相关论文: Non-closure of quantum correlation matrices and fa…

We explore the implications of hidden symmetries present in a particular quantum cosmological setting, extending the results reported in \cite{10,11}. In more detail, our case study is constituted by a spatially closed…

A domain $R$ is said to have the finite factorization property if every nonzero non-unit element of $R$ has at least one and at most finitely many distinct factorizations up to multiplication of irreducible factors by central units. Let $k$…

Let $\mathbb{F}$ be a field. Denote by $t_n(\mathbb{F})$ the greatest possible dimension for a vector space of $n$-by-$n$ matrices over $\mathbb{F}$ in which every element is triangularizable over $\mathbb{F}$. It was recently proved that…

All finite dimensional Nichols algebras with diagonal type of connected finite dimensional Yetter-Drinfeld modules over finite cyclic group $\mathbb Z_n$ are found. It is proved that finite dimensional Nichols algebra over $\mathbb Z_2$ is…

We describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed…

We identify and characterize all the local quantum channels that preserves the set of classical states, i.e., does not create any quantum correlations. At first we show that the quantum correlations cannot be created from without if and…

We study factorization and dilation properties of Markov maps between von Neumann algebras equipped with normal faithful states, i.e., completely positive unital maps which preserve the given states and also intertwine their automorphism…

In this paper we show that for every $2\leq n\in \mathbb{N}$, the statement "there is an $n$-entangled set, but there are no $n+1$-entangled sets" is consistent. We also prove some theorems which improve our understanding of entangled sets…

In this paper we give a general integral representation for separable states in the tensor product of infinite dimensional Hilbert spaces and provide the first example of separable states that are not countably decomposable. We also prove…

Given a finite set $\{M_0,\dots,M_{d-1}\}$ of nonnegative $2\times 2$ matrices and a nonnegative column-vector $V$, we associate to each $(\omega_n)\in\{0,\dots,d-1\}^\mathbb N$ the sequence of the column-vectors…

The von Neumann entropy of a $k$-body reduced density matrix $\gamma_k$ quantifies the entanglement between $k$ quantum particles and the remaining ones. In this short paper, we rigorously prove general properties of this entanglement…

The large N limit of a one-dimensional infinite chain of random matrices is investigated. It is found that in addition to the expected Kosterlitz--Thouless phase transition this model exhibits an infinite series of phase transitions at…

We provide new results for computing and comparing the quantum gate fidelity of quantum channels via their Choi matrices. We extend recent work that showed there exist non-dual pairs of quantum channels with equal gate fidelity by providing…

Let $K$ be a totally real number field of degree $n \geq 2$. The inverse different of $K$ gives rise to a lattice in $\mathbb{R}^n$. We prove that the space of Schwartz Fourier eigenfunctions on $\mathbb{R}^n$ which vanish on the…

Parties connected to independent sources through a network can generate correlations among themselves. Notably, the space of feasible correlations for a given network, depends on the physical nature of the sources and the measurements…

Several important measures of quantum correlations of a state of a finite-dimensional composite system are defined as linear combinations of marginal entropies of this state. This paper is devoted to the infinite-dimensional generalizations…

Many alternative approaches to construct quantum channels with large entangling capacity were proposed in the past decade, resulting in multiple isolated gates. In this work, we put forward a novel one, inspired by convolution, which…

Higher-dimensional entanglement is a valuable resource for several quantum information processing tasks, and is often characterized by the Schmidt number and specific classes of entangled states beyond qubit-qubit and qubit-qutrit systems.…

Two or more quantum systems are said to be in an entangled or non-factorisable state if their joint (supposedly pure) wave-function is not expressible as a product of individual wave functions but is instead a superposition of product…

The recent development of single-atom-resolved probes has made full counting statistics measurements accessible in quantum gas experiments. This capability provides access to high-order moments of physical observables, from which cumulants,…