24,820 research outputs found
Probabilistic theories with purification
We investigate general probabilistic theories in which every mixed state has
a purification, unique up to reversible channels on the purifying system. We
show that the purification principle is equivalent to the existence of a
reversible realization of every physical process, namely that every physical
process can be regarded as arising from a reversible interaction of the system
with an environment, which is eventually discarded. From the purification
principle we also construct an isomorphism between transformations and
bipartite states that possesses all structural properties of the
Choi-Jamiolkowski isomorphism in quantum mechanics. Such an isomorphism allows
one to prove most of the basic features of quantum mechanics, like e.g.
existence of pure bipartite states giving perfect correlations in independent
experiments, no information without disturbance, no joint discrimination of all
pure states, no cloning, teleportation, no programming, no bit commitment,
complementarity between correctable channels and deletion channels,
characterization of entanglement-breaking channels as measure-and-prepare
channels, and others, without resorting to the mathematical framework of
Hilbert spaces.Comment: Differing from the journal version, this version includes a table of
contents and makes extensive use of boldface type to highlight the contents
of the main theorems. It includes a self-contained introduction to the
framework of general probabilistic theories and a discussion about the role
of causality and local discriminabilit
Conservation of information and the foundations of quantum mechanics
We review a recent approach to the foundations of quantum mechanics inspired
by quantum information theory. The approach is based on a general framework,
which allows one to address a large class of physical theories which share
basic information-theoretic features. We first illustrate two very primitive
features, expressed by the axioms of causality and purity-preservation, which
are satisfied by both classical and quantum theory. We then discuss the axiom
of purification, which expresses a strong version of the Conservation of
Information and captures the core of a vast number of protocols in quantum
information. Purification is a highly non-classical feature and leads directly
to the emergence of entanglement at the purely conceptual level, without any
reference to the superposition principle. Supplemented by a few additional
requirements, satisfied by classical and quantum theory, it provides a complete
axiomatic characterization of quantum theory for finite dimensional systems.Comment: 11 pages, contribution to the Proceedings of the 3rd International
Conference on New Frontiers in Physics, July 28-August 6 2014, Orthodox
Academy of Crete, Kolymbari, Cret
(Quantumness in the context of) Resource Theories
We review the basic idea behind resource theories, where we quantify quantum
resources by specifying a restricted class of operations. This divides the
state space into various sets, including states which are free (because they
can be created under the class of operations), and those which are a resource
(because they cannot be). One can quantify the worth of the resource by the
relative entropy distance to the set of free states, and under certain
conditions, this is a unique measure which quantifies the rate of state to
state transitions. The framework includes entanglement, asymmetry and purity
theory. It also includes thermodynamics, which is a hybrid resource theory
combining purity theory and asymmetry. Another hybrid resource theory which
merges purity theory and entanglement can be used to study quantumness of
correlations and discord, and we present quantumness in this more general
framework of resource theories.Comment: review articl
On the Heisenberg principle, namely on the information-disturbance trade-off in a quantum measurement
Common misconceptions on the Heisenberg principle are reviewed, and the
original spirit of the principle is reestablished in terms of the trade-off
between information retrieved by a measurement and disturbance on the measured
system. After analyzing the possibility of probabilistically reversible
measurements, along with erasure of information and undoing of disturbance,
general information-disturbance trade-offs are presented, where the disturbance
of the measurement is related to the possibility in principle of undoing its
effect.Comment: 13 LeTeX pages, 2 figures, fortschritte.sty. To appear on
Fortschritte der Physik. Presented at Quantum Interferometry IV, Trieste,
March 200
Ruling out higher-order interference from purity principles
As first noted by Rafael Sorkin, there is a limit to quantum interference.
The interference pattern formed in a multi-slit experiment is a function of the
interference patterns formed between pairs of slits, there are no genuinely new
features resulting from considering three slits instead of two. Sorkin has
introduced a hierarchy of mathematically conceivable higher-order interference
behaviours, where classical theory lies at the first level of this hierarchy
and quantum theory theory at the second. Informally, the order in this
hierarchy corresponds to the number of slits on which the interference pattern
has an irreducible dependence. Many authors have wondered why quantum
interference is limited to the second level of this hierarchy. Does the
existence of higher-order interference violate some natural physical principle
that we believe should be fundamental? In the current work we show that such
principles can be found which limit interference behaviour to second-order, or
"quantum-like", interference, but that do not restrict us to the entire quantum
formalism. We work within the operational framework of generalised
probabilistic theories, and prove that any theory satisfying Causality, Purity
Preservation, Pure Sharpness, and Purification---four principles that formalise
the fundamental character of purity in nature---exhibits at most second-order
interference. Hence these theories are, at least conceptually, very "close" to
quantum theory. Along the way we show that systems in such theories correspond
to Euclidean Jordan algebras. Hence, they are self-dual and, moreover,
multi-slit experiments in such theories are described by pure projectors.Comment: 18+8 pages. Comments welcome. v2: Minor correction to Lemma 5.1, main
results are unchange
Dilation of states and processes in operational-probabilistic theories
This paper provides a concise summary of the framework of
operational-probabilistic theories, aimed at emphasizing the interaction
between category-theoretic and probabilistic structures. Within this framework,
we review an operational version of the GNS construction, expressed by the
so-called purification principle, which under mild hypotheses leads to an
operational version of Stinespring's theorem.Comment: In Proceedings QPL 2014, arXiv:1412.810
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