Related papers: Bitwise Quantum Min-Entropy Sampling and New Lower…
Compact expressions for the average subentropy and coherence are obtained for random mixed states that are generated via various probability measures. Surprisingly, our results show that the average subentropy of random mixed states…
Random bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require "strong" RBGs that produce high-entropy bit…
This paper starts by considering the minimization of the Renyi divergence subject to a constraint on the total variation distance. Based on the solution of this optimization problem, the exact locus of the points $\bigl( D(Q\|P_1),…
We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a…
It is well known that n bits of entropy are necessary and sufficient to perfectly encrypt n bits (one-time pad). Even if we allow the encryption to be approximate, the amount of entropy needed doesn't asymptotically change. However, this is…
Shannon entropy is the shortest average codeword length a lossless compressor can achieve by encoding i.i.d. symbols. However, there are cases in which the objective is to minimize the \textit{exponential} average codeword length, i.e. when…
The minimum energy, and, more generally, the minimum cost, to transmit one bit of information has been recently derived for bursty communication when information is available infrequently at random times at the transmitter. Furthermore, it…
In classical and quantum information theory, operational quantities such as the amount of randomness that can be extracted from a given source or the amount of space needed to store given data are normally characterized by one of two…
While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely…
Relative entropy is the standard measure of distinguishability in classical and quantum information theory. In the classical case, its loss under channels admits an exact chain rule, while in the quantum case only asymptotic, regularized…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
We present a comprehensive software framework for the finite-size security analysis of quantum random number generation (QRNG) and quantum key distribution (QKD) protocols, based on the Entropy Accumulation Theorem (EAT). Our framework…
We consider query-based data acquisition and the corresponding information recovery problem, where the goal is to recover $k$ binary variables (information bits) from parity measurements of those variables. The queries and the corresponding…
The Entropy Accumulation Theorem (EAT) was introduced to significantly improve the finite-size rates for device-independent quantum information processing tasks such as device-independent quantum key distribution (QKD). A natural question…
Quantum-proof randomness extractors are an important building block for classical and quantum cryptography as well as device independent randomness amplification and expansion. Furthermore they are also a useful tool in quantum Shannon…
Certified randomness guaranteed to be unpredictable by adversaries is central to information security. The fundamental randomness inherent in quantum physics makes certification possible from devices that are only weakly characterised, i.e.…
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…
Let $ X_1, \ldots, X_n $ be independent random variables taking values in the alphabet $ \{0, 1, \ldots, r\} $, and $ S_n = \sum_{i = 1}^n X_i $. The Shepp--Olkin theorem states that, in the binary case ($ r = 1 $), the Shannon entropy of $…
Expansion and amplification of weak randomness plays a crucial role in many security protocols. Using quantum devices, such procedure is possible even without trusting the devices used, by utilizing correlations between outcomes of parts of…
The classical problem of maximizing the Shannon entropy of a sum of independent random variables supported on a finite alphabet is considered and settled in the ternary case. Namely, the following theorem is established: if…