相关论文: Convexity of quantum $\chi^2$-divergence
We present the uncertainty relations in terms of the symmetrized \r{ho}-absolute variance, which generalizes the uncertainty relations for arbitrary operator (not necessarily Hermitian) to quantum channels. By recalling the quantity…
Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these `lattice spacing' weights do not have to be independent of the direction of the arrow. We use this…
We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By…
A new notion of displacement convexity on a matrix level is developed for density flows arising from mean-field games, compressible Euler equations, entropic interpolation, and semi-classical limits of non-linear Schr\"odinger equations.…
In this paper we study diagonal quantum channels and their structure by proving some results and giving most applicable instances of them. Firstly, it is shown that action of every diagonal quantum channel on pure state from computational…
It is commonly stated that decoherence in open quantum systems is due to growing entanglement with an environment. In practice, however, surprisingly often decoherence may equally well be described by random unitary dynamics without…
In this paper, we establish some new integral inequalities for $(\alpha, m)-$convex functions and quasi-convex functions, respectively. Our results in special cases recapture known results.
We obtain two new additivity results of quantum channels. The first one is the additivity of the channel R\'enyi information associated with the sandwiched R\'enyi divergence of order $\alpha\in[\frac{1}{2},1)$. To prove this, we introduce…
It is easy to show coincidence of the entanglement-assisted classical capacity and the Holevo capacity for any c-q channel between finite dimensional quantum systems. In this paper we prove the converse assertion: coincidence of the…
In this work we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant…
We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy…
We analyse the correlation function of the quantum curvature in complex quantum systems, using a random matrix model to provide an exemplar of a universal correlation function. We show that the correlation function diverges as the inverse…
The group symmetries inherent in quantum channels often make them tractable and applicable to various problems in quantum information theory. In this paper, we introduce natural probability distributions for covariant quantum channels.…
If $\alpha$ is a probability on $\mathbb{R}^d$ and $t>0,$ consider the Dirichlet random probability $P_t\sim\mathcal{D}(t\alpha) ;$ it is such that for any measurable partition $(A_0,\ldots,A_k)$ of $\mathbb{R}^d$ then…
We establish Bernstein's inequalities for functions of general (general-state-space and possibly non-reversible) Markov chains. These inequalities achieve sharp variance proxies and encompass the classical Bernstein inequality for…
We address the problem of optimally approximating the action of a desired and unavailable quantum channel $\Phi $ having at our disposal a single use of a given set of other channels $\{\Psi_i \}$. The problem is recast to look for the…
Variational quantum algorithms are poised to have significant impact on high-dimensional optimization, with applications in classical combinatorics, quantum chemistry, and condensed matter. Nevertheless, the optimization landscape of these…
For the two-parameter matrix quantum group GLp,q(2) all bicovariant differential calculi (with a four-dimensional space of 1-forms) are known. They form a one-parameter family. Here, we give an improved presentation of previous results by…
The common perception is that strong coupling to the environment will always render the evolution of the system density matrix quasi-classical (in fact, diffusive) in the long time limit. We present here a counter-example, in which a…
We study the mixing time of two popular discrete-time Markov chains in continuous space, the Unadjusted Langevin Algorithm and the Proximal Sampler, which are discretizations of the Langevin dynamics. We extend mixing time analyses for…