Quantum Communication Networks and Quantum repeaters...4 What is Quantum Communication? “Quantum...

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Quantum Communication Networksand Quantum repeaters

Winter School on Quantum Computing at Emory (WiSQCE)

Paul Hilaire, Edwin Barnes, Sophia Economou

January 9th 2020

Privacy of long-distancecommunications usingquantum mechanics

Winter School on Quantum Computing at Emory (WiSQCE)

Paul Hilaire, Edwin Barnes, Sophia Economou

January 9th 2020

Communications

0 𝑜𝑟 1

What is Quantum Communication?

“Quantum communication is the art of transferring a quantum state from one place to another”

N. Gisin and R. Thew, Nat. Photon. (2007)

Ψ = 𝛼 0 + 𝛽|1⟩

What is a Quantum Network?

A network which facilitates the transfer of quantum information.

Routing Q informationCommon language

Network of quantum networks:Quantum internet!

S. Wehner et al., Science (2018)

H. J. Kimble, Nature (2008)

Sharing the network

Complex topology

Different devices

Why Quantum Communications?

Distributedquantum computing

Improved accuracySecure communications

Security QuantumComputing

Sensing

Why Quantum Communications?

Security

QuantumComputing

SensingQKD

TelescopeobservationD. Gottesman et al., PRL (2012)

Stolen from a talk of R. Van Meter…

DistributedQuantum computing

R. Beals et al., Proc. R. Soc. A (2013)

Accurateclock synchro

P. Komar et al., Nat. Phys. (2014)

BlindQC

A. Broadbent et al., IEEE. (2009)

Bizantine agreementLeader election

M. Fitzi et al., Phys. Rev. Lett. (2001)

Outline

Part 1: General tutorial

Part 2: Recent results (if time)

To show that you are able to read state-of-the-art QC papers now!

To learn more about quantum communications (QC)

Outline

Quantum Network and distributed quantum computing

Quantum Key Distribution (QKD)

Long-distance Quantum Communications with Quantum Repeaters

Free-space long-distance Quantum Communications

Practical implementations

Outline

How to distribute a message?

Asymmetric encryption (RSA)

𝑛 = 𝑝 × 𝑞

DecryptEncrypt

𝑛 = 𝑝 × 𝑞

HardShor’s algorithm

Protected by computational hardness

P. W. Shor , SIAM review (1999)

One-way functionwith trapdoor

One-time padSymmetric key

Provably secure

Eve, the eavesdropper

Symmetric key

“00101…”

How to distribute the key in a secure way?

“00101…”

𝑥 = 𝑚⊕ 𝑘 𝑚 = 𝑥 ⊕ 𝑘

…01100101011110…

𝑚…00110011110111……01010110101001… 𝑘

0⊕ 0 = 00⊕ 1 = 11⊕ 0 = 11⊕ 1 = 0

𝑥 ⊕ 𝑘 = 𝑚⊕ 𝑘⊕ 𝑘

𝑥 ⊕ 𝑘 = 𝑚⊕ 0

𝑥 ⊕ 𝑘 = 𝑚

Quantum key distribution

Provably secure symmetric key distribution, using the law quantum mechanics.

No cloning-theoremQuantum superposition Quantum measurement

𝜓 ⊗ |0⟩ → 𝜓 ⊗ |𝜓⟩|𝜓⟩ = 𝛼 0 + 𝛽|1⟩ 𝑃0(|𝜓⟩) = |𝛼|²

𝜓 → |0⟩ W.K. Wootters and W.H. Zurek. Nature (1982)

Photonic qubit

• …

• Polarization: 𝑉 = |1⟩𝐻 = |0⟩

𝜔𝑏 = |1⟩• Energy: 𝜔𝑟 = |0⟩

𝑡1 = |1⟩𝑡0 = |0⟩

• Time:

Quantum superposition and measurement

𝐴 =1

2( 𝐻 − |𝑉⟩)

𝐷 =1

2𝐻 + 𝑉 )

Polarizer

𝜆/2𝑉

Modify incident state:Ψ → |𝑉⟩

Measurement → |𝑉⟩

𝜆/2𝐴

X basis

Z basis

One cannot make a measurement without perturbating the system.

Conjugate coding

Encode:

Basis PolarizationBit value

1 |𝐴⟩

|𝐻⟩

|𝑉⟩

|𝐷⟩

Choose:

1If you don’t know the basis,

You cannot recover fully the bit by measuring it

No-Cloning Theorem

An unknown arbitrary quantum state cannot be copied.

|𝜙⟩

|𝜙⟩𝑈

|Ψ⟩

|Ψ⟩𝑈

𝑈( 𝜙 ⊗ |0⟩) = 𝜙 ⊗ |𝜙⟩𝑈( Ψ ⊗ |0⟩) = Ψ ⊗ |Ψ⟩

𝑈†𝑈 = 1

Impossible

Proof: Calculate A = ⟨Ψ| ⊗ 0 𝑈†𝑈 𝜙 ⊗ |0⟩

𝑈†𝑈 = 1 ⇒ 𝐴 = (⟨Ψ| ⊗ 0 )(|𝜙⟩ ⊗ |0⟩ )⇒ 𝐴 = ⟨Ψ|𝜙⟩

Ψ|𝜙 = ⟨Ψ 𝜙 2 Only true if Ψ = |𝜙⟩ or if Ψ|𝜙 = 0

W.K. Wootters and W.H. Zurek. Nature (1982)

𝑈( 𝜙 ⊗ |0⟩) = 𝜙 ⊗ |𝜙⟩⇒ 𝐴 = (⟨Ψ| ⊗ ⟨Ψ|)(|𝜙⟩ ⊗ |𝜙⟩) = ⟨Ψ 𝜙 2

Exercise?

QKD with single photons

CH. Bennet and G. Brassard, Proc. IEEE (1984)

Prepare: Measure:

BasisPolarization Value

|𝐴⟩

|𝐻⟩

|𝑉⟩

|𝐷⟩

𝑋 00110101011011000

XZXZXZZXXZXXZZXXZ

00110101011010100

ZZXZXXZXZXXXZXZXX

Key: 0110011010

ZZXZXXZXZXXXZXZXX

00110101011010100 00110101011011000

XZXZXZZXXZXXZZXXZ

Key: 0110011010

…XXZ……XZZ…

What about the eavesdropper?

CH. Bennet and G. Brassard, Proc. IEEE (1984)

Key: 0111010011

Measure: Measure 𝑍Prepare |𝐻⟩

0 𝑜𝑟 1 0 𝑜𝑟 1

Key: 0110011010

What about errors?

Key: 0111010011

Measure 𝑍Prepare |𝐻⟩

Key: 0110011010

𝑍, 1𝑍, 0 𝑍, 0 or

Errors or Eavesdropper?

𝜖 ≤ 0.110 Unconditional security

𝜖 ≤ 0.146 Secure against individual attacks

ϵ Qubit Error Rate1 − ϵ

P.W. Shor et al., Phys. Rev. Lett. (2000)

N. Gisin et al., Rev. Mod. Phys (2002)

Classical error correction + privacy amplificationCH. Bennett et al., J. Cryptology. (1992)

Very diverse field

AK. Eckert, Phys. Rev. Lett. (1991)

2-state

6-state

With decoy-state

“Quantum hacking”:Trojan horse attacks / Real life imperfection

Internet Interfacing

With attenuated laser

Original proposal BB84 (4-state with single photons)CH. Bennet and G. Brassard, Proc. IEEE (1984)

L. Lydersen et al., Nat. Photon. (2010)

HK. Lo et al., Phys. Rev. Lett. (2005)

Commercially available

With entangled Bell pairs (E91)

Real world QKD

Challenge: Photon losses

Photon loss 𝜂𝑡 𝐿 = 𝑒−

𝐿𝐿𝑎𝑡𝑡

𝐿𝑎𝑡𝑡 ≈ 20𝑘𝑚

How to extend QKD to long distances?

Outline

Free-space communications

𝐿𝑎𝑡𝑡 ≈ 20𝑘𝑚

Problem: Eye of sight

R. Ursin et al., Nat. Phys. (2007)

“Quantum Satellite”

J. Liao et al., Phys. Rev. Lett. (2018)

J. Yin et al., Science (2017)

Quantum Satellite: Trusted repeater

J. Liao et al., Phys. Rev. Lett. (2018)

Trusting the repeater Untrusted repeater?

Entanglement

2𝐻𝑎𝐻𝑏 + 𝑉𝑎𝑉𝑏 =

2𝐷𝑎𝐷𝑏 + 𝐴𝑎𝐴𝑏

AK. Eckert, Phys. Rev. Lett. (1991)

Work for QKD

Measure:

or XZMeasure:

Alice and Bob can verify that the source is sending the desired state

by measuring Bell inequalities

Untrusted “quantum satellite”!J. Yin et al., Science (2017)

Untrusted repeater = … + Entanglement

Trusted repeater = Quantum superposition + Measurement

Quantum Satellite: Untrusted repeater

Problems of satellite communications

Keep fibers?

Expensive

Weather dependent

Intermittent

Outline

How to overcome fiber losses?

In classical communications

Repeater

No-cloning theorem

Quantum amplifier?

+ AmplifierDivide the distance

Quantum teleportation!

Quantum teleportation

What it is.

Faster than light?

What it is NOT.

|Ψ′⟩

|Ψ⟩

Faster than light transfer of objects

Transfer of quantum informationWithout transfer of matter.

|Ψ⟩|Ψ⟩

|Ψ⟩

Classical information

Quantum teleportation

|Ψ′⟩

Ψ± =1

200 ± 11

Bell state measurement(BSM)

20𝑎0𝑏 + 1𝑎1𝑏

Φ± =1

201 ± 10

|Ψ⟩|Ψ⟩

Quantum teleportation (math)

Total state

|𝜙⟩ = 𝛼 01 + 𝛽|11⟩ ⊗ 0203 + 1213 )State to transfer𝜓 = 𝛼 01 + 𝛽|11⟩

Ψ+ = 0203 + |1213⟩Shared entangled state

Ψ12± = 0102 ± 1112

Φ12± = 0112 ± 1102

Bell state measurement

Φ12− → 𝜓3 = −𝛽 03 + 𝛼 13 = 𝑍𝑋|𝜓⟩

Measurement outcome:

|Ψ12− ⟩ → 𝜓3 = 𝛼 03 − 𝛽 13 = 𝑍|𝜓⟩

|Ψ12+ ⟩ → 𝜓3 = 𝛼 03 + 𝛽 13 = |𝜓⟩

Φ12+ → 𝜓3 = 𝛽 03 + 𝛼 13 = 𝑋|𝜓⟩

Classical information

𝑑𝑒𝑓 𝑡𝑒𝑙𝑒𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛 𝑞 :𝑞𝑎 , 𝑞𝑏 = 𝑏𝑒𝑙𝑙()𝑏1, 𝑏2 = 𝑎𝑙𝑖𝑐𝑒 𝑞𝑎 , 𝑞 = 𝑏𝑒𝑙𝑙_𝑚𝑒𝑎𝑠(𝑞𝑎 , 𝑞)𝑟𝑒𝑡𝑢𝑟𝑛 𝑏𝑜𝑏(𝑞𝑏 , 𝑏1, 𝑏2)

𝑞𝑏

𝑞𝑎

Alice H

𝑎𝑙𝑖𝑐𝑒 𝑞𝑎, 𝑞

𝑏𝑜𝑏(𝑞𝑏,𝑏1, 𝑏2)

𝑏𝑒𝑙𝑙()

𝑏1|Ψ⟩

|Ψ⟩

Entanglement Swapping

Teleporting half of an entangled state?

Ψ12+ ⊗ |Ψ34

+ ⟩BSM (2,3)

Ψ14± 𝑜𝑟|Φ14

± ⟩

Dividing the distance

𝑑𝑒𝑓 𝑒𝑛𝑡𝑎𝑛𝑔𝑙𝑒𝑚𝑒𝑛𝑡_𝑠𝑤𝑎𝑝𝑝𝑖𝑛𝑔 𝑞 :𝑞𝑎 , 𝑞𝑐1 = 𝑏𝑒𝑙𝑙()𝑞𝑏 , 𝑞𝑐2 = 𝑏𝑒𝑙𝑙()𝑏1, 𝑏2 = 𝑐ℎ𝑎𝑟𝑙𝑖𝑒 𝑞𝑐1, 𝑞𝑐2 = 𝑏𝑒𝑙𝑙_𝑚𝑒𝑎𝑠(𝑞𝑐1, 𝑞𝑐2)𝑟𝑒𝑡𝑢𝑟𝑛 𝑏𝑜𝑏(𝑞𝑏 , 𝑏1, 𝑏2)

𝑞𝑏

𝑞𝑐2

𝑞𝑐1

CharlieH

𝑞𝑎Alice

2|0𝑎0𝑏⟩ + |1𝑎1𝑏⟩

Quantum relay

BSMBSM

BSM with linear optics:

Success probability of 1

𝐿0 =𝐿

𝑁𝑄𝑅

𝜂𝑡𝐿

2𝑁𝑄𝑅

= 𝑒−

𝐿2𝑁𝑄𝑅𝐿𝑎𝑡𝑡

2𝑁𝑄𝑅

= 𝜂𝑡(𝐿)

BC. Jacobs et al., Phys. Rev. A (2002)

Ingredient missing…→ a memory!

Distant spin-spin heralded entanglement

Spin-photon entanglement

↑ 0𝑝ℎ + ↓ |1𝑝ℎ⟩

“Failure”

Transfer measurement outcome

Classical signaling

Try swap entanglement

“Success”

SuccessFail

Quantum Repeater

Idea:• Include memories• Fail? → Try again! Bahskar et al., Arxiv (2019)

Briegel et al., Phys. Rev. Lett. (1998)

N. Sangouard et al., Rev. Mod. Phys.(2011)

Coherence time

How long can you store quantum information?

Quantum information is fragile

𝜓(𝑡) = 𝛼 0 + 𝛽𝑒𝑖𝛿𝜃(𝑡)|1⟩

Environment

𝜓(𝑡) = 𝛼 0 + 𝛽|1⟩

Induce errors

Store info for limited time 𝑇2

Error correctionL. Jiang et al., Phys. Rev. A (2009)

Quantum memory multiplexingCollins et al., Phys Rev Lett. (2007)

Entanglement purification

JW. Pan et al., Nature (2001)

W. Dür et al., Phys. Rev. A (1999)

Plenty of proposals

Munro et al., Nat. Phys. (2012)

Hosegawa et al., Nat. Comm. (2019)

F. Ewert et al., Phys. Rev. Lett. (2016)

K. Azuma et al., Nat. Comm. (2015)

Not using quantum memories(Error correction instead)

Childress et al., Phys. Rev. Lett. (2006)

Collins et al., Phys Rev Lett. (2007)

S. Muralidharan et al., Phys. Rev. Lett. (2014)

Using quantum memories

Rozpcedek et al., Phys. Rev. A (2019)

S. Muralidharan et al., Sci. Rep. (2016)

Outline

Secure computation

𝑓(|𝑥⟩) = ? ? ?

Personal data

Algorithm Solution |𝑦⟩

Quantum algorithm

IBM Quantum computer

Problem: No Quantum computational power

Alice:• Alice don’t want anybody to learn about

what she is doing. (𝑓, 𝑥 , 𝑦 )• Alice want to check that she’s receiving

the right solution.

Towards quantum internet: Today

Quantum channel

Classical channel

𝑓, |𝑥⟩

|𝑦⟩𝑓 |𝑥⟩|𝑦⟩𝑓 |𝑥⟩Knows

𝑦 = 𝑓(|𝑥⟩)

Can you do better?(IBM still knows everything!)

Quantum channel

Towards quantum internet: Future

Classical channel

|𝑥⟩

|𝑦⟩𝑓 |𝑥⟩Knows

𝑦 = 𝑓(|𝑥⟩)𝑦

Q Teleportation

IBM does not know your personal information but knows 𝑓.

Can we do better?

Universal Blind Quantum Computation

Classical channel

𝑓, |𝑥⟩

|𝑦⟩𝑓 |𝑥⟩Knows

𝑦 = 𝑓(|𝑥⟩)𝑦

Q TeleportationQuantum channel

JF. Fitzsimons, npj QI (2017)

A. Broadbent et al., IEEE. (2009)

IBM knows nothing!Alice can check if IBM is cooperating

(|𝑦⟩ is the right answer)

Alice don’t need to trust IBM to work with it!

Building blocks of a quantum internet

User with different capacities

UQRTQR

Quantum Repeaters

Fibers

Challenges

Routing quantum information

Find common language

Sharing the network

Complex topology

Different devices/technology

AsynchronousResource-efficientInhomogeneity: different distances and resourcesTake into account errors

R. Van Meter Quantum networking (2014)

Outline

QKD and trusted repeater network

M. Lucamarini, Optics Express (2013)

Detector Telecom fiber

Attenuatedlaser

Qubit encoding

Qubit decoding

Columbus (OH)

Soccer World CupSouth Africa 2010

Source of single photons

Multiplexing

Quantum emitters

Heralded single photon source

Spontaneous ParametricDownConversion (SPDC) sources

F. Kaneda and PG. Kwiat, Science. Advances (2019)

ME. Reimer and C. Cher, Nat. Photonics (2019)

Quantum dot

Conduction band

Valence band

N. Somaschi et al., Nat. Photonics (2016)

Low single-photon probability

Source of entangled photons

Quantum emitters

Quantum dot

Conduction band

Valence band

2|𝐻𝑠𝑉𝑖⟩ + |𝑉𝑠𝐻𝑖⟩

Low probability source of entangled photons

Hui Wang et al., Phys. Rev. Lett. (2019)

A. Beveratos et al., Eur. Phys. J. D (2014)

“Natural” quantum memories

Trapped ions

Requirements:• Entanglement with photons• Long-lived

C. Monroe et al., Phys. Rev. A (2014)

Long-lived memories (>1min)

Experimentally difficult to manipulate…

Atomic ensembles

N. Sangouard et al., Rev. Mod. Phys. (2011)

Not “real” qubitsStrong light-matter interactions Light-matter interactions enhanced by cavities

Solid-state quantum memories

Short-lived memories…

Charged Quantum dotsDefects in diamonds

Distant spin-spin entanglement

Long-lived quantum memory (≈ 1𝑠)

B. Hensen et al., Nature (2015)

Photon conversion

Most quantum emitters emits optical single photons

(visible or NIR)

Low-loss fiber= telecom wavelength (1.5µm)

A. Dréau et al., Phys. Rev. App. (2018)

Conclusion Part 1

Blind quantum computing:• Collaboration without trust• Entanglement

Quantum network

Quantum Key Distribution• First application of QIT• Quantum superposition + measurement• Small trusted network

Applications on privacy (but not only)

Can be a trusted oruntrusted network

Long-distance quantum communications

Via Quantum repeater(with entanglement swapping)

Via Satellite (free space)

Require multiple building blocksThat communicate together

Questions?

Outline

To show that you are able to read state-of-the-art QC papers now!

To learn more about quantum communications (QC)

Outline

“Experimental demonstration of memory-enhanced quantum communication”, M. Bhaskar et al., ArXiv (2019)

“Satellite-based entanglement distribution over 1200 kilometers”, J. Yin et al., Science (2017)

Presentation Bhaskar et al. (2019)

Impressive results!Combination of QKD and quantum repeaters.Illustrate the variety of quantum protocol schemes

Why this paper?

Prepare:|±⟩ or |𝑖±⟩

Measure

QuantumMemory

Prepare:|±⟩ or |𝑖±⟩

Features:• Only one quantum memory • Cannot be cascaded (no entanglement swapping)• Works only for QKD• The memory sends receives the photons• Time-bin photon encoding / attenuated laser

Protocol

Quantum memory node

Quantum memory node:• SiV center 𝑆 = 1/2• Embedded in a cavity• With a measurement device

1 = |𝑙𝑎𝑡𝑒⟩

0 = |𝑒𝑎𝑟𝑙𝑦⟩

Photonic qubit:Time-bin encoding

Cavity-mediated spin-photon interaction

Eigenstates: polaritons (𝜔𝑐 = 𝜔𝑠)𝐸± = 𝜔 ± 𝑔

| ↑⟩| ↓⟩

Cavity-QED (with a two-level system):𝐻 = 𝜔𝑐𝑎†𝑎 + 𝜔𝑠𝜎

+𝜎− + 𝑔(𝜎+𝑎 + 𝜎−𝑎†)

𝐸− 𝐸+

2𝑒𝑎𝑟𝑙𝑦 + 𝑒𝑖𝜙1 𝑙𝑎𝑡𝑒

2↑ + ↓

2↓ +𝑚1𝑚2𝑒

𝑖𝜙2+𝜙1 ↑

2↓ 𝑒𝑎𝑟𝑙𝑦 + 𝑒𝑖𝜙1 ↑ 𝑙𝑎𝑡𝑒

2↓ + 𝑚1𝑒

𝑖𝜙1 ↑

After the second photon

Spin measurement in X basis:𝑚3

If 𝜙1 + 𝜙2 ∈ 0, 𝜋 :1

2↑ ± ↓

→ Asynchronous BSM(𝑚1𝑚2𝑚3 = ±1)

Performances

Overall quantum bit error:𝑄𝐵𝐸𝑅 = 0.097 ± 0.006

Cavity-QED:𝐶 = 105 ± 11

Fidelity:𝐹 = 0.944 ± 0.008

≤ 0.110 Unconditional security

≤ 0.146 Secure against individual attacks

70𝑑𝐵 → 350 𝑘𝑚 of telecom fiber

Entanglement efficiency:𝜂 = 0.423 ± 0.004

4x improvement

Outline

“Experimental demonstration of memory-enhanced quantum communication”, M. Bhaskar et al., ArXiv (2019)

“Satellite-based entanglement distribution over 1200 kilometers”, J. Yin et al., Science (2017)

Presentation J. Yin et al. (2017)

Record of length for provably secure communicationsIllustration of the E91 protocol.Illustration of technological challenge

Why this paper?

Entangled photons

Producing entangled photons from space

Laser pump

Source

Send entangled photon from space

Requirement of a tracking system

ATP tracking system

Beam divergence 1.2mrad

Photon detection

Verifying the satellite is not cheating

Set detectionbasis

Look at the Bell inequalityviolation

𝑆 = |𝐸(𝜙 1 , 𝜙 2 ) – 𝐸(𝜙 1 , 𝜙 2 ′) + 𝐸(𝜙 1 ′, 𝜙 2 ) + 𝐸(𝜙 1 ′, 𝜙 2 ′)| ≤ 2

𝑆 = 2.37 ± 0.09

Conclusion

Distribution of entanglement over 1200 km12-18 orders of magnitude improvement compared to direct fibered transmission

Rate > 1𝐻𝑧

Only working 275s per day

Fidelity 86.9 ± 8.5%

Thank you!

Quantum Communication Networks and Quantum repeaters...4 What is Quantum Communication? “Quantum...

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