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Interplay between Quantum
Computation and Quantum
Information
Interplay between Quantum
Computation and Quantum
Information
Akihisa Tomita
Quantum Computation and Information Project,ERATO-SORST, JST
Graduate School of Information Science and Technology, Hokkaido University
AQIS'1010th Asian Conference onQuantum Information Science
and and
ExperimentExperiment
2
Contents• Introduction– Fundamental concepts of quantum information
processing– Quantum Computation Science, Quantum
Information Science, and Physics– ERATO-SORST Project and Quantum Networks
• Quantum k-Merlin Arthur Game• Quantum Leader Election
– algorithm– implementation
• Quantum key distribution• Conclusion
Fundamental concepts ofComputer Science and Information Science
3
This figure is taken from the text book “Quantum Computation and Quantum Information” by M.A. Nielsen & I. Chuang (Cambridge Univ. Press)
Quantum State (qubit)• A vector in 2-dim Hilbert space
• Implementation by photon– Polarization– Relative phase
– vacuum/one photon– and more
( ) ( )12sin02cos
1 where1022
θθψ
βαβαψϕie+=
=++=
Bloch sphere
ϕϕϕϕ
θθθθ
|0>
|1>
z
x
y
2
10 +
2
10 i+
4
Mixed States
• an ensemble of pure quantum states denoted by classical probability distribution pi taking state
• described with a density operator– eigen values ρ ≥0 ; Tr ρ =1
• Reduced density operator– If , then
5
iψ
∑=i
iiip ψψρ
( )ABB
A ρρ Tr=σρρ ⊗=AB ( ) ρσρρ =⊗= B
A Tr
Quantum gates• quantum gates ====Unitary trans.
– single qubit gates =2x2=2x2=2x2=2x2 Unitary matrices– Any 2x22x22x22x2 unitary matrices can be
approximated with three matrices
xzy
yxz
i
iI
σσσ
σσσ
=
−=
=
−=
=
01
10,
01
10,
10
01,
10
01
=
=
1
01,
0
10
01,10:
01,10:
11,00:
iiy
x
z
−→→
→→
−→→
σσ
σ
NOT
Two-qubit gate (ex. CNOT)
( )1021 +
0
( )11002
1 +
TCTC
TCTC
TCTC
TCTC
0111
1101
1010
0000
→
→
→
→
C-Unitary gate ++++single qubit gates ====universal
C-unitary gates, in general
NOT op. only when C=1
Quantumness relevant to information processing
• Superposition– Quantum parallelism
– No cloning
• Entanglement (inseparability)– State control– Monogamy
• Measurement– State collapse; projection
8
Quantum Computation
0 0 0
x0 + x1 + x2 + x3 + x4 + x5 + x6 + x7
2N states
0〉〉〉〉+ 1〉〉〉〉 0〉〉〉〉+ 1〉〉〉〉 0〉〉〉〉+ 1〉〉〉〉N qubits
0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
Quantum parallelism
interferenceentanglement
solution
solution extraction(amplifying state amplitude)
( )1111101011000110100010008
1
2
10
2
10
2
10
+++++++=
+
+
+=ψSuperposition
( )ψf ( ) ( ) ( )821 ,,, xfxfxf L
ex: Quantum Fourier Transform
U
9
Quantum InformationMission impossible:
to distinguish two states with a single measurement• classical states = possible• orthogonal states = possible• non-orthogonal states = impossible
accept!
reject!
If you had many copies, it would be possible without a trace
disturbance upper bound of information
error free
50% error
10
• Pure states and :– Fidelity
• Mixed states ρ and σ :
• Properties– F=1 for identical states
– F=0 for perfectly distinguishable states
––
How close are the two states?
11
σ
R
Entanglement• non-local (quantum mechanical) correlation
S=0S=±1S=Ŧ1S=+1S=-1
Measurement results of two remote particles, which interacted in the past, yield a correlation, though no interaction is applied between two.
12
J
J
J J
J
J
JJ
J
J
J
J J
J
J
JJ
J
J
0
1000
2000
3000
4000
5000
0 30 60 90 120 150 180
Azimuth angle of HWP
Entanglement (cont.)
• Correlation– entanglement assisted communication
– exponential speed up (?)
– quantum game (pseudo-telepathy); multi-prover interactive poof
• monogamy– quantum cryptography
• decoherence– information-disturbance trade-off; error correction
13
Alice
Bob
Eve = Eavesdropper, Environment
?
Entangled state• Separable states
– ex.
• Entangled states– not described by a tensor product – Bell states
– GHZ state
– W state
• Partial trace of a pure state– separable: pure
– entangled: mixed
BAABBAABρρρψψ ⊗=′⊗=Ψ ;
BA01
( );01102
1BABA
± ( )BABA
11002
1 ±
A B
14
( ) 2111000 LL +
( ) N01000100100010 LLLLL +++
( )( )ϕϕBS Trdeg. of entanglement:
The two cultures: Computer Science and Information Science
15
Algorithmclasscomplexity
pure statesp>1/2
Channel, Codingcapacitydistinguishablity
mixed statese<2-k
This figure is taken from the text book “Quantum Computation and Quantum Information” by M.A. Nielsen & I. Chuang (Cambridge Univ. Press)
The three cultures:CS, IS, and Physics
• “They are playing their own games, which are almost independent of physics, once the rules are established. We still have to consider physical systems (It’s annoying…)”
• “They cannot treat things rigorously, and tend to jump to unreasonable conclusions, so that we have to direct them.”
• “They made a useful theory, only after we taught them what really matters.”
16
ERATO-SORST Project
• Designed to promote cooperation between QCS, QIS, and Physics (theory & experiment)
• Five (3+2) year Project; the successor of ERATO Quantum Computation and Information Project (2000.10-2005.10) headed by Prof. Imai (Univ. Tokyo)17
Quantum Informationexperiment
Quantum Computing Quantum Informationtheory
Tokyo
Tsukuba
18
Cryptography Computation
・・・・Government, Defense・・・・Electronic Commerce・・・・Medical, genome, biometrical , etc.
(1) Menace to conventional crypto
Quantum Cryptographyunconditionally, provable security
supercomputers
65TFLOPS PFLOPS
(1) Fundamental limit in computers limit in nano-lithography
(2) Ultra-high speed computing
・・・・power ・・・・physical limit in FETs
(2) Increasing demand for secure network
with innovating technology
・・・・climate, molecular design (pharmacy),..drive innovation
government
business
database
Q-NW
Quantum ICT network
Quantum Computersquantum parallelism
medical
QQQQ
Q
academic
quantum distributed computing
Ex. designing protein structure
Challenges in IT and Quantum Solution
e-commerce
UltraUltraUltraUltra----fast fast fast fast
Data ProcessingData ProcessingData ProcessingData Processing
e-voting
長距離量子暗号網
Photonic NWPhotonic NW
Masquerade DetectionMasquerade DetectionMasquerade DetectionMasquerade Detection
Q-NW
KE
YK
EY
KE
YK
EY
◎
◎◎
RepeaterRepeaterRepeaterRepeater QKDQKDQKDQKD
Access
long haul
Intranet
Government
Data ProtectionData ProtectionData ProtectionData Protection
Data storage
Quantum Protocol
Safe and Secure Society by Quantum Network
19
Quantum Network
20
Physical layer• implementation ……………..
• state preparation/measurement• devices (memory, gate, ……...)
Communication layer• channel capacity• coding theory …• network theory...
Application layer• distributed computing• cryptography ………..
Quantum Computing Gr.
Quantum Information Theory Gr.
Quantum Information Experiment Gr.
• Algorithm– distributed computation
– complexity
• Protocols– non-cryptographic
• Quantum Leader Election
– cryptographic• Pseudo-telepathy Game
• Quantum Key Distribution
• Computational Cryptography• Interactive Proof
Application layer
21
• Algorithm– distributed computation
– complexity
• Protocols– non-cryptographic
• Quantum Leader Election
– cryptographic• Pseudo-telepathy Game
• Quantum Key Distribution
• Computational Cryptography• Interactive Proof
Application layer
22
• An Improved Claw Finding Algorithm Using Quantum Walk• Optimal Claw Finding Algorithm Using Quantum Walk• Quantum Property Testing of Group Solvability• Computational Geometry Analysis of Quantum State Space and Its Applications
• Exponential Separation of Quantum and Classical Online Space Complexity• Quantum Weakly Nondeterministic Communication Complexity• The One-Way Communication Complexity of Group Membership•The quantum query complexity of certification
• Exact Quantum Algorithms for the Leader Election Problem
•Generating facets for the cut polytope of a graph by triangular elimination• Bell inequalities stronger than the Clauser-Horne-Shimony-Holt inequality for three-level isotropic states• On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables
• Practical Evaluation of Security for Quantum Key Distribution• Upper bounds of eavesdropper's performances in finite-length code with the decoy method• General theory for decoy-state quantum key distribution with arbitrary number of intensities• Security Analysis of Decoy State Quantum Key Distribution Incorporating Finite Statistics
•Oracularization and Two-Prover One-Round Interactive Proofs against Nonlocal Strategies• Quantum Merlin-Arthur Proof Systems: Are Multiple Merlins More Helpful to Arthur?• Quantum Communication Between Anonymous Sender and Anonymous Receiver in Presence of Strong Adversary• Quantum Non-local Boxes and their Use in Computer Security
Communication layer
• Quantum network architecture– entanglement, robustness, routing
• Quantum coding– channel capacity
• quantum/classical, entanglement assisted, …
– QECC
– network coding
• Entanglement theory
23
Communication layer
• Quantum network architecture– entanglement, robustness, routing
• Quantum coding– channel capacity
• quantum/classical, entanglement assisted, …
– QECC
– network coding
• Entanglement theory
24
• On the minimum number of unitaries needed to describe a random-unitary channel• Superbroadcasting and classical information• Optimal Visible Compression Rate For Mixed States Is Determined By Entanglement Purification• Properties of Conjugate Channels with Applications to Additivity and Multiplicativity• Public and private communication with a quantum channel and a secret key
•Information-Disturbance Tradeoff in Quantum State Discrimination• A minimum-disturbing quantum state discriminator• Quantum Erasure of Decoherence• Entanglement measures and approximate quantum error correction• Global information balance in quantum measurements• Information extraction versus irreversibility in quantum measurement processes• Towards a unified approach to information-disturbance tradeoffs in quantum measurements
•Additivity and multiplicativityproperties of some Gaussian channels for Gaussian inputs• Monogamy inequality for multipartite distributed Gaussian entanglement• Universal distortion-free entanglement concentration• Statistical analysis of testing of an entangled state based on the Poisson distribution framework• Irreversibility of entanglement loss •(4,1)-Quantum Random Access Coding Does Not Exist--
One qubit is not enough to recover one of four bits• Prior entanglement between senders enables perfect quantum network coding with modification• General Scheme for Perfect Quantum Network Coding with Free Classical Communication
Physical layer• System
– QKD
• Circuits over a network
• Entanglement generation/distribution
• Implementation– qubit/qudit– gate, memory
– interface25
Physical layer• System
– QKD
• Circuits over a network
• Entanglement generation/distribution
• Implementation– qubit/qudit– gate, memory
– interface26
•Practical quantum cryptosystem for metro area applications• Experimental Decoy State Quantum Key Distribution with Unconditional Security Incorporating Finite Statistics• Ultra fast quantum key distribution over a 97-km installed telecom fibre with wavelength-division multiplexing clock synchronization• Ensuring Quality of Shared Keys through Quantum Key Distribution for Practical Application• High speed quantum key distribution system•Quantum Key Distribution Over 50km with High-Performance Quantum dot Single Photon Source at 1.5-µm Wavelength• Technologies for Quantum Key Distribution Networks Integrated With Optical Communication Networks
• Experimental demonstration of quantum leader election in liner optics• Measurement of the off-diagonal geometric phase of a mixed-state photon via a Franson interferometer• Asymptotic Quantum teleportation to enable universal quantum processor• Quantum teleportation scheme by selecting one of multiple output ports
• Generation of Polarization-entangled Photom Pairs Using Periodically Poled Lithium Niobate Waveguides in a Fiver Loop• Highly efficient polarization entangled-photon source from Periodically Poled Lithium Niobate wavegides• Efficient generation of a photon pair in a bulk periodically poled potassium titanyl phosphate• Efficient Photon Pair Generation Using Two-wavelength Spontaneous Parametric Down-conversion Module• Performance of hybrid entanglement photon pair source for quantum key distribution
•Quantum-nondemolition measurement of photon-arrival using an atom-cavity system• Mode Identification of High-quality-factor Single-defect Nanocavities in Quantum Dot-embedded Photonic Crystals• Photon-arrival detector with a controlled phase flip operation between a photon and a V-type atomic system• Positive operator valued measure for practical single-photon avalanche photodiode• Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor• Cut-off rate analysis of practical quantum receivers• Multipixel silicon avalanche photodiode with ultralow dark count rate at liquid nitrogen temperature
27 Chicago J. Theoretical Computer Science, Article 3 (2009)
ex. 1ex. 1
(Quantum) Interactive Proof System
• {Yes, No} question
• Prover: always tells “Answer is Yes.”– any Unitary operation allowed
• Verifier: checks P’s assertion with high probability through communication – quantum polynomial time computation
• Related to many problems:– Cryptography
– Inapproximabilityof certain optimization problems (e.g. max-3sat, creek, etc)
– Locally decodable/testable code 28
ProverVerifier
Quantum Merlin-Arthur Game
• Merlin sends a quantum proof.
• Characteristics:– Completeness: The verifier accepts a poof with probability
at least c, if the answer is “Yes.”– Soundness: The verifier rejects any proofs with probability
at least 1-s, if the answer is “No.”
• It is interesting for physicists that calculating the ground state energy of a many body system is QMA.
29
Eg(H)a b
Given Hamiltonian H, Promise: Eg(H)<a or Eg(H)>band Merlin says “ Eg(H)<a ”!
> 1/poly(N)accuracy
ex. c=2/3, s=1/3
Multiple-Merlin; QMA(k)
• Arthur receives k quantum proofs.
• KMY shows QMA(k)=QMA(2) – iff ‘For any two-sided bounded error completeness-
soundness pair (c,s), QMA(2,c,s)=QMA(2,2/3,1/3)’
• Aaronson, Beigi, Drucker, et al. (*)shows that the Additivity Conjecture implies that QMA(k)=QMA(2), etc.
30
)()()( YfXfYXf +=⊗ ?
V
P’s
(*)Theory of Computing, 5:1-42 (article 1) 2009
KMY ~ main result• For any k∈poly and any two-sided bounded error
completeness-soundness pair (c,s)[*], QMA(k,c,s) ⊆⊆⊆⊆ QMA(2,1-2-q,1-1/p) p,q ∈poly[*] c-s ∈poly-1 and 2-q ≤ s < c ≤ 1-2-q
poly: set of all polynomially bounded function
• Proof:– Construct 2-proof system for 3-proof system by
(R1,S1) and (R2,S2) expectingand separability test & simulation test
– QMA(3,1-εεεε,1-δδδδ) ⊆⊆⊆⊆ QMA(2,1-εεεε/2/2/2/2,1-δδδδ/20)– QMA(3k+r,1-εεεε,1-δδδδ) ⊆⊆⊆⊆ QMA(2k+r,1-εεεε/2/2/2/2,1-δδδδ/20)
31
0 1s c
1/poly
322311 ; φφψφφψ ⊗=⊗=
Applies Technique from Quantum Information
Tests in two-proof system• Separability test (control swap test)
– Expecting but R1 and S1 (or R2 and S2) may be entangledTest on , where psep=(1+Tr(ρσ))/2, and ρ =σ if R,S separable.
• Simulation test – will simulate the original verifier, if entanglement is small
(pass the separability test) – Apply V(x) to (V,R1,R2,S1).
– psim is given by Fidelity between the state to be tested |α⟩and its projection |β⟩ onto the accepting states:
– Tr(ρσ) (>1-δ/5) provides the bound to the fidelity and then desired soundness
32
322311 ; φφψφφψ ⊗=⊗=
2211 21Tr;Tr ψψσψψρ ′′=′′= RR
( )2, ααββ VVFpsim
+=
33
Select one leader fromidentical computers
• Classical – coin toss– finite probability of “even”
– unsolved with finite communication
identical operation
Anonymous leader election
• Quantum– quantum communication
+ quantum operation– no probability of “even”
– solved with finite communication
ex. 2
It is easy using pre-shared entanglement
• Suppose W state is shared by N-party.
• After measurement, the state is collapsed to one of
34
( ) N01000100100010 LLLLL +++
010,0010,,0100,010 LLLLL
E. D’Hondt and P. Panangaden, Quantum Information and Computation 6, 173 (2006)
QLE (algorithm I)
35
1
0
2
10 +
0
call SUB A
S=C & status=1
R0 R1 Sstatus
measure R0,R1call SUB B
no
yes
status=1
yes
call SUB C
*
z
z=zmax
zmax
no
put 0
no
yes
k=n
k=k-1
go to * until k=2
C
C
GHZ C
Ψ I0
set
measure S
superposition
S. Tani, H. Kobayashi, and K. Matsumoto , LNCS 3404,pp.581-592,2005
classical
Two party QLE• initial state:
• SUB A – “copy” R0:
– quantum communication:
– inverse “copy”:
• SUB B : erase amplitude of
– apply U , if g=0,
36
+⊗
+2
10
2
10
212
1100
2
1100
+⊗
+ghghghgh
2
11110110010100002211
+++ghgh
( ) ( )2
111001001100,2,1,2.1,2,1,2,1,2,1,2,1 gghhhhgghhhh
+++
−−
=1
1
2
1
i
i11;00
( )2
1001,2.1,2,1 hhhh
+
S S
37
Quantum circuit for two-party QLE
H U
H
U
Alice
Bob
host
guest
host
guest
entangling feed forwardquantum comm.
0
0
0
0
Q: So, how can we implement the circuit ? – A: Photonics !
Quantum Information with photons
- pro & con -
• Good for Transmission (and Proof of Principle)– Low Loss Channel (fiber)– Weak Decoherence– Qubits by polarization, phase,…– Single Qubit Operation
• Bad for Processing– Weak Interaction
Hard to make a Controlled-gate
– NO Amplifiers
Single qubit gate for polarization
• waveplate: birefringence– HWP
– QWP
• appropriate alignment of optical axes– any single qubit operation
−10
01
i0
01
nx
ny
d
( )λ
−π yx nnd2
θ−θθθ
=
θθ−θθ
−
θθθ−θ
2cos2sin
2sin2cos
cossin
sincos
10
01
cossin
sincos
( )( )
θ+θθθ−θθ−θ+θ
=
θθ−θθ
θθθ−θ
22
22
sincossincos1
sincos1sincos
cossin
sincos
0
01
cossin
sincos
ii
ii
i
40
Two-qubit gates• Gate implementation with linear optics
0
1
( )01102
1 +
BS
12
3
4 HH
H
H
VV
V
V
HV
H
V
VH
HV
PBS
entangler(photon number basis)
probabilistic CNOT(polarization basis)
Success Fail
H
H
output
control
target
Parity
check
XOR
PBS
H
1
2
3
4
1'
2'
3'
4'
H
H
41
C-NOT construction
parity check
XOR
T. B. Pittman et al, Phys.Rev.A 66,052305
Prob. 1/4w. feed forward
Polarization entangled photon generation by type I crystal
42
Spontaneous Parametric Down Conversion
(SPDC)
Two-crystal geometry
Nonlinear Crystal
( )pp kr
,ω ( )ii kr
,ω
( )ss kr
,ω
( )ekkn
ck
kkk isp
isp
rrr
vrr
,,ω=ω
+=
ω+ω=ω
( )VVHH +2
1
No Which crystal information
superposition=entanglement
Entanglement in fiber-optics
43
Z0(X0)
Pulsegenerator
532nm
810nm1550nm
Delaycontroller
SMF
Photon-pairmodule
CW
2.5nsPBS
time-polarization transformer 2.5ns
Z0
Z1
Z1(X1)
OR
AliceBob
H
V
Lens2x4PLC
λλλλ/2
space20cm
Trigger
Two color, hybrid entanglement
X0
X1
0o
(22.5o)
Trigger delay [ns]
C.C
. [c/
10s]
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
50 50.2 50.4 50.6 50.8 51
A0-B0
A0-B1
A1-B0
A1-B1
PLC temp [℃]
0
0. 1
0. 2
0. 3
0. 4
0. 5
0. 6
0. 7
0. 8
0. 9
1
5 5.5 6 6.5 7 7.5 8
A0-B0
A0-B1
A1-B0
A1-B1
delay length [mm]V
isib
ility
X basis (D,A&phase)Vis. 88%, 950c/s
Z basis (H,V&time)Error 2.1%, 820c/s
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
18 20 22 24 26 28
A0-B0
A0-B1
A1-B0
A1-B1
44
45
Quantum circuit for two-party QLE
H
U
H
U
Alice
Bob
host
guest
host
guest
entangling feed forwardquantum comm.
0
0
0
0
U
H
1
2
3
4
Polarization-qubit implementation
46
H
U
H
Alice
Bob
guest
host
guest
quantum comm.
2
VVHH +
H
2
VVHH +
H
entangled photon source feed forward
1
2
3
4host
Polarization-qubit implementation
1. A,B create entangled photons
2. exchange one3. PBS: H (1 to 3, 2 to 4), V (1 to 4, 2 to 3)4. Hadamard (wave plate) to 4
5. measure 4, the outcome: (A,B)={(H,H),(V,V),(H,V),(V,H),
(0,HH),(0,VV),(HH,0),(VV,0)}the projected state
6. apply Unitary to 3 and measure 47
(H,H),(V,V)
(H,V),(V,H)
48
Photon number based implementation1. entangling
3. phase gate.
2. quantum commun.
BS
BS
BS
BS
4. measurement
Y. Okubo, et al, Phys. Rev. A 77, 032343 (2008).
49
[ ]( ) ( ) ( ) ( )[ ]
BghAghBghAgh
BABA
B
ghgh
A
ghgh
110000112
1
2
0110
2
0110
++
ΨΨ+ΨΨ→
+⊗
+
+−−+
State after phase gates
Distinguishable states appear from product of identical stateQLE is always successful, by defining the winner as 11 and +Ψ
measurement after two photon interference
distinguishable
detectors: A1 A2 B1 B2
Alice and Bob yield
different detection pattern
1
2input
click A1, B2
A is leader
Measurement
BA
−+ ΨΨ
50
A1 A2 B1 B2 Leader
1 - - 1 Alice- 1 1 - Bob2 - - - Alice- 2 - - Alice- - 2 - Bob- - - 2 Bob
two to one port
one photon to each port
Alice Bob failure in usual setting
Expected Result (success with prob. 1)
51
52
Symmetric configuration
Two-photon interferometers
SPDC
π/2
BBO
Experimental set-up
53
error
A1B1&A2B2
8
1
4
1
theoryobserved (counts)
A1 A2 B1 B2 Leader
1 - - 1 Alice- 1 1 - Bob2 - - - Alice- 2 - - Alice- - 2 - Bob- - - 2 Bob
Result
0
100
200
300
400
500
600
700
0.0 5.0 10.0 15.0 20.0
Coi
ncid
ence
/1s
Piezo Voltage (V)
Two photon interference
Piezo-Voltage (~Phase Difference)
54
A1 A2 B1 B2 Result
2 - - -- 2 - -- - 2 -- - - 21 1 - -- - 1 11 - - 1- 1 1 -1 - 1 -
×- 1 - 1
two photons detected
55
one photon each
Communication complexity in classical protocol
2
1
2
1
2
1
2
1
2
1
2
1
421
1 ==∑∞
=−
nn
classical nN
Alice Bob
2bit
expectation value of communication bits to success:
failure: 50%
Communication complexity of QLE (with imperfect apparatus)
A1 A2 B1 B21 - - 1- 1 1 -1 - 1 - ×- 1 - 1 ×
2 bits CC required to verify the results between Alice and Bob
exchange guest qubits(QC)2bits
two photon detected
=protocol succeeded
=no CC required
2 bits in total
measurement
one photon each?
4 bits in total
2
1
2
1
failure (try again!)
success (finish)
not leader!Leader!!
Leader!Leader!
41 ν−
41 ν+
2
1
41 ν−
41 ν+
2
1verification
N
Communication complexity of QLE (with imperfect apparatus) cont.
prob. to success at k-th round
What’s interesting?• Leader Election:
– Create asymmetric states from a symmetric state only with symmetric operations.
– Impossible! (as in classical protocols) So in quantum. But, because of non-locality in quantum state (entanglement), appropriate cut yields effective asymmetry.
• as a Practical photonic implementation– Appropriate definition on success events result
in deterministic operation with linear optics – even loss helps the successful leader election!
59
60
experiment
Quantum Computing Quantum Information
ex. 2 QLE
ex. 1: QMA
ex. 3: QKD
61
Secure key distribution with quantum communication
transmission
error correction
Privacy amp.
Application
BobAlice
Eve
TX RX
common random numbers
Quant. Comm.
erase leakage info
key key
secure key
estimate leakage informationCoding
Decoding
ex. 3
62
1. single photon source– one photon for one bit
2. infinite computational resource– infinite code length
(asymptotic)3. infinite code length,
infinite time to measure– no estimation error– no fluctuation
1. weak coherent light– 0,1,2,.. photons for one
bit2. finite memory capacity,
execution time– finite code length
3. finite code length, finite time– sampling error– fluctuation
ideal practical
Assumptions on BB84 protocol
Can we extract secure keys under the practical assumptions?Yes, with decoy method (Hwang, Wang, Lo, et al for 1 and Hayashi, et al for 2,3.)
62
Estimation of sacrifice bits• Estimation of channel (Eve’s strategy) from the
transmission date– decoy method: improving the estimation by increasing
the number of constraints
• Errors in estimation– fluctuation of data (environment, equipment)
– estimation error from finite number of data– sampling error in finite-length code
J. Hasegawa, et al., arXiv 0707.3541
Transmission Data
Channel Parameters
Sacrifice bits in Data block
δ ′−2
63
QKD transmitter/receiver� including laser, encoder, modulator� error detecting modulation� 625MHz & 1.25GHz clock
Transmitter (Alice)
+⋅
−=2
exp2
cos 2121 φφφφiEE inout
( )SF +2
1 DDMZM
1φ
2φ
PLC (Planer Lightwave Circuit) enables stable operation without active control
64 This board is developed by NEC under the contracted research with NICT
PLC-Interferometer
Port Port
Long path waveguide
Short path waveguideCoupler
Coupler
TEC
1:x
(0.4-1m)
Telecom wavelength(1.55µm)
Optical delay: 2.5/0.8/0.4 ns
Low loss ≤ 1dB
Negligible PDL
Polarization insensitive
Temperature ( C)
Pow
er (
arb.
unit)
10 15 20 25 30 35
°°°°
n
6 TETM
Out of phaseIn phase
A B C∆∆∆∆φφφφ=(2N+1) ππππ
2222∆∆∆∆φφφφ=2Nππππ ∆∆∆∆φφφφ=(2N+1)ππππ
Temperature ( C)
Pow
er (
arb.
unit)
10 15 20 25 30 35
°°°°
n
6 TETM
Out of phaseIn phase
A B C∆∆∆∆φφφφ=(2N+1) ππππ
2222∆∆∆∆φφφφ=2Nππππ ∆∆∆∆φφφφ=(2N+1)ππππ
Y. Nambu, et al, Jpn. J. Appl. Phys. 43 L1109 (2004)65
nonlinear optimization of discontinuous functions under constraint
Key generation time
Q.C.
EC
PA
Random permutation
Leakage information estimation
present (~15s in total)
15s
10s
code length: nfuture
O(1)
O(n2)
O(n)
smaller errorlonger code
less fluctuation
O(n2)
66
Fast key distillation• Hardware logic for key distillation
– Function: sift, error correction, privacy amplification
– Form factor: Advanced TCA (PICMIG 3.0 Advanced TCA Base Specification)
Quantum
L2Distillation Distillation
FPGAs FPGAs
MAC
MAC
ServerSocket
PCI-E
Quantum
Server
67
Key distillation boardfront view
rear view
lower view
XFP(10G Optical IF)
stacking connector
Input FPGA(frame sync, & sift)
FPGA(EC/PA/comm)
Back board connector(GbE x 4)
SMA(500MHz CLK1Gbps data)
PCI-Express(to CPU)
� external IF� 10G optical IF (XFP)• T&Rx3、、、、Rx6� 10/100/1000Ether x4� SMAx 2 • 500MHz CLK input
1Gbps Data output� PCI-Express x8� FPGA IF� 10Gbps Bus (XAUI)� total memory 5GB
68 This board is developed by NEC under the contracted research with NICT
69
Conclusions
• Three examples on cooperation between CS, IS, and PS;– East is East, and West is West, but
Quantum is also Quantum
• These cooperation will be more important for Quantum Networks (Quantum Distributed ***) – The studies will include
• What possible,• How efficient,
• How it works,• How to make, …
Members (current)• Head: Hiroshi Imai• Quantum Computation
Group– Leader: K. Matsumoto– Researcher: J.
Hasegawa– Student members:
• N. Fu• R. Aoshima• T. Sato
• Quantum Information Theory Group– Leader: T. Hiroshima– Researcher: M.-H. Hsieh
– Student members:• Vorepong Suppakitpaisarn
• Quantum Information Experiment Group– Leader: A. Tomita– Researcher: K. Tsujino
• Staffs– T. Nagatsu (admin.)
• H. Yokota
– A. Tomita (tech.)• H. Takeshima
70
Members (past)• M. Amaike (admin)• T. Yamakami (researcher)• Y. Kikuchi (researcher)• X.-B. Wang (researcher)• T. Ohno (admin)• C. Matsumoto (admin)• M. Yasuda (admin)• Y. Iuni (student)• J. Nishitoba (student)• M. Hayashi (group leader)• M. Asada (student)• Y.-K. Jiang (researcher)• S. Nagaoka (student)
• F. Buscemi (researcher)• Ku. Kojima (researcher)• Y. Tokuda (student)• Ko. Kojima (student)• S. Tani (researcher)• F. Le Gall (researcher)• H. Kobayashi (researcher)• Y. Okubo (student)• K. Yoshizoe (researcher)• J. Sprojcar (researcher)• K.-Y. Cheong (researcher)• M. Kimura (admin)
71
Members (ERATO)• Quantum Computing (Tokyo)
– K. Tadaki– M. Hachimori– F. Yura– H. Fan– W.-Y. Hwang– A. Carlini– Y. Tokunaga– T. Yamazaki– M. Toda– S. Moriyama– T. Kawakami– A. Miyake– T. Ito– Y. Sasaki– S. Tokumoto– T. Yamada– M. Owari
• Quantum Information (Tsukuba & Tokyo)– M. Hamada– B.-S. Shi– Y. Tuda– Achanta V. Gopal– K. Kazui– S. Natori
• Quantum Circuit Programming (Kyoto)– K. Iwama– S. Yamashita– T. Koshiba– H. Nishimura– Chelliah Pethuru Raj– A. Kawachi– M. Amano– Y. Iio– Rudy Raymond Harry Putra– A. Matsuura– K. Kobayashi– R. Nishimaki– Y. Murakami– T. Inoue
• Admin– Y. Umezawa– T. Sakuragi– M. Inagaki– E. Bandai– M. Ohyama (Kyoto)
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Thank you!