10,324 research outputs found
Distinguishability, Ensemble Steering, and the No-Signaling Principle
We consider a fundamental operational task, distinguishing systems in
different states, in the framework of generalized probabilistic theories and
provide a general formalism of minimum-error discrimination of states in convex
optimization. With the formalism established, we show that the
distinguishability is generally a global property assigned to the ensemble of
given states rather than other details of a given state space or pairwise
relations of given states. Then, we consider bipartite systems where ensemble
steering is possible, and show that show that with two operational tasks,
ensemble steering and the no-signaling condition, the distinguishability is
tightly determined. The result is independent to the structure of the state
space. This concludes that the distinguishability is generally determined by
the compatibility between two tasks, ensemble steering on states and the
non-signaling principle on probability distributions of outcomes.Comment: In Proceedings QPL 2013, arXiv:1412.791
Pattern Recognition In Non-Kolmogorovian Structures
We present a generalization of the problem of pattern recognition to
arbitrary probabilistic models. This version deals with the problem of
recognizing an individual pattern among a family of different species or
classes of objects which obey probabilistic laws which do not comply with
Kolmogorov's axioms. We show that such a scenario accommodates many important
examples, and in particular, we provide a rigorous definition of the classical
and the quantum pattern recognition problems, respectively. Our framework
allows for the introduction of non-trivial correlations (as entanglement or
discord) between the different species involved, opening the door to a new way
of harnessing these physical resources for solving pattern recognition
problems. Finally, we present some examples and discuss the computational
complexity of the quantum pattern recognition problem, showing that the most
important quantum computation algorithms can be described as non-Kolmogorovian
pattern recognition problems
Theoretical framework for quantum networks
We present a framework to treat quantum networks and all possible
transformations thereof, including as special cases all possible manipulations
of quantum states, measurements, and channels, such as, e.g., cloning,
discrimination, estimation, and tomography. Our framework is based on the
concepts of quantum comb-which describes all transformations achievable by a
given quantum network-and link product-the operation of connecting two quantum
networks. Quantum networks are treated both from a constructive point of
view-based on connections of elementary circuits-and from an axiomatic
one-based on a hierarchy of admissible quantum maps. In the axiomatic context a
fundamental property is shown, which we call universality of quantum memory
channels: any admissible transformation of quantum networks can be realized by
a suitable sequence of memory channels. The open problem whether this property
fails for some nonquantum theory, e.g., for no-signaling boxes, is posed.Comment: 23 pages, revtex
Quantum information as a non-Kolmogorovian generalization of Shannon's theory
In this article we discuss the formal structure of a generalized information
theory based on the extension of the probability calculus of Kolmogorov to a
(possibly) non-commutative setting. By studying this framework, we argue that
quantum information can be considered as a particular case of a huge family of
non-commutative extensions of its classical counterpart. In any conceivable
information theory, the possibility of dealing with different kinds of
information measures plays a key role. Here, we generalize a notion of state
spectrum, allowing us to introduce a majorization relation and a new family of
generalized entropic measures
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