Related papers: Sampling of min-entropy relative to quantum knowle…
Given a random subspace $H_n$ chosen uniformly in a tensor product of Hilbert spaces $V_n\otimes W$, we consider the collection $K_n$ of all singular values of all norm one elements of $H_n$ with respect to the tensor structure. A law of…
Statistical model checking avoids the exponential growth of states associated with probabilistic model checking by estimating properties from multiple executions of a system and by giving results within confidence bounds. Rare properties…
In most data-scientific approaches, the principle of Maximum Entropy (MaxEnt) is used to a posteriori justify some parametric model which has been already chosen based on experience, prior knowledge or computational simplicity. In a…
Consider the problem of estimating the Shannon entropy of a distribution over $k$ elements from $n$ independent samples. We show that the minimax mean-square error is within universal multiplicative constant factors of $$\Big(\frac{k }{n…
We develop a quantum version of the probability estimation framework [arXiv:1709.06159] for randomness generation with quantum side information. We show that most of the properties of probability estimation hold for quantum probability…
We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
Random sampling is an essential tool in the processing and transmission of data. It is used to summarize data too large to store or manipulate and meet resource constraints on bandwidth or battery power. Estimators that are applied to the…
We develop a simple Quantile Spacing (QS) method for accurate probabilistic estimation of one-dimensional entropy from equiprobable random samples, and compare it with the popular Bin-Counting (BC) method. In contrast to BC, which uses…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
Planck-scale quantum spacetime undergoes probabilistic local curvature fluctuations whose distributions cannot explicitly depend on position otherwise vacuum's small-scale quantum structure would fail to be statistically homogeneous. Since…
Randomness is a central feature of quantum mechanics and an invaluable resource for both classical and quantum technologies. Commonly, in Device-Independent and Semi-Device-Independent scenarios, randomness is certified using projective…
We study the entanglement of a pure state of a composite quantum system consisting of several subsystems with $d$ levels each. It can be described by the R\'enyi-Ingarden-Urbanik entropy $S_q$ of a decomposition of the state in a product…
How much information about an unknown quantum state can be obtained by a measurement? We propose a model independent answer: the information obtained is equal to the minimum entropy of the outputs of the measurement, where the minimum is…
High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local…
Apart from their foundational significance, entropic uncertainty relations play a central role in proving the security of quantum cryptographic protocols. Of particular interest are thereby relations in terms of the smooth min-entropy for…
The nonlocal behavior of quantum mechanics can be used to generate guaranteed fresh randomness from an untrusted device that consists of two nonsignalling components; since the generation process requires some initial fresh randomness to…
The problem considered here is motivated by a work by B. Nachtergaele and H.T. Yau where the Euler equations of fluid dynamics are derived from manybody quantum mechanics, see [10]. A crucial concept in their work is that of local quantum…
In this work, we investigate the amount of energy that can be extracted or charged through unitary operations when only minimal information about the state is known. Assuming knowledge of only the mean energy of the state, we start by…
De, Trevisan and Tulsiani [CRYPTO 2010] show that every distribution over $n$-bit strings which has constant statistical distance to uniform (e.g., the output of a pseudorandom generator mapping $n-1$ to $n$ bit strings), can be…