Related papers: From Information Theory Puzzles in Deletion Channe…
In this work we derive a number of chain rules for mutual information quantities, suitable for analyzing quantum cryptography with imperfect devices that leak additional information to an adversary. First, we derive a chain rule between…
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about…
Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…
We prove new quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well known no-cloning and…
The max-relative entropy and the conditional min-entropy it induces have become central to one-shot information theory. Both may be expressed in terms of a conic program over the positive semidefinite cone. Recently, it was shown that the…
Quantum conditional entropies play a fundamental role in quantum information theory. In quantum key distribution, they are exploited to obtain reliable lower bounds on the secret-key rates in the finite-size regime, against collective…
The discrete memoryless interference channel is modelled as a conditional probability distribution with two outputs depending on two inputs and has widespread applications in practical communication scenarios. In this paper, we introduce…
We show that it is possible to transmit and preserve information at short time scales over an n-fold composition of quantum channels $(\Xi^n)_{n \in \mathbb{N}}$ modelled as a discrete quantum Markov semigroup, long enough to generate…
This paper considers a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit is added after it with probability i, or it is…
Min-entropy sampling gives a bound on the min-entropy of a randomly chosen subset of a string, given a bound on the min-entropy of the whole string. K\"onig and Renner showed a min-entropy sampling theorem that holds relative to quantum…
Quantum channels represent a broad spectrum of operations crucial to quantum information theory, encompassing everything from the transmission of quantum information to the manipulation of various resources. In the domain of states, the…
We present a new technique for proving the security of quantum key distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement purification scheme can be found.…
This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…
Differential privacy is a notion of privacy that has become very popular in the database community. Roughly, the idea is that a randomized query mechanism provides sufficient privacy protection if the ratio between the probabilities of two…
Subword tokenization is a key part of many NLP pipelines. However, little is known about why some tokenizer and hyperparameter combinations lead to better downstream model performance than others. We propose that good tokenizers lead to…
Recently, a secrecy measure based on list-reconstruction has been proposed [2], in which a wiretapper is allowed to produce a list of $2^{mR_{L}}$ reconstruction sequences and the secrecy is measured by the minimum distortion over the…
We study the problem of generating an approximately i.i.d. string at the output of a discrete memoryless channel using a limited amount of randomness at its input in presence of causal noiseless feedback. Feedback does not decrease the…
Channels with synchronization errors, exhibiting deletion and insertion errors, find practical applications in DNA storage, data reconstruction, and various other domains. Presence of insertions and deletions render the channel with memory,…
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
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…