scholarly journals Finite de Finetti theorem for conditional probability distributions describing physical theories

2009 ◽  
Vol 50 (4) ◽  
pp. 042104 ◽  
Author(s):  
Matthias Christandl ◽  
Ben Toner
Keyword(s):  
Conditional Probability ◽  
Probability Distributions ◽  
De Finetti Theorem ◽  
De Finetti

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.

scholarly journals NONCONGLOMERABILITY FOR COUNTABLY ADDITIVE MEASURES THAT ARE NOT κ-ADDITIVE

2016 ◽  
Vol 10 (2) ◽  
pp. 284-300 ◽  
Author(s):  
MARK J. SCHERVISH ◽  
TEDDY SEIDENFELD ◽  
JOSEPH B. KADANE
Keyword(s):  
Conditional Probability ◽  
Inaccessible Cardinal ◽  
Conditional Probabilities ◽  
Uncountable Cardinal ◽  
Additive Probability ◽  
De Finetti ◽  
Additive Measures

AbstractLet κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes a result of Schervish, Seidenfeld, & Kadane (1984), which established that each finite but not countably additive probability has conditional probabilities that fail to be conglomerable in some countable partition.

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (02) ◽  
pp. 426-445
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of r t+k and r t+1+⋯+r t+k when (r t ) t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

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