Related papers: On the 'Polarized distances between quantum states…

Let $\gamma_1,\gamma_2$ be a pair of constant-degree irreducible algebraic curves in $\mathbb{R}^d$. Assume that $\gamma_i$ is neither contained in a hyperplane nor in a quadric surface in $\mathbb{R}^d$, for each $i=1,2$. We show that for…

The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY.…

Let G: C^n \times C^n -> C, G((x_1,...,x_n),(y_1,...,y_n))=(x_1-y_1)^2+...+ (x_n-y_n)^2. We say that f: R^n -> C^n preserves distance d>0 if for each x,y \in R^n G(x,y)=d^2 implies G(f(x),f(y))=d^2. Let A(n) denote the set of all positive…

The Bures distance between two displaced thermal states and the corresponding geometric quantities (statistical metric, volume element, scalar curvature) are computed. Under nonunitary (dissipative) dynamics, the statistical distance shows…

We demonstrate that a high fidelity approximation to $| \Psi_b \rangle$, the quantum superposition over all bit strings within Hamming distance $b$ of the codewords of a dimension-$k$ linear code over $\mathbb{Z}_2^n$, can be efficiently…

In this short note, we propose a scheme, in which two instances of an equatorial state (or a polar state) can be remotely prepared in one-shot operation to different receivers with prior entanglement and 1 bit of broadcasting. The trade-off…

Using the general sequential product proposed by Shen and Wu in [J. Phys. A: Math. Theor. 42, 345203, 2009], we derive three criteria for describing non-disturbance between quantum measurements that may be unsharp with such new sequential…

This is just a note for \cite[Chapter$3{1/2}_+$]{gromov}. Maybe this note is obvious for a reader who knows metric geometry. I wish that someone study further in this direction.

The concept of a "space of quantum field theories" or "theory space" was set out in the 1970's in work of Wilson, Friedan and others. This structure should play an important role in organizing and classifying QFTs, and in the study of the…

A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…

A generic model of measurement device which is able to directly measure commonly used quantum-state characteristics such as fidelity, overlap, purity and Hilbert-Schmidt distance for two general uncorrelated mixed states is proposed. In…

General quasi-probabilities are introduced to visualize time-dependent quantum correlations of light in phase space. They are based on the generalization of the Glauber-Sudarshan P function to a time-dependent P functional [W. Vogel, Phys.…

In 2017 M. Bessenyei and Z. P\'ales introduced a definition of a triangle function which generates a concept of a generalized triangle inequality in semimetric spaces. Inspired by this concept we discuss already known inequalities in metric…

The binary divergences that are divergences between probability measures defined on the same 2-point set have an interesting property. For the chi-squared divergence and the relative entropy, it is known that their binary divergence attain…

To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…

In this paper, we generalize \cite{IosevichParshall}, \cite{LongPaths} and \cite{cycles} by allowing the \emph{distance} between two points in a finite field vector space to be defined by a general non-degenerate bilinear form or quadratic…

The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…

Since general relativity is a consistent low energy effective field theory, it is possible to compute quantum corrections to classical forces. Here we compute a quantum correction to the gravitational potential between a pair of polarizable…

If $X$ is a convex surface in a Euclidean space, then the squared intrinsic distance function $\dist^2(x,y)$ is DC (d.c., delta-convex) on $X\times X$ in the only natural extrinsic sense. An analogous result holds for the squared distance…

We establish a necessary and sufficient condition for the differentiability of the distance function generated by a nonempty closed set K in a real normed linear space X under a proximinality condition on K. We do not assume the uniform…