The adventures of Alice, Bob & Eve in the Quantumland. Stefano Mancini. University of Camerino, Italy. Outline (part 3). From probabilistic to deterministic quantum cryptography From qubit to qudit up to cv Quantum Secret Sharing Beyond QKD: Quantum bit commitment Conclusion.
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Two way quantum channel
Encoding by quantum operation
(Alice can encode without knowing the state!)
Number of message bits per protocol run = 1-c
Eve wants to eavesdrop one message transfer without being detected; probability
Terms correspond to Eve having survived 0,1,2… controls before she gets h(d) bits of information
After n successful attacks Eve gains nh(d) bits and survive with probability pn
Probability to successfully eavesdrop nh(d) bits
Protocol asymptotically secure!
POVMEavesdropping in KD (individual incoherent attack)
Distinguish between orthogonal subspacesDistinguish between nonorthogonal states
d<0.23 required vs d<0.15 of BB84
d<0.18 required vs d<0.15 of BB84
Theoretical Efficiency E=ub/(tq+tb)
E=1-c; BB84 E=1/6;
Practical Efficiency E’ accounts for losses
E’=EP2; BB84 E’=EP;
(P being the probability to safely transmit
a qubit over Alice-Bob distance)
For P>1/(6(1-c)) the scheme surpasses BB84
Quantum theory can be viewed not as a mechanical theory of waves and particles but as a theory about the possibilities and impossibilities of information transfer
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