Metrical characterization of conformal capacity zero

Quantum states characterization for the zero-error capacity

The zero-error capacity of quantum channels was defined as the least upper bound of rates at which classical information is transmitted through a quantum channel with probability of error equal to zero. This paper investigates some properties of input states used to attain the zero-error capacity of quantum channels. Initially, we reformulate the problem of finding the zero-error capacity in th...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

A note on zero-one laws in metrical Diophantine approximation

q ψ(q) diverges but A(ψ) is of zero measure. In other words, without the monotonicity assumption, Khintchine’s theorem is false and the famous Duffin-Schaeffer conjecture provides the appropriate statement. The key difference is that in (1), we impose coprimality on the integers p and q. Let A(ψ) denote the resulting subset of A(ψ). The Duffin-Schaeffer conjecture states that the measure of A(ψ...

Quasi-Superactivation of Classical Capacity of Zero-Capacity Quantum Channels

One of the most surprising recent results in quantum Shannon theory is the superactivation of the quantum capacity of a quantum channel. This phenomenon has its roots in the extreme violation of additivity of the channel capacity and enables to reliably transmit quantum information over zerocapacity quantum channels. In this work we demonstrate a similar effect for the classical capacity of a q...

Information Geometric Superactivation of Asymptotic Quantum Capacity and Classical Zero-Error Capacity of Zero-Capacity Quantum Channels

The superactivation of zero-capacity quantum channels makes it possible to use two zerocapacity quantum channels with a positive joint capacity at the output. Currently, we have no theoretical background for describing all possible combinations of superactive zerocapacity channels; hence, there may be many other possible combinations. In this PhD Thesis I provide an algorithmic solution to the ...