CV%20Cryptography%20Using%20a%20Bidirectional%20Quantum%20Channel

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CV Cryptography Using a Bidirectional Quantum
Channel
University of Camerino, Italy

• Stefano Mancini

in collaboration with S. Pirandola, S. Lloyd S.
Braunstein (quant-ph/0611167)
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Outline

• A general framework for QKD protocols with CV
• The security analysis
• From PM protocols to PTM protocols
• The use of a bidirectional quantum channel
• The security analysis and the superadditivity of
  security thresholds
• Conclusions

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A general framework for CV QKD

• modulated with variance V-1 (with Vgtgt1)
  givesBobs measurements give

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• Xs are correlated random variables characterized
  by I(XAXB). To access this information, either
  Bob estimates Alices encoding (direct
  reconciliation, DR), or Alice estimates Bobs
  outcomes (reverse reconciliation, RR).
• To get shared secret information the honest
  parties have to estimate the noise in the
  channel (by broadcasting and comparing part of
  their data) so to bound the information I(XAE)
  or I(XBE) which has been potentially stolen by
  Eve

A secret key can be established iff
(Csiszar Korner, 1978)
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How to bound Eves information?

• Collective Gaussian attacks are the most powerful
  for the Gaussian state protocols M. Navascues et
  al., PRL 2006 R. Garcia-Patron N. Cerf, PRL
  2006
• Quadratures encode independent variables
  individual Gaussian interactions do not need to
  mix quadratures to be optimal
  individual Gaussian interaction can be modeled by
  entangling cloner F. Grosshans et al., Nature
  2003

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Security thresholds (R 0)
Results in accordance with F. Grosshans, PRL 2005
and M. Navascues A. Acin, PRL 2005.
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Prepare Measure schemes vs Entanglement based
schemes
virtual entanglement
Resources (energy or entanglement) are in the
hands of Alice What is about distributing them
among Alice and Bob? Remind dense coding
protocol!
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A shift paradigm from PM to PTM, use a two-way
quantum channel
b
ba
Two-way quantum channel for QubitKD was put
forward by K. Bostrom T. Felbinger, PRL 2002
and M. Lucamarini S. Mancini, PRL 2005.
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What are the advantages ?
Eve is forced to a double perturbation of the
quantum channel (double exploitment of
uncertainty principle)
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Security thresholds (collective attacks)
Quantities refer to a single use of the quantum
channel
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Summary of the results
Superadditivity behaviour of the security
theresholds (the exception being Hom2 DR for TgtTc
0.86 in DR) When the channel is too noisy for
one-way QKD, it can still be used to provide
secure QKD!
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What is about a quantum Bob?
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Are there other dangerous attacks ?

• Coherent attacks exploiting quantum interference
  between forward and backward path of the quantum
  channel
• Quantum impersonation where Eve short-circuits
  the two paths of the quantum channel

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How to prevent them ?
Alice and Bob have to check the coherence of the
attacks, i.e. the memory of the quantum channel
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Towards unconditional scheme exploiting
superadditivity of multiway quantum channel
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Conclusions

• Virtual entanglement can be profitably used as a
  cryptographic primitive to assist QKD, when
  two-way quantum communication is used
• Improvement of QKD security performances
  (superadditivity of security thresholds)
• A class of attacks has been related to quantum
  memory channels predicting a link between
  correlated noise effects and privacy
• The given formulation paves the way for the study
  of secure multi-way quantum communication
• Apply two-(or multi)way quantum communication to
  other cryptographic tasks, secret sharing, data
  hiding etc.