相关论文: Dyson Indices and Hilbert-Schmidt Separability Fun…

We compile a sample of 341 binary and multiple star systems with the aim of searching for and characterising Kuiper belt-like debris discs. The sample is assembled by combining several smaller samples studied in previously published work…

Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators is…

We study the moments of $\overline{|\det(H-E)|^q}$ and the associated large deviations of $\log |\det(H-E)|$ where $H$ are random matrix operators involving Laplace operators and random potentials. This includes as a special case Hessians…

By means of a well-grounded mapping scheme linking Schwinger unitary operators and generators of the special unitary group $\mathrm{SU(N)}$, it is possible to establish a self-consistent theoretical framework for finite-dimensional discrete…

This paper gives a self-contained introduction to the Hilbert projective metric $\mathcal{H}$ and its fundamental properties, with a particular focus on the space of probability measures. We start by defining the Hilbert pseudo-metric on…

Since the theorems of Schur and van der Waerden, numerous partition regularity results have been proved for linear equations, but progress has been scarce for non-linear ones, the hardest case being equations in three variables. We prove…

We present estimators for smooth Hilbert-valued parameters, where smoothness is characterized by a pathwise differentiability condition. When the parameter space is a reproducing kernel Hilbert space, we provide a means to obtain efficient,…

In this paper, we present the separability criteria to identify non-$k$-separability and genuine multipartite entanglement in mixed multipartite states using elements of density matrices. Our criteria can detect the non-$k$-separability of…

We derive upper bounds for Hilbert-Schmidt's quantum coherence of general states of a $d$-level quantum system, a qudit, in terms of its incoherent uncertainty, with the latter quantified using the linear and von Neumann's entropies of the…

We study separability properties in a 5-dimensional set of states of quantum systems composed of three subsystems of equal but arbitrary finite Hilbert space dimension d. These are the states, which can be written as linear combinations of…

We derive the spectral density of the equiprobable mixture of two random density matrices of a two-level quantum system. We also work out the spectral density of mixture under the so-called quantum addition rule. We use the spectral…

This paper aims to study reducible and irreducible approximation in the set $\textsl{CSO}$ of all complex symmetric operators on a separable, complex Hilbert space $\mathcal H$. When ${\rm dim} \mathcal H=\infty$, it is proved that both…

We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators $\rho_1$ and $\rho_2$ of rank d, the supports of which jointly span a 2d-dimensional Hilbert space. Based on two…

The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for…

Given N quantum systems prepared according to the same density operator \rho, we propose a measurement on the N-fold system which approximately yields the spectrum of \rho. The projections of the proposed observable decompose the Hilbert…

In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…

We consider low rank density operators $\varrho$ supported on a $M\times N$ Hilbert space for arbitrary $M$ and $N$ ($M\leq N$) and with a positive partial transpose (PPT) $\varrho^{T_A}\ge 0$. For rank $r(\varrho) \leq N$ we prove that…

We consider the time evolution of the density matrix $\rho$ in a 2-dimensional complex Hilbert space. We allow for dissipation by adding to the von Neumann equation a term $D[\rho]$, which is of Lindblad type in order to assure complete…

A conceptually simpler proof of the separability criterion for two-qubit systems, which is referred to as "Hefei inequality" in literature, is presented. This inequality gives a necessary and sufficient separability criterion for any mixed…

The large deviations at various levels that are explicit for Markov jump processes satisfying detailed-balance are revisited in terms of the supersymmetric quantum Hamiltonian $H$ that can be obtained from the Markov generator via a…