Quantum Cryptography December, 3 rd 2007 Philippe LABOUCHERE Annika BEHRENS
1.Introduction 2.Photon sources 3.Quantum Secret Sharing
1.Introduction 2.Photon sources 3.Quantum Secret Sharing
How to measure information (1) Claude E. Shannon 1948 Information entropy Mutual information [bits]
How to measure information (2) Relation between H and I Mutual information between 2 parties
Venn diagrams
The BB84 protocol
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
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 Bob reports basis of received bits RDRDDR Alice says which were correct noOK noOK Presumably shared information Bob reveals some key bits at random Alice confirms them..OK.. Remaining shared bits Quantum transmission Public discussion
Mutual information vs quantum bit error rate
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
1.Introduction 2.Photon sources 3.Quantum Secret Sharing
Sources of photons Thermal light Coherent light Squeezed light Average photon number of photons in a mode Number of photons
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
Entangled photon pairs Spontaneous Parametric Down Conversion Idler photon acts as trigger for signal photon Very inefficient
Single-photon sources Intercept/resend attack => error rate < dark count rate ! Condition for security: Drawback : dark counts & afterpulses Transmission efficiency Detection yield
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)
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 / 1300 nm: 0.35dB / 1550 nm: 0.25 dB /km
1.Introduction 2.Photon sources 3.Quantum Secret Sharing
Quantum Secret Sharing (1)
QSS (2) N-qubit GHZ source Define
Goodbye GHZ, welcome single qubit
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
Questions ?