Related papers: Monotonicity Properties of Certain Measures over t…
In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can,…
We consider fixed-point equations for probability measures charging measured compact metric spaces that naturally yield continuum random trees. On the one hand, we study the existence/uniqueness of the fixed-points and the convergence of…
This paper considers metrics whose curvature tensor makes sense as a distribution. A class of such metrics, the regular metrics, was defined and studied by Geroch and Traschen. Here, we generalize their definition to form a wider class:…
This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum…
We investigate the detailed properties of Observational entropy, introduced by \v{S}afr\'{a}nek et al. [Phys. Rev. A 99, 010101 (2019)] as a generalization of Boltzmann entropy to quantum mechanics. This quantity can involve multiple…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
We revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's…
Coherence is the most fundamental quantum feature of the nonclassical systems. The understanding of coherence within the resource theory has been attracting increasing interest among which the quantification of coherence is an essential…
An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…
We formulate the Frobenius-norm-based measures for quantum coherence and asymmetry respectively. In contrast to the resource theory of coherence and asymmetry, we construct a natural measure of quantum coherence inspired from optical…
For a broad class of integral functionals defined on the space of $n$-dimensional convex bodies, we establish necessary and sufficient conditions for monotonicity, and necessary conditions for the validity of a Brunn-Minkowski type…
We define a one-parameter family of canonical volume measures on Lorentzian (pre-)length spaces. In the Lorentzian setting, this allows us to define a geometric dimension - akin to the Hausdorff dimension for metric spaces - that…
The diverse quantization phenomena in 2D condensed-matter systems, being due to a uniform perpendicular magnetic field and the geometry-created lattice symmetries, are the focuses of this book. They cover the diversified magneto-electronic…
We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of…
Reporting about the density matrix theory for a composite quantum system of flavor eigenstates, we introduce the idea of flavor-weighted energies. It provides us with the right correlation between the energies of flavor eigenstates and…
Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a…
We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (``qubits''). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of…
In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, $T$, in a product space whose alphabet is a countable set. More specifically, we show…
The non-classical nature of quantum states, often illustrated using entanglement measures or quantum discord, constitutes a resource for quantum information protocols. However, the non-classicality of a quantum system cannot be encapsulated…
We introduce a measure of the compatibility between quantum states--the likelihood that two density matrices describe the same object. Our measure is motivated by two elementary requirements, which lead to a natural definition. We list some…