scholarly journals Extended de Finetti theorems for boolean independence and monotone independence

2017 ◽  
Vol 370 (3) ◽  
pp. 1959-2003 ◽  
Author(s):  
Weihua Liu
Keyword(s):  
De Finetti ◽  
Boolean Independence

scholarly journals Computable de Finetti measures

2012 ◽  
Vol 163 (5) ◽  
pp. 530-546 ◽  
Author(s):  
Cameron E. Freer ◽  
Daniel M. Roy
Keyword(s):  
De Finetti

scholarly journals Errata

1991 ◽  
Vol 37 ◽  
pp. 491-491
Keyword(s):  
Royal Society ◽  
Royal Statistical Society ◽  
De Finetti

Biographical Memoirs of Fellows of the Royal Society Volume 36 (1990) Sir Harold Jeffreys Page 301, line 2: for 2 April read 22 April Page 303, line 2: for 2 April read 22 April Page 315, line 19: for suggestion J.D. Bernal proposed read suggestion by J.D. Bernal, proposed Page 326, line 6: for Jeffreys, at much the same time as Bruno de Finetti in Italy, read Bruno de Finetti, in Italy, at much the same time as Jeffrey, Page 330, line 24: for Royal Meteorological Society read Royal Statistical Society

scholarly journals A most compendious and facile quantum de Finetti theorem

2009 ◽  
Vol 50 (1) ◽  
pp. 012105 ◽  
Author(s):  
Robert König ◽  
Graeme Mitchison
Keyword(s):  
De Finetti Theorem ◽  
De Finetti ◽  
Quantum De Finetti Theorem

scholarly journals Apply current exponential de Finetti theorem to realistic quantum key distribution

2014 ◽  
Vol 33 ◽  
pp. 1460370 ◽  
Author(s):  
Yi-Bo Zhao ◽  
Zhen-Qiang Yin
Keyword(s):  
Quantum Key Distribution ◽  
Key Distribution ◽  
Small Error ◽  
Heterodyne Detection ◽  
Finite Dimensional Subspace ◽  
Dimensional System ◽  
Finite Dimensional ◽  
Security Proof ◽  
De Finetti Theorem ◽  
De Finetti

In the realistic quantum key distribution (QKD), Alice and Bob respectively get a quantum state from an unknown channel, whose dimension may be unknown. However, while discussing the security, sometime we need to know exact dimension, since current exponential de Finetti theorem, crucial to the information-theoretical security proof, is deeply related with the dimension and can only be applied to finite dimensional case. Here we address this problem in detail. We show that if POVM elements corresponding to Alice and Bob's measured results can be well described in a finite dimensional subspace with sufficiently small error, then dimensions of Alice and Bob's states can be almost regarded as finite. Since the security is well defined by the smooth entropy, which is continuous with the density matrix, the small error of state actually means small change of security. Then the security of unknown-dimensional system can be solved. Finally we prove that for heterodyne detection continuous variable QKD and differential phase shift QKD, the collective attack is optimal under the infinite key size case.

Symmetry Arguments in Probability

2017 ◽  
Author(s):  
Sandy Zabell
Keyword(s):  
Probability Theory ◽  
Probability Function ◽  
Ancient Greece ◽  
17Th Century ◽  
Species Problem ◽  
History Of ◽  
De Finetti ◽  
Jeffrey Conditioning ◽  
Partial Exchangeability

The history of the use of symmetry arguments in probability theory is traced. After a brief consideration of why these did not occur in ancient Greece, the use of symmetry in probability, starting in the 17th century, is considered. Some of the contributions of Bernoulli, Bayes, Laplace, W. E. Johnson, and Bruno de Finetti are described. One important thread here is the progressive move from using symmetry to identify a single, unique probability function to using it instead to narrow the possibilities to a family of candidate functions via the qualitative concept of exchangeability. A number of modern developments are then discussed: partial exchangeability, the sampling of species problem, and Jeffrey conditioning. Finally, the use or misuse of seemingly innocent symmetry assumptions is illustrated, using a number of apparent paradoxes that have been widely discussed.

DE FINETTI ON RISK AVERSION

2009 ◽  
Vol 25 (2) ◽  
pp. 153-159
Author(s):  
Joseph B. Kadane ◽  
Gaia Bellone
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Risk Premia ◽  
Absolute Risk Aversion ◽  
Kenneth Arrow ◽  
De Finetti ◽  
Constant Absolute Risk Aversion ◽  
Special Case

According to Mark Rubinstein (2006) ‘In 1952, anticipating Kenneth Arrow and John Pratt by over a decade, he [de Finetti] formulated the notion of absolute risk aversion, used it in connection with risk premia for small bets, and discussed the special case of constant absolute risk aversion.’ The purpose of this note is to ascertain the extent to which this is true, and at the same time, to correct certain minor errors that appear in de Finetti's work.

A note on exchangeable events

1979 ◽  
Vol 16 (03) ◽  
pp. 662-664
Author(s):  
Yu-Sheng Hsu
Keyword(s):  
Infinite Sequence ◽  
Finite Sequence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
De Finetti ◽  
Necessary And Sufficient

Kendall [2] gave a thorough discussion of De Finetti constants for a sequence (finite or infinite) of exchangeable events. Galambos [1] and Ridler-Rowe [3] also found some interesting results in this area. In this paper, we intend to give a necessary and sufficient condition for a finite sequence of exchangeable events to be extendable to an infinite sequence of exchangeable events.

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