Related papers: Reliable Entropy Estimation from Observed Statisti…
Our ability to trust that a random number is truly random is essential for fields as diverse as cryptography and fundamental tests of quantum mechanics. Existing solutions both come with drawbacks -- device-independent quantum random number…
Data-driven extrapolation methods aim to extend the dynamics of quantum observables from measurements, but they often lack guarantees on prediction accuracy. We introduce a framework based on atomic norm minimization that can certify…
Random number generators play an essential role in cryptography and key distribution. It is thus important to verify whether the random numbers generated from these devices are genuine and unpredictable by any adversary. Recently, quantum…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
The extraction of randomness from weakly random seeds is a problem of central importance with multiple applications. In the device-independent setting, this problem of quantum randomness amplification has been mainly restricted to specific…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
Randomness is an invaluable resource in today's life with a broad use reaching from numerical simulations through randomized algorithms to cryptography. However, on the classical level no true randomness is available and even the use of…
Random number generators (RNG) based on quantum mechanics are captivating due to their security and unpredictability compared to conventional generators, such as pseudo-random number generators and hardware-random number generators. This…
A natural measure for the amount of quantum information that a physical system E holds about another system A = A_1,...,A_n is given by the min-entropy Hmin(A|E). Specifically, the min-entropy measures the amount of entanglement between E…
The device-independent framework constitutes the most pragmatic approach to quantum protocols that does not put any trust in their implementations. It requires all claims, about e.g. security, to be made at the level of the final classical…
We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an…
The laws of quantum mechanics allow unconditionally secure key distribution protocols. Nevertheless, security proofs of traditional quantum key distribution (QKD) protocols rely on a crucial assumption, the trustworthiness of the quantum…
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…
Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement…
We put forth a new computational notion of entropy, measuring the (in)feasibility of sampling high-entropy strings that are consistent with a given generator. Specifically, the i'th output block of a generator G has accessible entropy at…
Many papers proved the security of quantum key distribution (QKD) system, in the asymptotic framework. The degree of the security has not been discussed in the finite coding-length framework, sufficiently. However, to guarantee any…
In this paper, we report an experiment about the device-independent tests of classical and quantum entropy based on a recent proposal [Phys. Rev. Lett. 115, 110501 (2015)], in which the states are encoded on the polarization of a biphoton…
Recently, a novel framework for semi-device-independent quantum prepare-and-measure protocols has been proposed, based on the assumption of a limited distinguishability between the prepared quantum states. Here, we discuss the problem of…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…