Why do people study QIS
computations effectively performed simultaneously (quantum parallelism)
classically intractable problems may become feasible quantum-mechanically
unbreakable shared codes teleportation
QIS
ComputationComputation
CommunicationCommunication
Modern Modern electronicselectronics
Quantum V.S. Classical (1)
In principle, classical states can be faithfully distinguished from each other.
Quantum V.S. Classical (2)
Quantum states are non-orthogonal in general.
Quantum states cannot be identified faithfully.
0
Quantum V.S. Classical (3)
Quantum states can be superposed states.
qubit = a | 0 > + b | 1 >
The principle of superposition
Quantum V.S. Classical (4)
Quantum states can be non-local.
可能狀
態古典的 | 1 1 >| 1 0 >
| 0 1 >| 0 0 >
Entangled states :)11|00(|
21
)10|01(|2
1
Quantum no-cloning theorem unknown quantum states cannot
be copied due to linearity of QM.S US U
Not possible
Do we need Quantum Communication?
(1) Quantum computer can break some of the best public key cryptosystems.
(2) Quantum key distribution provides provably secure distribution of private information.
(3) Quantum cryptography is technically viable and affordable.
However, QC..
does not provide a complete solution for all cryptographic purposes.
authentication
rapid delivery of keys
robustness
distance and location independence
resistance to traffic analysisQuantum communication network?
Quantum Communcation
Protocols
BB84 protocol
利用光的 2 個偏振方向,代表 “ 0” 與“ 1”
竊聽者
Bennett & Brassard
BB84
Alice 隨機選擇光的極化
Bob 隨機選擇測量方向Bob 公告測量方向Alice 告訴 Bob 哪些測量方向選對了。這些方向當作共同的加解密金匙!
Bit value “1”
BB84--example
Alice
Bob
Bob
Alice
Bob
Key 1 0 0 0
Bit survival rates: 50%Key-breaking prob.
34N
B92 protocol
Alice prepares a random classical bit “a”, and sends Bob the following quantum state depending on the “a” value.
0 if a 0012
if a 1
Bennett, PRL 68,3121(1992)
Bit values “0”
B92 protocol
Bob also prepares a random classical bit a’, and measureshis quantum bit with one of the following bases accordingto the value of a’.
(Z basis) 1 , 0
(X basis)1 0
2
a’=0
a’=1
“0” bits
B92 protocol—example
Alice(a)
0 0 1 0 1 1 1 0
Bob(a’)
1 0 1 1 0 1 0 1
Bit-result
s
1 0 0 0 1 0 1 0
key 01
10
10
bases
Bob anoucesit publicly
for Alice
for Bob
Bit survival rates: 25%
Key-breaking prob.
34N
Quantum nature of signals
Signals are non-orthogonal states.
Eavesdropper cannot clone signals Eavesdropping will inevitably incur
disturbance to the signal.qubits.
cannot be distinguished with 100% confidence
Ekert scheme (EPR protocol)
EkertPRL 67, 661(1991)
Entangled pairs of qubits are prepared as EPR states
01102
Alice
Bob
EPR protocol
Randomly select a subset of EPR pairs
Test violation of Bell’s inequality
The fidelity of the remaining EPR pairs is then inferred from the test.
Alice and Bob obtain correlated classical bit strings------ secret keys
Other protocols Variations of BB84 Two-state protocols Six-state protocol
Respect the symmetry of the qubit state space
Reduce Eve’s info gains
QC experiments…
Photon source
Photon counter
Quantum channel
Optical fiberFree space
Single-mode fibers
Free-space links
Telecommunication optical fiber
~ 1300, 1550 nm
~ 800 nmcommercial photon counterlow absorption
Silicon-base APD
Quantum channels
< 0.3 dB/km
InGaAs/InP APD
Free space links
Transmission in free space
low-loss window
line-of-sight communication
~ 770 nm
~ < 10 km
beam-pointingis difficult for movingtargets
Free space links High transmission window at ~ 770 nm compatible w. commercial silicon APD photon-
counter
Atmosphere is weakly dispersive and nonbirefirngent at the wavelengths. plain polarization coding is possible.
Energy transmitted spread out in space- higher loss during transmission.
Background lights can couple into the receiver - higher error rate.
It depends on weather conditions.
QC via optical fiber
~ 100 km
Cambridge research laboratory of Toshiba Research Europe
Swiss communication group & idQuantique in Europe
MagiQ technology in USA
Photon sources
Faint laser pulses
Entangled photon pairs by parametric down conversion or Franson’s method
Single-photon Fock states are difficult to realizedexperimently.
coherent stateswith an untra-lowmean photon number
semiconductor laser & attenuators
Producing entangled photons
Parametric down conversion.
Franson’s method.(using unbalanced Mach-Zender interferometer)
Parametric down conversion PDC is a process that a pump photon in a
nonlinear crystal has a small probability of splitting into two photons of lower frequency.
p 1 2 conserv. of energy
kp k1 k2 conserv. of momentum
Type II: two converted photons have orthogonal polarizations
PDCbeta-BaB2O4
Faint laser pulses
Pn, n
neProb. of finding n photons
Most pulses are empty Pn 0 1
decrease in bit rate
Pn 1n 0
2Pulse contains more than 1 photon
mean photon number ~ 0.1
Photon pairs by PDC Very inefficient ----- it takes 1010 pump
photons to create a pair in a given mode. The system can be made compact and handy.
40 cm × 45 cm ×15 cm
Single-photon detectors Avalanche photodiodes, photomultipliers,
Josephson junctions, quantum dots, MODFET
Most experiments used APD’s Silicon APD’s ~ 800 nm Ge APD’s ~ 1300 nm InGaAs/InP APD’s ~ 1500 nm Some group design photon-detecting
device for QC experiment. Toshiba team at Cambridge use MODFET
Exp. with faint laser pulses Polarization coding
Phase coding
Polarization coding
Bennett, Bessette, etc.1992
30 cm
BB84 four-state protocol
the pulseattenuated bythe filters
emits classical pulse
Beamsplitter:base choice
Polarization coding
(1) Polarization transformation induced by long optical fibers is unstable. require active alignment of bases.
(2) No polarization-maintaining fibers actually maintain polarization.
Drawbacks:
Polarization coding
Swisscom used optical fibers for QCexperiments between Geneva and Nyon, 1996
Nyon
Geneva
Transmission distance 23km
Phase coding
LD
PM AAlicePM B
APD’s
time
cou
nt
sDouble Mach-Zender implementation
Bob
~ 100 km
long+short
Phase coding(BB84)
1 eiAB2 Cos2A B2Interference
Bit value(Alice)
Bit value(Bob)
0 0 0 0 00 0 /2 3/2 ?1 0 11 /2 /2 ?0 /2 0 /2 ?0 /2 /2 0 01 3/2 0 3/2 ?1 3/2 /2 1
A B A B
Destructive interfere
Exp with photon pairs Polarization entanglement
Energy-time entanglement
dis/advantage w. photon pairs
advantage disadvantage Prevent unintended info leakage
Prevent multiphoton splitting attacks
Analyzers are simple and efficient. (polarization entanglement)
(polarization -based)
Decoherence is more serious than faint laser pulses (energy-time entanglement) Chromatic dispersion will destroy strong time correlation not adequate for QC over long optical fibers
Low key generation rate
Polarization entanglement
BBO pumped by argon laser
analyzer: simple and efficient
Both BB84 & Ekert’sscheme were realizedwith distances less than 1 km.
Energy-time-entangled photon pairs yr 2001
KNbO3 crystal
BB84 protocol, yr 2001.
Active groups worldwideJapan National Institute of
Informatics Australia Innsbruck
USA Caltech, Columbia UniversityHarvard UniversityIBM, Los Alamos,MagiQ TechnologiesMIT, Stanford, Berkeley,…
EuropeVienna - Quantum Experiments and the Foundations of Physics
Genève – GAP OptiqueUniversity of Padova, ItalyENS - LKB ,FranceIPT Russian Academy of Sciences - Quantum Computer Physics LaboratoryMax-Planck-Institut für QuantenoptikQuantum Information in Braunschweigid Quantique
UK CQC – CambridgeCQC - OxfordBangor UniversityImperial CollegeLoughborough University
Asia Quantum Lah in SingaporeNCKU, Taiwan
Quantum cryptography in Taiwan?
We can do it, since we have
(1) physicists who know quantum information theory well.
(2) experienced researchers who have good knowledge on quantum optics.
(3) well-established laboratories of quantum optics.
and most of the exp. components are commercial and easy to get.
Possible first QC lab in Taiwan
中央大學:徐子民教授,欒丕綱、陳彥宏助理教授 , 中原大學:周志隆助理教授 NCTS: 徐立義博士中華電信:蔡一鳴博士
以及
願意投入 QC 研究的學者、學生… ..
The End
Key distillation
Classical error correction
Privacy amplification
raw key distilled key
Producing entangled photons
Parametric down conversion.
Franson’s method.(using unbalanced Mach-Zender interferometer)
Parametric down conversion PDC is a process that a pump photon in a
nonlinear crystal has a small probability of splitting into two photons of lower frequency.
p 1 2 conserv. of energy
kp k1 k2 conserv. of momentum
Type II: two converted photons have orthogonal polarizations
PDCbeta-BaB2O4
Franson’s method
1 2D1
D2
D4
D3
12
time correlatedphoton source
s1, s2 ei121, 2
Mach-Zenderinterferometer
By looking in coincidence, we get the entangled state
Single-mode fibers well suited to carry single quanta Transmission loss. geometric phase Even small birefringence will remain a
concern in quantum communication.(both polarization-based & phase-based systems)
Polarization mode dispersion. Polarization-dependent loss. Chromatic dispersion (phase-and time coding).
Q-dot as single-photon detector Conventionally single photons are detected by
multiplying a photo-generated electron using an avalanche process. The Toshiba researchers, in collaboration with Cambridge University, developed a device for detection of single photons based on a GaAs/AlGaAs modulation doped field effect transistor (MODFET) which does not rely on avalanche processes.