in particular, our main results of quantum unified $(r,s)$-relative entropy are established on the separable complex…
The recently introduced resource theory of imaginarity facilitates a systematic investigation into the role of complex numbers in quantum mechanics and quantum information theory. In this work, we propose well-defined measures of…
The use of imaginary numbers in modelling quantum mechanical systems encompasses the wave-like nature of quantum states. Here we introduce a resource theoretic framework for imaginarity, where the free states are taken to be those with…
Given a positive function $f$ on $(0,\infty)$ and a non-zero real parameter $\theta$, we consider a function $I_f^\theta(A,B,X)=Tr X^*(f(L_AR_B^{-1})R_B)^\theta(X)$ in three matrices $A,B>0$ and $X$. In the literature $\theta=\pm1$ has been…
Imaginarity, stemming from the complex structure of quantum mechanics, has recently emerged as a fundamental resource, yet its dynamical generation remains largely unexplored. In this work, we introduce the notion of imaginarity-generating…
It is a fundamental question that why quantum mechanics uses complex numbers instead of only real numbers. To address this topic, recently, a rigorous resource theory for the imaginarity of quantum states were established, and several…
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…
Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems, their dynamics, and interaction. Since the inception of quantum theory, it has been…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
Real numbers provide a sufficient description of classical physics and all measurable phenomena; however, complex numbers are occasionally utilized as a convenient mathematical tool to aid our calculations. On the other hand, the formalism…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
The monotonicity of entropy is investigated for real quadratic rational maps on the real circle $\mathbb{R}\cup\{\infty\}$ based on the natural partition of the corresponding moduli space $\mathcal{M}_2(\mathbb{R})$ into its monotonic,…
Entropy-like functionals on operator algebras have been studied since the pioneering work of von Neumann, Umegaki, Lindblad, and Lieb. The most well-known are the von Neumann entropy $trace (\rho\log \rho)$ and a generalization of the…
Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…