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)

72

73

Thank you!