Related papers: Fidelity is a sub-martingale for discrete-time qua…
Current measurements of the low and high redshift Universe are in tension if we restrict ourselves to the standard six parameter model of flat $\Lambda$CDM. This tension has two parts. First, the Planck satellite data suggest a higher…
Realism about quantum theory naturally leads to realism about the quantum state of the universe. It leaves open whether it is a pure state represented by a wave function, or an impure (mixed) one represented by a density matrix. I…
Motivated by recent development in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We get…
In this survey paper we review classical results and recent progress about a certain topic in the spectral theory of two-dimensional canonical systems. Namely, we consider the questions whether the spectrum $\sigma$ is discrete, and if it…
Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…
Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…
We illustrate through numerical results a number of features of environment-induced decoherence under a broad class of apparatus-environment interactions in quantum measurements wherein the reduced system-apparatus density matrix evolves…
Quantum fidelity is one of the most important measures of similarity between mixed quantum states. However, the usual formulation is cumbersome and hard to understand when encountering the first time. This work shows in a novel, elegant…
In a previous FAST paper, I presented a quantitative model of the process of trust building, and showed that trust is accumulated like wealth: the rich get richer. This explained the pervasive phenomenon of adverse selection of trust…
Evolution of the reduced density matrix for a subsystem is studied to determine deviations from its Markov character for a system consisting of a closed chain of $N$ oscillators with one of them serving as a subsystem. The dependence on $N$…
We consider a central system which is coupled via dephasing to an open system, i.e. an intermediate system which in turn is coupled to another environment. Considering intermediate and far environment as one composite system, the coherences…
In this paper we give a new way to quantify the folklore notion that quantum measurements bring a disturbance to the system being measured. We consider two observers who initially assign identical mixed-state density operators to a…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
The fidelity of quantum cloning is very often limited by the accompanying unwanted transitions. We show how the fidelity can be improved by using a coherent field to cycle away the unwanted transitions. We demonstrate this explicitly in the…
In the theory of quantum transmission of information the concept of fidelity plays a fundamental role. An important class of channels, which can be experimentally realized in quantum optics, is that of Gaussian quantum channels. In this…
In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are in general different. Therefore one reaches the remarkable…
We present examples of continuous variable (CV) states having high fidelity to a given target, say $F > 0.9$ or $F > 0.99$, and still showing striking differences in their physical properties, including classical and quantum states within…
In a large scale trapped atomic ion quantum computer, high-fidelity two-qubit gates need to be extended over all qubits with individual control. We realize and characterize high-fidelity two-qubit gates in a system with up to 4 ions using…
From the key composite quantum system made of a two-level system (qubit) and a harmonic oscillator (photon) with resonant or dispersive interactions, one derives the corresponding quantum Stochastic Master Equations (SME) when either the…
Fidelity-based quantum kernels provide a direct interface between quantum feature maps and classical kernel methods, but they can exhibit exponential concentration: with increasing system size or circuit expressivity, the Gram matrix…