1. Quantum Cryptography December, 3 rd 2007 Philippe LABOUCHERE Annika BEHRENS

2. 1.Introduction 2.Photon sources 3.Quantum Secret Sharing

3. 1.Introduction 2.Photon sources 3.Quantum Secret Sharing

4. How to measure information (1) Claude E. Shannon 1948 Information entropy Mutual information [bits]

5. How to measure information (2) Relation between H and I Mutual information between 2 parties

6. Venn diagrams

7. The BB84 protocol

8. The BB84 protocol: principle 2 conjugate basis Information encoded in photon’s polarization → ’0’ ≡ — & / → ’1’ ≡ | & \ Quantum & classical channels used for key exchange Charles H. Bennett Gilles Brassard

9. From random bits to a sifted key Alice’s random bits 011OO1 Random sending bases DDRRDR Photon Alice sends /\ —— / — Random receiving bases RDRDDR Bits as received by Bob 111001 Bob reports basis of received bits RDRDDR Alice says which were correct noOK noOK Presumably shared information.11.01 Bob reveals some key bits at random..1.0. Alice confirms them..OK.. Remaining shared bits. 1... 1 Quantum transmission Public discussion

10. Mutual information vs quantum bit error rate

11. The no-cloning theorem Dieks, Wootters, Žurek 1982 ”It is forbidden to create identical copies of an arbitrary unknown quantum state.” Quantum operations : unitary & linear transformations on the state of a quantum system

12. 1.Introduction 2.Photon sources 3.Quantum Secret Sharing

13. Sources of photons Thermal light Coherent light Squeezed light Average photon number of photons in a mode Number of photons

14. Faint-laser pulses = μ ~ 0.1 photon / pulse Photon-number splitting attack! Dark counts of detectors vs high pulse rate & weaker pulses ! Detection yield Transmission efficiency Tradeoff

15. Entangled photon pairs Spontaneous Parametric Down Conversion Idler photon acts as trigger for signal photon Very inefficient

16. Single-photon sources Intercept/resend attack => error rate < dark count rate ! Condition for security: Drawback : dark counts & afterpulses Transmission efficiency Detection yield

17. Practical limits of QC Realization of signal Stability under the influence of the environment (transportation) - Birefringence - Polarization dispersion - Scattering Need of efficient sources & detectors (measurements)

18. Bite rate as function of distance after error correction and privacy amplification Pulse rate = 10 MHz μ = 0.1 (faint laser pulses) Losses : @ 800nm : 2dB / km @ 1300 nm: 0.35dB / km @ 1550 nm: 0.25 dB /km

19. 1.Introduction 2.Photon sources 3.Quantum Secret Sharing

20. Quantum Secret Sharing (1)

21. QSS (2) N-qubit GHZ source Define

22. Goodbye GHZ, welcome single qubit

23. Sequentially polarized single photon protocol Original BB84Modified BB84 Diagonal and R ectilinear bases Classes X and Y / and — ≡ ‘0’ | and \ ≡ ‘1’ φ j = {0, π/2} ≡ ’0’ φ j = {π, 3π/2} ≡ ’1’ Correlated results if same bases used Correlated results if

24. Questions ?