1,097,941 research outputs found
Improving zero-error classical communication with entanglement
Given one or more uses of a classical channel, only a certain number of
messages can be transmitted with zero probability of error. The study of this
number and its asymptotic behaviour constitutes the field of classical
zero-error information theory, the quantum generalisation of which has started
to develop recently. We show that, given a single use of certain classical
channels, entangled states of a system shared by the sender and receiver can be
used to increase the number of (classical) messages which can be sent with no
chance of error. In particular, we show how to construct such a channel based
on any proof of the Bell-Kochen-Specker theorem. This is a new example of the
use of quantum effects to improve the performance of a classical task. We
investigate the connection between this phenomenon and that of
``pseudo-telepathy'' games. The use of generalised non-signalling correlations
to assist in this task is also considered. In this case, a particularly elegant
theory results and, remarkably, it is sometimes possible to transmit
information with zero-error using a channel with no unassisted zero-error
capacity.Comment: 6 pages, 2 figures. Version 2 is the same as the journal version plus
figure 1 and the non-signalling box exampl
Linear Codes are Optimal for Index-Coding Instances with Five or Fewer Receivers
We study zero-error unicast index-coding instances, where each receiver must
perfectly decode its requested message set, and the message sets requested by
any two receivers do not overlap. We show that for all these instances with up
to five receivers, linear index codes are optimal. Although this class contains
9847 non-isomorphic instances, by using our recent results and by properly
categorizing the instances based on their graphical representations, we need to
consider only 13 non-trivial instances to solve the entire class. This work
complements the result by Arbabjolfaei et al. (ISIT 2013), who derived the
capacity region of all unicast index-coding problems with up to five receivers
in the diminishing-error setup. They employed random-coding arguments, which
require infinitely-long messages. We consider the zero-error setup; our
approach uses graph theory and combinatorics, and does not require long
messages.Comment: submitted to the 2014 IEEE International Symposium on Information
Theory (ISIT
Quantum decision making by social agents
The influence of additional information on the decision making of agents, who
are interacting members of a society, is analyzed within the mathematical
framework based on the use of quantum probabilities. The introduction of social
interactions, which influence the decisions of individual agents, leads to a
generalization of the quantum decision theory developed earlier by the authors
for separate individuals. The generalized approach is free of the standard
paradoxes of classical decision theory. This approach also explains the
error-attenuation effects observed for the paradoxes occurring when decision
makers, who are members of a society, consult with each other, increasing in
this way the available mutual information. A precise correspondence between
quantum decision theory and classical utility theory is formulated via the
introduction of an intermediate probabilistic version of utility theory of a
novel form, which obeys the requirement that zero-utility prospects should have
zero probability weights.Comment: This paper has been withdrawn by the authors because a much extended
and improved version has been submitted as arXiv:1510.02686 under the new
title "Role of information in decision making of social agents
Zero Error Coordination
In this paper, we consider a zero error coordination problem wherein the
nodes of a network exchange messages to be able to perfectly coordinate their
actions with the individual observations of each other. While previous works on
coordination commonly assume an asymptotically vanishing error, we assume
exact, zero error coordination. Furthermore, unlike previous works that employ
the empirical or strong notions of coordination, we define and use a notion of
set coordination. This notion of coordination bears similarities with the
empirical notion of coordination. We observe that set coordination, in its
special case of two nodes with a one-way communication link is equivalent with
the "Hide and Seek" source coding problem of McEliece and Posner. The Hide and
Seek problem has known intimate connections with graph entropy, rate distortion
theory, Renyi mutual information and even error exponents. Other special cases
of the set coordination problem relate to Witsenhausen's zero error rate and
the distributed computation problem. These connections motivate a better
understanding of set coordination, its connections with empirical coordination,
and its study in more general setups. This paper takes a first step in this
direction by proving new results for two node networks
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