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

Measurements of Entanglement and a Quantum de Finetti Theorem

2004 ◽  
Vol 43 (7/8) ◽  
pp. 1841-1847 ◽  
Author(s):  
R. L. Hudson
Keyword(s):  
De Finetti Theorem ◽  
De Finetti ◽  
Quantum De Finetti Theorem

scholarly journals Remarks on the Quantum de Finetti Theorem for Bosonic Systems

2014 ◽  
Author(s):  
M. Lewin ◽  
P. T. Nam ◽  
N. Rougerie
Keyword(s):  
De Finetti Theorem ◽  
De Finetti ◽  
Quantum De Finetti Theorem

scholarly journals Quantum de Finetti theorem in phase-space representation

2009 ◽  
Vol 80 (1) ◽  
Author(s):  
Anthony Leverrier ◽  
Nicolas J. Cerf
Keyword(s):  
Phase Space ◽  
Space Representation ◽  
De Finetti Theorem ◽  
De Finetti ◽  
Quantum De Finetti Theorem ◽  
Phase Space Representation

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 SU(p,q) coherent states and a Gaussian de Finetti theorem

2018 ◽  
Vol 59 (4) ◽  
pp. 042202 ◽  
Author(s):  
Anthony Leverrier
Keyword(s):  
Coherent States ◽  
De Finetti Theorem ◽  
De Finetti

scholarly journals Security of continuous-variable quantum key distribution: towards a de Finetti theorem for rotation symmetry in phase space

2009 ◽  
Vol 11 (11) ◽  
pp. 115009 ◽  
Author(s):  
A Leverrier ◽  
E Karpov ◽  
P Grangier ◽  
N J Cerf
Keyword(s):  
Phase Space ◽  
Quantum Key Distribution ◽  
Key Distribution ◽  
Continuous Variable ◽  
Rotation Symmetry ◽  
De Finetti Theorem ◽  
De Finetti

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 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
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