Related papers: On Information Links
It is well-known:Suppose there are three 1-dimensional links $K_+$, $K_-$, $K_0$ such that $K_+$, $K_-$, and $K_0$ coincide out of a 3-ball $B$ trivially embedded in $S^3$ and that $K_+\cap B$, $K_-\cap B$, and $K_0\cap B$ are drawn as…
We define a sequence of integer-valued invariants $\gamma^k(L)$ for a $3$-component link $L$. We prove that the resulting $\gamma$-invariants are invariant under concordance, and more generally under weak cobordism, and that they lift…
We study the relation between the quantum conditional mutual information and the quantum $\alpha$-R\'enyi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the…
Lieb and Ruskai's strong subadditivity theorem, which shows that the conditional mutual information must be nonnegative, is fundamental in quantum theory. It has numerous applications, such as in quantum error correction. When the mutual…
If L_1 and L_2 are two Brunnian links with all pairwise linking numbers 0, then we show that L_1 and L_2 are equivalent if and only if they have homeomorphic complements. In particular, this holds for all Brunnian links with at least three…
Here we prove an asymptotically optimal lower bound on the information complexity of the k-party disjointness function with the unique intersection promise, an important special case of the well known disjointness problem, and the…
Many network information theory problems face the similar difficulty of single letterization. We argue that this is due to the lack of a geometric structure on the space of probability distribution. In this paper, we develop such a…
Interaction information is one of the multivariate generalizations of mutual information, which expresses the amount information shared among a set of variables, beyond the information, which is shared in any proper subset of those…
One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$…
Extracting higher-order structures from multivariate data has become an area of intensive study in complex systems science, as these multipartite interactions can reveal insights into fundamental features of complex systems like emergent…
We consider an extension of $\epsilon$-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the…
I review the relation of the Bell inequalities - characteristic of (classical) probabilities defined on Boolean logics - with noncontextual and local hidden variables theories of quantum mechanics and with quantum information.
Combining the Information Bottleneck model with deep learning by replacing mutual information terms with deep neural nets has proved successful in areas ranging from generative modelling to interpreting deep neural networks. In this paper,…
We establish a reversal of Lyapunov's inequality for monotone log-concave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne-Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also…
We give a congruence relating a one variable specialization of the two variable Kauffman polynomial of any periodic link to that of its mirror image. Consequently, we obtain a new and simple criterion for periodicity of links.
In this paper, a lower bound of quantum conditional mutual information is obtained by employing the Peierls-Bogoliubov inequality and Golden Thompson inequality. Comparison with the bounds obtained by other researchers indicates that our…
We provide necessary and sufficient conditions for hypercontractivity of the minima of nonnegative, i.i.d. random variables and of both the maxima of minima and the minima of maxima for such r.v.'s. It turns out that the idea of…
We present a new notion $R_\ell$ of higher-order common information, which quantifies the information that $\ell\geq 2$ arbitrarily distributed random variables have in common. We provide analytical lower bounds on $R_3$ and $R_4$ for…
It has been proposed that cobordism and K-theory groups, which can be mathematically related in certain cases, are physically associated to generalised higher-form symmetries. As a consequence, they should be broken or gauged in any…
In some scenarios there are ways of conveying information with many fewer, even exponentially fewer, qubits than possible classically. Moreover, some of these methods have a very simple structure--they involve only few message exchanges…