Document worth reading: “Entropy in Quantum Information Theory — Communication and Cryptography”
In this Thesis, numerous outcomes in quantum knowledge precept are collected, most of which use entropy because the precept mathematical machine. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves in one other approach. A protracted-standing open question is, whether or not or not there are quantum analogues of unconstrained non-Shannon form inequalities. Here, a model new constrained non-von-Neumann form inequality is confirmed, a step in the route of a conjectured unconstrained inequality by Linden and Winter. *IID quantum state merging is perhaps optimally achieved using the decoupling technique. The one-shot outcomes by Berta et al. and Anshu at al., nonetheless, wanted to convey in further mathematical tools. We introduce a pure generalized decoupling paradigm, catalytic decoupling, which will reproduce the aforementioned outcomes when used analogously to the equipment of atypical decoupling in the asymptotic case. *Port based totally teleportation, a variant of atypical quantum teleportation protocol, cannot be carried out utterly. We present numerous lower bounds on the obligatory number of output ports N to achieve port based totally teleportation for given error and enter dimension, displaying that N diverges uniformly in the dimension of the teleported quantum system, for vanishing error. As a byproduct, a model new lower sure for the dimensions of this method register for an approximate widespread programmable quantum processor is derived. *In the ultimate half, we give a model new definition for information-theoretic quantum non-malleability, strengthening the sooner definition by Ambainis et al. We current that quantum non-malleability implies secrecy, analogous to quantum authentication. Furthermore, non-malleable encryption schemes may be utilized as a primitive to assemble authenticating encryption schemes. We moreover current that the sturdy notion of authentication not too way back proposed by Garg et al. is perhaps fulfilled using 2-designs. Entropy in Quantum Information Theory — Communication and Cryptography