The communication complexity of non-signaling distributions

We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared quantum states, and XOR games. In this model, Alice gets an input x, Bob gets an input y, and their goal is to each produce an output a,b distributed according to some pre-specified joint distribution p(a,b|x,y). We introduce a new technique based on affine combinations of lower-complexity distributions. Specifically, we introduce two complexity measures, one which gives lower bounds on classical communication, and one for quantum communication. These measures can be expressed as convex optimization problems. We show that the dual formulations have a striking interpretation, since they coincide with maximum violations of Bell and Tsirelson inequalities. The dual expressions are closely related to the winning probability of XOR games. These lower bounds subsume many known communication complexity lower bound methods, most notably the recent lower bounds of Linial and Shraibman for the special case of Boolean functions. We show that the gap between the quantum and classical lower bounds is at most linear in the size of the support of the distribution, and does not depend on the size of the inputs. This translates into a bound on the gap between maximal Bell and Tsirelson inequality violations, which was previously known only for the case of distributions with Boolean outcomes and uniform marginals. Finally, we give an exponential upper bound on quantum and classical communication complexity in the simultaneous messages model, for any non-signaling distribution. One consequence is a simple proof that any quantum distribution can be approximated with a constant number of bits of communication.Comment: 23 pages. V2: major modifications, extensions and additions compared to V1. V3 (21 pages): proofs have been updated and simplified, particularly Theorem 10 and Theorem 22. V4 (23 pages): Section 3.1 has been rewritten (in particular Lemma 10 and its proof), and various minor modifications have been made. V5 (24 pages): various modifications in the presentatio

Investigation of nonlocal information as condition for violations of Bell inequality and information causality

On the basis of local realism theory, nonlocal information is necessary for violation of Bell's inequality. From a theoretical point of view, nonlocal information is essentially the mutual information on distant outcome and measurement setting. In this work we prove that if the measurement is free and unbiased, the mutual information about the distant outcome and setting is both necessary for the violation of Bell's inequality in the case with unbiased marginal probabilities. In the case with biased marginal probabilities, we point out that the mutual information about distant outcome cease to be necessary for violation of Bell's inequality, while the mutual information about distant measurement settings is still required. We also prove that the mutual information about distant measurement settings must be contained in the transmitted messages due to the freedom of measurement choices. Finally we point out that the mutual information about both distant outcome and measurement settings are necessary for a violation of information causality.Comment: 5 pages, 3 figures, big change, version as close as possible to the published version in Eur. Phys. J.

Unbounded violation of tripartite Bell inequalities

We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. The results are based on tools from the theories of operator spaces and tensor norms which we exploit to prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more accessible for a non-specialized reade

Richard Stallmanin tekijänoikeuskritiikin yhteiskuntafilosofinen analyysi

Käsittelen työssäni Richard Stallmanin vapaiden ohjelmistojen filosofiaa ja siihen sisältyvää tekijänoikeuskritiikkiä. Analyysin taustana ovat tekijänoikeuden perustasta esitetyt teoriat ja liberalistinen yhteiskuntafilosofia sekä kommunitaristien siihen kohdistama kritiikki. Tekijänoikeuden oikeutusta koskevat kolme keskeistä teoriaa ovat työteoria, persoonallisuusteoria ja utilitaristinen teoria. John Locken luonnonoikeusfilosofiaan nojaavassa työteoriassa katsotaan, että jostakin resurssista tulee tekijänsä omaisuutta, kun siihen sekoittuu tekijän työpanos. Persoonallisuusteoria perustuu Immanuel Kantin ja G. W. F. Hegelin näkemykseen omaisuudesta osana henkilön persoonallisuutta, jonka vapautta on suojattava. Utilitaristinen teoria katsoo tekijänoikeuden olevan perusteltua siihen liittyvän kannustimen vuoksi: enemmän teoksia syntyy, mikäli niiden tekijöille annetaan teokseen erityinen yksinoikeus. Stallman kyseenalaistaa tietokoneohjelmiin saatavan tekijänoikeuden oikeutuksen viittaamalla käyttäjien oikeuksiin. Stallmanin mukaan tietokoneohjelman käyttäjälle kuuluvat neljä vapautta: 1) vapaus käyttää ohjelmaa rajoituksetta, 2) vapaus muuttaa ohjelmaa tarpeiden mukaan, 3) vapaus levittää ohjelmaa muille, 4) vapaus parannella ohjelmaa ja jakaa se muiden kanssa. Näitä vapauksia Stallman perustelee viittaamalla yhteisöön. Hän ottaa moraalifilosofiseksi lähtökohdaksi vasta­vuoroisuuden periaatteen, jonka mukaan yhteisön jäsenten tulee auttaa toinen toisiaan esimerkiksi jakamalla tietokoneohjelmia. Tekijänoikeuden asettamat rajoitukset ovat esteitä tämäntyyppiselle solidaarisuudelle ja yhteisössä sekä yhteiskunnassa vallitsevalle avunannon ilmapiirille. Yhteiskuntafilosofiselta perusluonteeltaan Stallmanin filosofia edustaa liberalismia. Väite käyttäjien yksilöllisistä oikeuksista perustuu liberalistiseen ihmiskuvaan. Se on myös universalistinen: Stallman pitää käyttäjien oikeuksia joko luonnollisina oikeuksina tai ihmisoikeuksina. Toisaalta teoriassa on keskeisellä sijalla ajatus yhteisön eheydestä ja yhteisöllisen hyvän edistämisestä, mikä tuo siihen kommunitaristisia piirteitä. Toteuttamalla ohjelmistojen vapauden elämäntapaa yhteisö toteuttaa tietynlaista hyvän elämän politiikkaa. Teoriaa ei kuitenkaan voi kokonaisuudessaan pitää kommunitaristisena siihen sisältyvän vahvan universalismin vuoksi. Vapautta korostavan luon­teensa ja negatiivisen omaisuuskäsityksensä vuoksi osuvampi luonnehdinta Stallmanin filosofialle on digitaalinen anarkismi. Asiasanat: tekijänoikeus, liberalismi, kommunitarismi, Richard Stallman, vapaat ohjelmistot, avoin lähdekoodi, tietokoneohjelmisto

Defınıng Mılıtary Applıcatıons Of Wearable Informatıon Systems For A Sıngle Soldıer In Taf, In 2023.

Teknolojin günümüz dünyasında insanların yaşam biçimlerini ciddi bir şekilde etkilemektedir. Önemli teknolojik cihazlardan biri olan akıllı telefonların kabiliyetleri teknolojinin geldiği son noktayı göstermektedir. Türk Silahlı Kuvvetleri (TSK)?nde tek eNowadays it is a reality that; technology extremely affects the lifestyles of people in the world. The capabilities of smartphones illustrate the ultimate point where the technology comes. This study focuses on how Turkish soldiers use and will use this

Amortized Communication Complexity of Distributions

Consider the following general communication problem: Alice and Bob have to simulate a probabilistic function p, that with every (x, y) â X à Y associates a probability distribution on A à B. The two parties, upon receiving inputs x and y, need to output a â A, b â B in such a manner that the (a, b) pair is distributed according to p(x, y). They share randomness, and have access to a channel that allows two-way communication. Our main focus is an instance of the above problem coming from the well known EPR experiment in quantum physics. In this paper, we are concerned with the amount of communication required to simulate the EPR experiment when it is repeated in parallel a large number of times, giving rise to a notion of amortized communication complexity. In the 3-dimensional case, Toner and Bacon showed that this problem could be solved using on average 0.85 bits of communication per repetition. We show that their approach cannot go below 0.414 bits, and we give a fundamentally different technique, relying on the reverse Shannon theorem, which allows us to reduce the amortized communication to 0.28 bits for dimension 3, and 0.410 bits for arbitrary dimension. We also give a lower bound of 0.13 bits for this problem (valid for one-way protocols), and conjecture that this could be improved to match the upper bounds. In our investigation we ï¬nd interesting connections to a number of different problems in communication complexity. The results contained herein are entirely classical and no knowledge of the quantum phenomenon is assumed.info:eu-repo/semantics/publishe