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Achievable Bitrates for

Quantum Key Distribution

Alexander Hentschel

April 24, 2009

University of Calgary

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!

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 ?

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

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 :

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:

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

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%

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:

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

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

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

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

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