Achievable Bitrates for Quantum Key Distribution

1. Achievable Bitrates for Quantum Key Distribution Alexander Hentschel April 24, 2009 University of Calgary

2. Classical Cryptography • Classical Cryptography Schemes: Quantum Computer Classical Algorithms Are there efficient algorithms to crack cipher: unknown! ? • Do we have a Quantum Computer? Not yet!

3. Classical Cryptography One-Time-Pad Cryptography • Only classical cryptographic scheme: security mathematically proven Sender: Alice Receiver: Bob private key private key insecure medium (Internet) encrypted encrypted message message • Message: string of N bits + = • One-Time-Pad: random sequence of N bits • How do we securely share the key ?

4. Quantum Cryptography Solution:Quantum Cryptography • eavesdropper can have unlimited computational power • security guaranteed by physical laws BB84 Protocol: by Charles Bennett and Gilles Brassard in 1984 Eve Alice Bob • Generates a One-Time-Pad-Key for Alice & Bob • Guarantees detection of eavesdropping attempt during key sharing • If key shared safely: use key to encrypt message and send over public channel

5. Quantum Cryptography Quantum Mechanics: • Superposition: Qubit (quantum bit) can be an arbitrary mixture of 0 and 1 at the same time • Probability to measure qubit in state : state : • Measurement: destructive State after measurement • outcome : • outcome :

6. The BB84 Protocol Sharing the One-Time-Pad-Key: • Alice wants to share a One-Time-Pad-Key with Bob Alice generates random bit sequence s = 1 0 1 1 0 1 0 1 0 0 0 1 1 0 One-Time-Pad b = 0 1 1 0 1 0 0 1 0 1 1 1 0 0 Encoding basis • Encodes bits of s in polarization of single photon • Rectangular basis R: bi = 0: • Diagonal basis D: bi = 1:

7. The BB84 Protocol Receiving the One-Time-Pad-Key: Bob receives sequence of photons: • does not know encoding basis • chooses randomly measurement basis (decoding basis) For each photon: Bob saves • measurement basis • measurement result

8. The BB84 Protocol Receiving the One-Time-Pad-Key: Measurement in right basis: • measured polarization equals encoding polarization: Measurement in wrong basis: with 50% probability • result: with 50% probability • with probability 50%

9. The BB84 Protocol Receiving the One-Time-Pad-Key: Key • Alice and Bob interchange Alice’s encoding basis Bob’s decoding basis • Keep bits where both choose same basis Key has length n/2 • If Alice sends n bits:

10. The BB84 Protocol Eavesdropping • At time of transmission: encoding basis unknown to Eve X Tactic for Eve ? • guess basis • Copy quantum bit • After disclosure of encoding Basis: measure Quantum Information cannot be copied • Measure in basis Measurement • Send measurement result to Bob eavesdropping no eavesdropping • Alice and Bob use same basis: differentresult with probability 25% • Alice and Bob use same basis: same result Detecting an eavesdropper • Alice & Bob compare ½ of bits with

11. Feasibility of Quantum Key Distribution • Area of active research • First commercial devices available Id Quantique Technical challenges • Generate single photons • no photon • more than one photon • Transfer single photons into glass fiber • Absorption of optical fibre • Reliably detect single photon • detector efficiency • dark counts

12. Feasibility of Quantum Key Distribution mean Percent of matching key bits variance background noise Risk of eavesdropping frequency in kHz • simple setup • no error correction Experiment at Humboldt-University Berlin 2005: • Rate of non-matching key-bits: QBER = Quantum Bit Error Rate

13. Feasibility of Quantum Key Distribution State of the art (Toshiba Research Europe Ltd): • unconditionally secure key distribution • secure key rate:1.02 Mbit/s for fiber distance 20km • use compact non-cryogenic detectors • eavesdropper could hide behind noise use privacy amplification to prevent information leak (raw secure key rate) dark counts dominate nominal capacity usable capacity

14. Thank you for your attention