22 research outputs found
On optimal entanglement assisted one-shot classical communication
The one-shot success probability of a noisy classical channel for
transmitting one classical bit is the optimal probability with which the bit
can be sent via a single use of the channel. Prevedel et al. (PRL 106, 110505
(2011)) recently showed that for a specific channel, this quantity can be
increased if the parties using the channel share an entangled quantum state. We
completely characterize the optimal entanglement-assisted protocols in terms of
the radius of a set of operators associated with the channel. This
characterization can be used to construct optimal entanglement-assisted
protocols from the given classical channel and to prove the limit of such
protocols. As an example, we show that the Prevedel et al. protocol is optimal
for two-qubit entanglement. We also prove some simple upper bounds on the
improvement that can be obtained from quantum and no-signaling correlations.Comment: 5 pages, plus 7 pages of supplementary material. v2 is significantly
expanded and contains a new result (Theorem 2
Robust Multidimensional Mean-Payoff Games are Undecidable
Mean-payoff games play a central role in quantitative synthesis and
verification. In a single-dimensional game a weight is assigned to every
transition and the objective of the protagonist is to assure a non-negative
limit-average weight. In the multidimensional setting, a weight vector is
assigned to every transition and the objective of the protagonist is to satisfy
a boolean condition over the limit-average weight of each dimension, e.g.,
\LimAvg(x_1) \leq 0 \vee \LimAvg(x_2)\geq 0 \wedge \LimAvg(x_3) \geq 0. We
recently proved that when one of the players is restricted to finite-memory
strategies then the decidability of determining the winner is inter-reducible
with Hilbert's Tenth problem over rationals (a fundamental long-standing open
problem). In this work we allow arbitrary (infinite-memory) strategies for both
players and we show that the problem is undecidable
Games on graphs with a public signal monitoring
We study pure Nash equilibria in games on graphs with an imperfect monitoring
based on a public signal. In such games, deviations and players responsible for
those deviations can be hard to detect and track. We propose a generic
epistemic game abstraction, which conveniently allows to represent the
knowledge of the players about these deviations, and give a characterization of
Nash equilibria in terms of winning strategies in the abstraction. We then use
the abstraction to develop algorithms for some payoff functions.Comment: 28 page
Kleene Algebras and Semimodules for Energy Problems
With the purpose of unifying a number of approaches to energy problems found
in the literature, we introduce generalized energy automata. These are finite
automata whose edges are labeled with energy functions that define how energy
levels evolve during transitions. Uncovering a close connection between energy
problems and reachability and B\"uchi acceptance for semiring-weighted
automata, we show that these generalized energy problems are decidable. We also
provide complexity results for important special cases
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
Bell Correlations and the Common Future
Reichenbach's principle states that in a causal structure, correlations of
classical information can stem from a common cause in the common past or a
direct influence from one of the events in correlation to the other. The
difficulty of explaining Bell correlations through a mechanism in that spirit
can be read as questioning either the principle or even its basis: causality.
In the former case, the principle can be replaced by its quantum version,
accepting as a common cause an entangled state, leaving the phenomenon as
mysterious as ever on the classical level (on which, after all, it occurs). If,
more radically, the causal structure is questioned in principle, closed
space-time curves may become possible that, as is argued in the present note,
can give rise to non-local correlations if to-be-correlated pieces of classical
information meet in the common future --- which they need to if the correlation
is to be detected in the first place. The result is a view resembling Brassard
and Raymond-Robichaud's parallel-lives variant of Hermann's and Everett's
relative-state formalism, avoiding "multiple realities."Comment: 8 pages, 5 figure
Church Synthesis Problem for Noisy Input
Abstract. We study two variants of infinite games with imperfect in-formation. In the first variant, in each round player-1 may decide to hide his move from player-2. This captures situations where the input signal is subject to fluctuations (noises), and every error in the input signal can be detected by the controller. In the second variant, all of player-1 moves are visible to player-2; however, after the game ends, player-1 may change some of his moves. This captures situations where the input signal is subject to fluctuations; however, the controller cannot detect errors in the input signal. We consider several cases, according to the amount of errors allowed in the input signal: a fixed number of errors, finitely many errors and the case where the rate of errors is bounded by a threshold. For each of these cases we consider games with regular and mean-payoff winning conditions. We investigate the decidability of these games. There is a natural reduction for some of these games to (perfect infor-mation) multidimensional mean-payoff games recently considered in [6]. However, the decidability of the winner of multidimensional mean-payoff games was stated as an open question. We prove its decidability and provide tight complexity bounds.
Librarians learning from librarians: Networking and learning intersect at the Huddersfield Librarian TeachMeet
An overview of the librarian TeachMeet held at the University of Huddersfield, February 201