1. CV Cryptography Using a Bidirectional Quantum Channel
University of
Camerino, Italy
Stefano Mancini
in collaboration with S. Pirandola, S. Lloyd & S. Braunstein (quant-ph/ )

2. Outline A general framework for QKD protocols with CV
The security analysis
From P&M protocols to PT&M protocols
The use of a bidirectional quantum channel
The security analysis and the superadditivity of security thresholds
Conclusions

3. A general framework for CV QKD
modulated with variance V-1 (with V>>1) gives Bob’s measurements give

4. A secret key can be established iff
Xs are correlated random variables characterized by I(XA:XB). To access this information, either Bob estimates Alice’s encoding (direct reconciliation, DR), or Alice estimates Bob’s 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(XA:E) or I(XB:E) which has been potentially stolen by Eve
A secret key can be established iff
(Csiszar & Korner, 1978)

5. How to bound Eve’s 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]

7. Security thresholds (R = 0)
Results in accordance with F. Grosshans, PRL 2005 and M. Navascues & A. Acin, PRL 2005.

8. 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!

9. A shift paradigm: from P&M to PT&M, use a two-way quantum channelb
b+a
Two-way quantum channel for QubitKD was put forward by
K. Bostrom & T. Felbinger, PRL 2002; and M. Lucamarini & S. Mancini, PRL 2005.

10. What are the advantages ?
Eve is forced to a double perturbation of the quantum channel
(double exploitment of uncertainty principle)

11. Security thresholds (collective attacks)
Quantities refer to a single use of the quantum channel

12. Summary of the results
Superadditivity behaviour of the security theresholds
(the exception being Hom2 DR for T>Tc =0.86 in DR)
When the channel is too noisy for one-way QKD,
it can still be used to provide secure QKD!

13. What is about a quantum Bob?

14. 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

15. How to prevent them ?
Alice and Bob have to check the coherence of the attacks,
i.e. the memory of the quantum channel

16. Towards unconditional scheme exploiting superadditivity of multiway quantum channel

17. 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.