3 research outputs found
Entropy in general physical theories
Information plays an important role in our understanding of the physical
world. We hence propose an entropic measure of information for any physical
theory that admits systems, states and measurements. In the quantum and
classical world, our measure reduces to the von Neumann and Shannon entropy
respectively. It can even be used in a quantum or classical setting where we
are only allowed to perform a limited set of operations. In a world that admits
superstrong correlations in the form of non-local boxes, our measure can be
used to analyze protocols such as superstrong random access encodings and the
violation of `information causality'. However, we also show that in such a
world no entropic measure can exhibit all properties we commonly accept in a
quantum setting. For example, there exists no`reasonable' measure of
conditional entropy that is subadditive. Finally, we prove a coding theorem for
some theories that is analogous to the quantum and classical setting, providing
us with an appealing operational interpretation.Comment: 20 pages, revtex, 7 figures, v2: Coding theorem revised, published
versio
Quantum Tasks in Minkowski Space
The fundamental properties of quantum information and its applications to
computing and cryptography have been greatly illuminated by considering
information-theoretic tasks that are provably possible or impossible within
non-relativistic quantum mechanics. I describe here a general framework for
defining tasks within (special) relativistic quantum theory and illustrate it
with examples from relativistic quantum cryptography and relativistic
distributed quantum computation. The framework gives a unified description of
all tasks previously considered and also defines a large class of new questions
about the properties of quantum information in relation to Minkowski causality.
It offers a way of exploring interesting new fundamental tasks and
applications, and also highlights the scope for a more systematic understanding
of the fundamental information-theoretic properties of relativistic quantum
theory
The Hilbertian Tensor Norm and Entangled Two-Prover Games
We study tensor norms over Banach spaces and their relations to quantum
information theory, in particular their connection with two-prover games. We
consider a version of the Hilbertian tensor norm and its dual
that allow us to consider games with arbitrary output alphabet
sizes. We establish direct-product theorems and prove a generalized
Grothendieck inequality for these tensor norms. Furthermore, we investigate the
connection between the Hilbertian tensor norm and the set of quantum
probability distributions, and show two applications to quantum information
theory: firstly, we give an alternative proof of the perfect parallel
repetition theorem for entangled XOR games; and secondly, we prove a new upper
bound on the ratio between the entangled and the classical value of two-prover
games.Comment: 33 pages, some of the results have been obtained independently in
arXiv:1007.3043v2, v2: an error in Theorem 4 has been corrected; Section 6
rewritten, v3: completely rewritten in order to improve readability; title
changed; references added; published versio