In the field of
quantum information theory, Fuchs has worked on measures of fidelity and distinguishability for quantum states, bounds on accessible information, and relations between disturbance and information in quantum measurements. Some of these results appear in his doctoral thesis and in later work on quantum
cryptography and quantum communication. Fuchs and Jeroen van de Graaf introduced two-sided bounds connecting trace distance and fidelity, now called the
Fuchs–van de Graaf inequalities. They are widely used in literature for converting error and fidelity bounds in the analysis of quantum protocols. He was one of the originators of the concept "nonlocality without entanglement". This refers to sets of product quantum states that are perfectly distinguishable globally, but only imperfectly so with local measurements and classical communication (
LOCC). The same paper also implicitly introduces the notion of an "
unextendible product basis," which was later instrumental in establishing that the
Peres–Horodecki criterion for
entanglement is necessary but not sufficient. Together with
Charles H. Bennett and
John A. Smolin, he questioned whether the classical capacity of a noisy quantum channel might be increased by entangled codings, a result eventually established in the positive by
Matthew Hastings. Fuchs also collaborated in proving the
no-broadcasting theorem, a generalization of the
no-cloning theorem. Together with Carlton Caves and Rüdiger Schack, he developed a quantum version of
de Finetti's theorem. In May 2000, when Fuchs was a postdoc at the
Los Alamos National Laboratory, his home and most of his family's possessions were destroyed in the
Cerro Grande Fire. Fuchs had been actively corresponding over email with many prominent figures in the then-nascent field of quantum information. In an example of what he called "backing up my hard drive", he posted an edited collection of this correspondence to the
arXiv preprint server, with a foreword by
N. David Mermin. Later,
Växjö University Press printed a limited edition of this collection, and in 2011,
Cambridge University Press printed it (with a new introduction) under the title
Coming of Age with Quantum Information. == QBism ==