相关论文: Asymptotic Redundancies for Universal Quantum Codi…
We investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. We first show how a closed-form expression for the exact…
Hoeffding's formulation and solution to the universal hypothesis testing (UHT) problem had a profound impact on many subsequent works dealing with asymmetric hypotheses. In this work, we introduce a quantum universal hypothesis testing…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
Combining high and low probability densities in intensity hybrids, we study some of their properties in double-slit setups. In particular, we connect to earlier results on beam attenuation techniques in neutron interferometry and study the…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
The asymptotic equipartition property (AEP) states that in the limit of a large number of independent and identically distributed (i.i.d.) random experiments, the output sequence is virtually certain to come from the typical set, each…
The general scheme of data compression using the quantum noiseless coding theorem of Schumacher is dicussed for general quantum sources. When the Hilbert space of the quantum source is decomposable into orthogonal subspaces, one can first…
As an application of generalised statistical mechanics, it is studied a possible route toward a consistent generalised information theory in terms of a family of non-extensive, non-parametric entropies $H^\pm_D(P)$. Unlike other proposals…
We consider an ensemble of $2\times 2$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…
Universal fixed-to-variable lossless source coding for memoryless sources is studied in the finite blocklength and higher-order asymptotics regimes. Optimal third-order coding rates are derived for general fixed-to-variable codes and for…
The asymptotic form of the average probability to count $N$ indistinguishable identical particles in a small number $r \ll N$ of binned-together output ports of a $M$-port Haar-random unitary network, proposed recently in \textit{Scientific…
This work derives an analytical formula for the asymptotic state---the quantum state resulting from an infinite number of applications of a general quantum channel on some initial state. For channels admitting multiple fixed or rotating…
We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…
As a ubiquitous aspect of modern information technology, data compression has a wide range of applications. Therefore, a quantum autoencoder which can compress quantum information into a low-dimensional space is fundamentally important to…
In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the 'general tension-reduction' (GTR) model, able to describe general quantum-like measurements with an arbitrary number of…
In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…
We study the compression of n quantum systems, each prepared in the same state belonging to a given parametric family of quantum states. For a family of states with f independent parameters, we devise an asymptotically faithful protocol…