scholarly journals An information-theoretic proof of a finite de Finetti theorem

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Lampros Gavalakis ◽  
Ioannis Kontoyiannis
Keyword(s):  
Information Theoretic ◽  
Theoretic Proof ◽  
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.

Random assignment processes: strong law of large numbers and De Finetti theorem

Test ◽  
2014 ◽  
Vol 24 (1) ◽  
pp. 136-165
Author(s):  
Ricardo Vélez ◽  
Tomás Prieto-Rumeau
Keyword(s):  
Law Of Large Numbers ◽  
Random Assignment ◽  
Strong Law ◽  
Large Numbers ◽  
De Finetti Theorem ◽  
De Finetti

scholarly journals The de Finetti theorem for test spaces

2009 ◽  
Vol 11 (3) ◽  
pp. 033024 ◽  
Author(s):  
Jonathan Barrett ◽  
Matthew Leifer
Keyword(s):  
De Finetti Theorem ◽  
De Finetti
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