Related papers: Inaccessible Entropy I: Inaccessible Entropy Gener…
We derive a lower bound on the smallest output entropy that can be achieved via vector quantization of a $d$-dimensional source with given expected $r$th-power distortion. Specialized to the one-dimensional case, and in the limit of…
A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
Quantum systems may contain underlying correlations which are inaccessible to computationally bounded observers. We capture this distinction through a framework that analyses bipartite states only using efficiently implementable quantum…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
Generative Adversarial Networks (GANs) can produce high-quality samples, but do not provide an estimate of the probability density around the samples. However, it has been noted that maximizing the log-likelihood within an energy-based…
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…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
Entropy production is a fundamental concept that plays a crucial role in the second law of thermodynamics and the measure of irreversibility. It imposes rigorous constraints on the kinds of transformations allowed in thermodynamic…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…
This manuscript introduces a computationally efficient method to calculate the nonlinearity of a quantum feature map, as well as a method for determining whether a quantum feature map will have a high concentration of quantum states. The…
The entropy accumulation theorem, and its subsequent generalized version, is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. However, it has the drawback that the finite-size…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which detailed balance and time-reversal symmetry are broken. Despite…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
Entropy production is the crucial quantity characterizing irreversible phenomena and the second law of thermodynamics. Yet, a ubiquitous definition eludes consensus. Given that entropy production arises from incomplete access to…
Randomness extraction is a key problem in cryptography and theoretical computer science. With the recent rapid development of quantum cryptography, quantum-proof randomness extraction has also been widely studied, addressing the security…
We investigate the performance of entropy estimation methods, based either on block entropies or compression approaches, in the case of bidimensional sequences. We introduce a validation dataset made of images produced by a large number of…
In relative entropy coding, a sender aims to design a stochastic code such that, on input $X \sim P_X$, the receiver can generate a sample $Y \sim P_{Y \mid X}$. It is a standard result that (1) this requires at least $I(X; Y)$ bits, (2)…
Within the task of collaborative filtering two challenges for computing conditional probabilities exist. First, the amount of training data available is typically sparse with respect to the size of the domain. Thus, support for higher-order…