recent progress on measurement-device-independent (mdi)...
TRANSCRIPT
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Copyright 2018, Toshiba Corporation
Recent progress on
Measurement-Device-Independent (MDI)
Quantum Key Distribution (QKD)
Marco Lucamarini
Quantum Information Group
Cambridge Research Laboratory
Toshiba Research Europe Ltd
QCrypt 2018
Shanghai, China
27-31 August 2018
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ML’s video lecture on MDI-QKD
1st QCall school (2018, Baiona, Spain)
http://tv.uvigo.es/matterhorn/36609
Joshua Slater’s tutorial on MDI-QKD
QCrypt 2014 (Paris, France)
https://youtu.be/WL7OPSO0s_s
A couple of useful links
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QKD
MDI QKD - Notation
MDI-QKD
CharlieBELL MEASUREMENT
EPR SOURCE
MEASUREMENT
SOURCE/
TRANSMITTER
DETECTOR/
RECEIVER
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1. Motivation and Introduction of MDI-QKD
• Detector vulnerabilities and trusted networks
• Basic features of MDI-QKD
2. MDI-QKD origin and working mechanism
• Optical Interference
• Entanglement swapping
3. Experiments
4. Variants
• Twin-Field QKD
Outline of this tutorial
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1. Motivation and Introduction of MDI-QKD
• Detector vulnerabilities and trusted networks
• Basic features of MDI-QKD
2. MDI-QKD origin and working mechanism
• Optical Interference
• Entanglement swapping
3. Experiments
4. Variants
• Twin-Field QKD
Outline of this tutorial
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Motivation 1: Implementation Security
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Motivation 1: Implementation Security
Typical fibre-based one-way QKD setup
CAUTION
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Most targeted components
ArXiv:1505.05303.
Nature Photonics 8, 595-604 (2014).
It would be good to remove assumptions from detectors in QKD MDI-QKD
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Residential
Hospital
Bank
Backbone Network
(between cities)
Metro Network (within a city)
Access Network
(within a community)
Typical architecture
Office
Problem: the central node needs to be trusted
It would be good to connect the users via untrusted nodes MDI-QKD
Motivation 2: Trusted-node Networks
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Phys. Rev. X
6, 011024 (2016)
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• 8-by-4 mechanical optical switch to route the three users to the relay
• randomly switch any two users to the relay every two hours
13:40: Invited: Large scale quantum network in China by Yu-Ao
Chen
Phys. Rev. X
6, 011024 (2016)
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MDI/QKD Reconfigurable Network
3 nodes, 3 links
(fully connected network)3 nodes, 3 links
(1 relay)
3 nodes, 2 links
(1 relay/node)
Reconfigurable
network
Switch between
QKD and MDI-QKD
Fully connected network with N+1 nodes
N(N+1)/2 physical links
Fully connected MDI-QKD network with N+1 nodes
N physical links
MDI-QKD well matches star networks: it connects all the nodes with a
minimum amount of optical links
See also the 11:25 am talk by Mike Wang
“Enabling a scalable high-rate MDI-QKD network: theory and experiment”.
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OLT (node)ONU (user endpoints)
Z
X
QKD/Trusted node MDI-QKD/Untrusted node
OLT (node)ONU (user endpoints)
Z
Z
MDI/QKD Reconfigurable Network
G. L. Roberts et al., Nature Communications 8, 1098 (2017).
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MDI/QKD Reconfigurable Network
real fibre
QKD ~ Mb/s
MDI-QKD ~ 10 kb/s
G. L. Roberts et al., Nature Communications 8, 1098 (2017).
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MDI-QKD
Any detector vulnerability is removed
Users are linked by an untrusted relay
Operational range is longer than QKD
The key rate is smaller than QKD
Pros & Cons
Measurement-device-independent (MDI) QKD
Charlie
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MDI-QKD
Any detector vulnerability is removed
Users are linked by an untrusted relay
Operational range is longer than QKD
The key rate is smaller than QKD
Pros & Cons
Measurement-device-independent (MDI) QKD
If we consider the progress
in the last 4 months we
have to revise the last
statement
Charlie
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MDI-QKD
Any detector vulnerability is removed
Users are linked by an untrusted relay
Operational range is longer than QKD
The key rate is smaller than QKD for
standard MDI-QKD, not for Twin-Field QKD
Pros & Cons
Measurement-device-independent (MDI) QKD
Charlie
If we consider the progress
in the last 4 months we
have to revise the last
statement
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1. Motivation and Introduction of MDI-QKD
• Detector vulnerabilities and trusted networks
• Basic features of MDI-QKD
2. MDI-QKD origin and working mechanism
• Optical Interference
• Entanglement swapping
3. Experiments
4. Variants
• Twin-Field QKD
Outline of this tutorial
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1. Motivation and Introduction of MDI-QKD
• Detector vulnerabilities and trusted networks
• Basic features of MDI-QKD
2. MDI-QKD origin and working mechanism
• Optical Interference
• Entanglement swapping
3. Experiments
4. Variants
• Twin-Field QKD
Outline of this tutorial
![Page 20: Recent progress on Measurement-Device-Independent (MDI) …2018.qcrypt.net/wp-content/uploads/2018/slides/Wednesday/01.Mar… · Hong-Ou-Mandel interference. Phase-encoding MDI-QKD](https://reader036.vdocuments.mx/reader036/viewer/2022081410/60a3118d9267be704f4a1398/html5/thumbnails/20.jpg)
Simple interferometric MDI-QKD scheme
BobAlice
CharlieEve
security perimeter
1 v
1v + v1 / 2
𝜑𝑏𝜑𝑎
𝑃1 =1 + cos 𝜑𝑎 − 𝜑𝑏
2𝑃2 =
1 − cos 𝜑𝑎 − 𝜑𝑏
2𝜋0
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Simple interferometric MDI-QKD scheme
BobAlice
CharlieEve
security perimeter
1 v
1v + v1 / 2
𝜑𝑏 = {0, 𝜋}𝜑𝑎 = {0, 𝜋}
𝑃1 =1 + cos 𝜑𝑎 − 𝜑𝑏
2𝑃2 =
1 − cos 𝜑𝑎 − 𝜑𝑏
2𝜋0
1) Detectors are outside the security perimeter
2) The relay is untrusted
With this scheme we achieve the MDI goals:
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Simple interferometric MDI-QKD scheme
BobAlice
CharlieEve
security perimeter
1 v
1v + v1 / 2
𝜑𝑏 = {0, 𝜋}𝜑𝑎 = {0, 𝜋}
𝑃1 =1 + cos 𝜑𝑎 − 𝜑𝑏
2𝑃2 =
1 − cos 𝜑𝑎 − 𝜑𝑏
2𝜋0
However, how do we distribute the entangled state to distant parties?
We start from separable states and then use entanglement swapping.
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Phase-encoding MDI-QKD
𝐼1 = 𝛼 2 1 + cos 𝜑𝑎 − 𝜑𝑏
Alice Bob
𝜋0
CharlieEve
𝛼𝑒𝑖𝜑𝑎 𝛼𝑒𝑖𝜑𝑏
𝛼 ≈ 𝑒−𝛼 2
2 v + 𝛼 1 for 𝛼 ≪ 1
𝐼2 = 𝛼 2 1 − cos 𝜑𝑎 − 𝜑𝑏
𝛼 𝛽 ≈ 𝑒−𝛼 2+ 𝛽 2
2 v v + 𝛼 1 v + 𝛽 v 1 + 𝛼𝛽 1 1
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𝛼𝑒𝑖𝜑𝑎 𝛼𝑒𝑖𝜑𝑏
phase locked!
Limitations:
1) needs phase stabilization
2) limited distance
ArXiv:1111.3413. Also @ Phys. Rev. A 85, 042307 (2012).
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Phase-encoding MDI-QKD
Alice Bob
𝜋0
CharlieEve
𝛼𝑒𝑖𝜑𝑎 𝛼𝑒𝑖𝜑𝑏
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Phase-encoding MDI-QKD
Alice Bob
𝜋0
CharlieEve
1 1
separable states,
without any phase relation
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Phase-encoding MDI-QKD
Alice Bob
CharlieEve
1 1
separable states,
without any phase relation
Hong-Ou-Mandel interference
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Phase-encoding MDI-QKD
Alice Bob
CharlieEve
1 1
separable states,
without any phase relation
Hong-Ou-Mandel interference
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Phase-encoding MDI-QKD
Alice Bob
CharlieEve
1 1
Hong-Ou-Mandel interference
It is not easy to perfectly generate the states 1 , but we have approximations:
1. Heralding single-photon sources
2. Coherent states and decoy-state technique
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• S. Pirandola et al., Nature Photon. 9, 397 (2015)
• F. Xu et al., Nature Photon. 9, 772 (2015)
• S. Pirandola et al., Nature Photon. 9, 773 (2015)
ArXiv:quant-ph/9604021. Also @ Phys. Rev. A 54, 2651 (1996).Private spaces
ArXiv:1109.2330. Also @ Phys. Rev. Lett. 108, 130502 (2012).
1 1 1 1
Algorithmica 34, 340 (2002)
Schemes with heralding single photons
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ArXiv:1109.1473. Also @ Phys. Rev. Lett. 108, 130503 (2012).
1 1
Phase randomization + Decoy states
0
2𝜋 𝑑𝜑
2𝜋 𝛼𝑒𝑖𝜑 𝛼𝑒𝑖𝜑 =
𝑛𝑝𝑛 𝑛 𝑛
Privacy amplification
to “postselect” 1 1
𝛼𝑒𝑖𝜑𝑎 𝛼𝑒𝑖𝜑𝑏 𝜑𝑎 and 𝜑𝑏 are random variables
Scheme using coherent decoy states
encoding is done using polarization
intensity |𝛼|2 is varied for decoy states
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First MDI-QKD key rate
unknownknownmeasured
Decoy states
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First MDI-QKD key rate, finite size effects
Finite-size
M. Curty et al.,
Nature Commun. 5, 3732 (2014)
unknownknownmeasured
Decoy states
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𝒁 𝑿
𝒖 𝒗 𝒘 𝒖 𝒗 𝒘
𝒁
𝒖 𝑝𝑍𝑍𝑢𝑢 𝑝𝑍𝑍
𝑢𝑣 𝑝𝑍𝑍𝑢𝑤 𝑝𝑍𝑋
𝑢𝑢 𝑝𝑍𝑋𝑢𝑣 𝑝𝑍𝑋
𝑢𝑤
𝒗 𝑝𝑍𝑍𝑣𝑢 𝑝𝑍𝑍
𝑣𝑣 𝑝𝑍𝑍𝑣𝑤 𝑝𝑍𝑋
𝑣𝑢 𝑝𝑍𝑋𝑣𝑣 𝑝𝑍𝑋
𝑣𝑤
𝒘 𝑝𝑍𝑍𝑤𝑢 𝑝𝑍𝑍
𝑤𝑣 𝑝𝑍𝑍𝑤𝑤 𝑝𝑍𝑋
𝑤𝑢 𝑝𝑍𝑋𝑤𝑣 𝑝𝑍𝑋
𝑤𝑤
𝑿
𝒖 𝑝𝑋𝑍𝑢𝑢 𝑝𝑋𝑍
𝑣𝑢 𝑝𝑋𝑍𝑤𝑢 𝑝𝑋𝑋
𝑢𝑢 𝑝𝑋𝑋𝑢𝑣 𝑝𝑋𝑋
𝑢𝑤
𝒗 𝑝𝑋𝑍𝑢𝑣 𝑝𝑋𝑍
𝑣𝑣 𝑝𝑋𝑍𝑤𝑣 𝑝𝑋𝑋
𝑣𝑢 𝑝𝑋𝑋𝑣𝑣 𝑝𝑋𝑋
𝑣𝑤
𝒘 𝑝𝑋𝑍𝑢𝑤 𝑝𝑋𝑍
𝑣𝑤 𝑝𝑋𝑍𝑤𝑤 𝑝𝑋𝑋
𝑤𝑢 𝑝𝑋𝑋𝑤𝑣 𝑝𝑋𝑋
𝑤𝑤
The original decoy-state MDI-QKD adopts
2 bases (𝑋, 𝑍) and 3 independent intensities
(𝑢, 𝑣, 𝑤) 36 combinations
Data used in the decoy-state parameter
estimation, relevant for finite-size effects
Decoy states and finite size effect
ArXiv:1502.01262.
Also @ Phys. Rev. A 93, 042324 (2016).
4-intensity protocol
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𝒁 𝑿
𝒔 𝒖 𝒗 𝒘
𝒁 𝒔 𝑝𝑍𝑍𝑠𝑠 𝑝𝑍𝑋
𝑠𝑢 𝑝𝑍𝑋𝑠𝑣 𝑝𝑍𝑋
𝑠𝑤
𝑿
𝒖 𝑝𝑋𝑍𝑢𝑠 𝑝𝑋𝑋
𝑢𝑢 𝑝𝑋𝑋𝑢𝑣 𝑝𝑋𝑋
𝑢𝑤
𝒗 𝑝𝑋𝑍𝑣𝑠 𝑝𝑋𝑋
𝑣𝑢 𝑝𝑋𝑋𝑣𝑣 𝑝𝑋𝑋
𝑣𝑤
𝒘 𝑝𝑋𝑍𝑤𝑠 𝑝𝑋𝑋
𝑤𝑢 𝑝𝑋𝑋𝑤𝑣 𝑝𝑋𝑋
𝑤𝑤
• This protocol was first implemented in Comandar et al., Nature Photon. 10, 312 (2016),
where its composable security is proven and the highest MDI-QKD key rate is achieved.
• Then it was implemented in Yin et al., Phys. Rev. Lett. 117, 190501 (2016),
to achieve the longest fibre-based MDI-QKD transmission.
The new protocol(*) adopts 2 bases (𝑋, 𝑍) and 4
coupled intensities (𝑠; 𝑢, 𝑣, 𝑤) 16 combinations
ArXiv:1502.01262.
Also @ Phys. Rev. A 93, 042324 (2016).
Decoy states and finite size effect
4-intensity protocol
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Equivalent description with Time Bins
Polarization
Time bin
BS 1
1
Time
E L
Ψ12(−)
Ψ12(+)
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1. Motivation and Introduction of MDI-QKD
• Detector vulnerabilities and trusted networks
• Basic features of MDI-QKD
2. MDI-QKD origin and working mechanism
• Optical Interference
• Entanglement swapping
3. Experiments
4. Variants
• Twin-Field QKD
Outline of this tutorial
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1. Motivation and Introduction of MDI-QKD
• Detector vulnerabilities and trusted networks
• Basic features of MDI-QKD
2. MDI-QKD origin and working mechanism
• Optical Interference
• Entanglement swapping
3. Experiments
4. Variants
• Twin-Field QKD
Outline of this tutorial
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Watch Joshua Slater’s talk @ QCrypt 2014 website
https://youtu.be/WL7OPSO0s_s
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%
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Also @ Phys. Rev. Lett. 113, 190501 (2014)
@ 100 km, 3 kbps
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Key rate performance gap of MDI-QKD
State of the art up to 2015
[18] Y-L Tang et al, Phys. Rev. Lett. 2014. [19] R Valivarthi et al, J. Mod. Opt. 2015.
[14] A Rubenok et al, Phys. Rev. Lett. 2013. [16] T Ferreira da Silva et al, Phys. Rev. A 2013.
• In May 2016 the key rate was improved
• In June 2016 the distance was extended
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Experimental setup and novel light source
(*) L. Comandar et al., Nature Photon. 10, 312 (2016)
Phase randomisedIndistinguishable
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Going high-rate
(*)
(*) L. Comandar et al., Nature Photon. 10, 312 (2016)
Increased key rate in 2016
[18] Y-L Tang et al, Phys. Rev. Lett. 2014. [19] R Valivarthi et al, J. Mod. Opt. 2015.
[14] A Rubenok et al, Phys. Rev. Lett. 2013. [16] T Ferreira da Silva et al, Phys. Rev. A 2013.
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MDI-QKD: Finite sample size included
Finite-size MDI-QKD
Finite-size QKD
X. Ma et al, Phys. Rev A 2012M. Curty et al, Nat. Comm. 2014
4-intensity protocol
in Y.-H. Zhou et al.,
Phys. Rev. A 93,
042324 (2016)
refined and used
(*) L. Comandar et al., Nature Photon. 10, 312 (2016)
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ArXiv:1606.06821.
Phys. Rev. Lett.
117, 190501 (2016).
Going long distance
• Phase randomised WCP
• Time bin encoding and 4 intensities for decoy states
• 5 IMs in each user! 1 pulse shaping, 2 decoys, 2 time-bin encoding (ToA)
• 3 months: 2584 bits (0.00034 bits/s), no EC, no PA
• Detectors: SNSP efficiency 65%, dark counts 30 Hz
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Going long distance
(*) H.-L. Yin et al., arXiv:1606.06821. Also @ Phys. Rev. Lett. 117, 190501 (2016).
Longest fibre-based secure quantum communication until recently
Still the longest distance for experimental fibre-based MDI-QKD
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QKD
MDI
QKD
𝜂chan𝜂det
𝑝dark
𝜂chan𝜂chan
𝜂det, 𝑝dark
𝑁
𝑆≈
𝑝dark
𝜂chan𝜂det
𝑁
𝑆≈
2𝑝dark
𝜂chan𝜂det
Long distance performance of MDI QKD
How far can we go with a decent key rate?
see N. Gisin et al., Rev. Mod. Phys. 74, 145 (2002)
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1. Motivation and Introduction of MDI-QKD
• Detector vulnerabilities and trusted networks
• Basic features of MDI-QKD
2. MDI-QKD origin and working mechanism
• Optical Interference
• Entanglement swapping
3. Experiments
4. Variants
• Twin-Field QKD
Outline of this tutorial
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1. Motivation and Introduction of MDI-QKD
• Detector vulnerabilities and trusted networks
• Basic features of MDI-QKD
2. MDI-QKD origin and working mechanism
• Optical Interference
• Entanglement swapping
3. Experiments
4. Variants
• Twin-Field QKD
Outline of this tutorial
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Fundamental limit of QKD
“PLOB” bound
𝑆𝐾𝐶 𝜂 = log2
1
1 − 𝜂
“TGW” bound for the secret key capacity (SKC)
𝑆𝐾𝐶 𝜂 ≤ log2
1 + 𝜂
1 − 𝜂
In a point-to-point configuration it is impossible to overcome the SKC bounds
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DV-QKD
CV-QKD
MDI-QKD
repeater-less
bounds
∝ 𝜂
𝜂1/3
𝜂1/4
𝜂1/2
TGW
PLOB
sp QKD
dec QKD
sp MDI
dec MDI
See 14:15 talk by Alberto Boaron:
“2.5 GHz clocked QKD over 379 km”
Can we go beyond the direct-link bounds?
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C. Panayi, M. Razavi, X. Ma, N. Lütkenhaus
Other solutions
ArXiv:1306.3095. Also @
Phys. Rev. A 89, 012301 (2014)
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single
photons
single
photons
Other solutions
The implementation of these schemes is still challenging!
It turns out that we can overcome the direct-link
bounds with a scheme nearly as simple as MDI-QKD
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CharlieIM
VOA
LS
𝜑𝑎PM
𝜇𝑎
Alice
𝛿𝑎 𝛿𝑏
RN
G
IM
VOA
LS
𝜑𝑏 PM
𝜇𝑏
Bob
RN
G0 1
PM
phase locking
global phase randomisation
Twin-Field QKD
𝛼𝑒𝑖𝜑𝑎 𝛼𝑒𝑖𝜑𝑏
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CharlieIM
VOA
LS
𝜑𝑎PM
𝜇𝑎
Alice
𝛿𝑎 𝛿𝑏
RN
GIM
VOA
LS
𝜑𝑏 PM
𝜇𝑏
Bob
RN
G0 1
PM
Twin-Field QKD
phase locking
global phase randomisation
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CharlieIM
VOA
LS
𝜑𝑎PM
𝜇𝑎
Alice
𝛿𝑎 𝛿𝑏
RN
GIM
VOA
LS
𝜑𝑏 PM
𝜇𝑏
Bob
RN
G0 1
PM
global phase randomisation
phase locking
Twin-Field QKD
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CharlieIM
VOA
LS
𝜑𝑎PM
𝜇𝑎
Alice
𝛿𝑎 𝛿𝑏
RN
GIM
VOA
LS
𝜑𝑏 PM
𝜇𝑏
Bob
RN
G0 1
PM
discard
phase locking
global phase randomisation
Twin-Field QKD
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CharlieIM
VOA
LS
𝜑𝑎PM
𝜇𝑎
Alice
𝛿𝑎 𝛿𝑏
RN
GIM
VOA
LS
𝜑𝑏 PM
𝜇𝑏
Bob
RN
G0 1
PM
phase locking
global phase randomisation
Twin-Field QKD
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CharlieIM
VOA
LS
𝜑𝑎PM
𝜇𝑎
Alice
𝛿𝑎 𝛿𝑏
RN
GIM
VOA
LS
𝜑𝑏 PM
𝜇𝑏
Bob
RN
G0 1
PM
These fields are twins: accept!
The users end up in a situation similar to decoy-state QKD,
but with a twice-as-long fibre in between
phase locking
global phase randomisation
Twin-Field QKD
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DV-QKD
CV-QKD
MDI-QKD
repeater-less
bounds
∝ 𝜂
𝜂1/3
𝜂1/4
𝜂1/2
TGW
PLOB
sp QKD
dec QKD
sp MDI
dec MDI
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DV-QKD
CV-QKD
MDI-QKD
TGW
PLOB
sp QKD
dec QKD
sp MDI
dec MDI
repeater-less
bounds
∝ 𝜂
𝜂1/3
𝜂1/4
𝜂1/2
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Very recent (and very promising) progress
• 15 May X. Ma, P. Zeng & H. Zhou, “Phase-matching QKD”,
arXiv:1805.05538. Also @ Phys. Rev. X 8, 031043 (2018).
• 15 May K. Tamaki, H.-K. Lo, W. Wang & ML, “IT security of QKD overcoming
the repeaterless secret key capacity bound”, arXiv:1805.05511.
• 28 May X.-B. Wang, Z.-W. Yu & X.-L. Hu, “Sending or not sending:
Twin-Field QKD with large misalignment error”, arXiv:1805.09222.
• 6 July C. Cui, Z.-Q. Yin, R. Wang, W. Chen, S. Wang, G.-C. Guo & Z.-F. Han,
“Phase-matching QKD without phase post-selection”, arXiv:1807.02334.
• 19 July M. Curty, K. Azuma & H.-K. Lo, “Simple security proof of Twin-Field
type QKD protocol”, 1807.07667.
• 26 July J. Lin & N. Lütkenhaus, “A simple security analysis of phase-matching
MDI-QKD”, 1807.10202.
See next talk (10:50 am) by Pei Zeng: “Global Phase Encoding QKD”
See Poster 14
See Poster 99
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𝜂1/2
𝜂1/3
𝜂1/4
Curty et al, arXiv:1807.07667 (10 Hz)
Jin & Lutkenhaus, arXiv:1807.10202 (80 Hz)
Cui et al, arXiv:1807.02334 (80 Hz)
Wang et al, arXiv:1805.09222 (10 Hz)
Ma et al, PRX 8, 031043 (2018) (80 Hz)
Tamaki et al, arXiv:1805.05511 (10 mHz)
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CW laserpolarisation
controlvariable length
optical fibres detectors
interfering
beam
splitter
beam
splitter
variable
optical
attenuators
Alice
Bob
Phase drift: 𝛿𝑏 − 𝛿𝑎 =2𝜋
𝑠∆𝑣 𝐿 + 𝑣 ∆𝐿
With 6 rad/ms, a feedback
every ~50 µs is necessary
to make the optical error
rate lower than 3%
fibre spools: up to 275 km each
Twin-Field QKD Feasibility
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Conclusions
MDI-QKD is only 6 year-old, but we already have impressive results
in terms of performance (key rate, distance) and functionalities
(untrusted-node networks). This means the community is strong
and responsive to innovations.
The research on MDI-QKD has led to developments like
o all-optical quantum repeaters
o coherent-state HOM interference
o optically-injected laser sources for quantum communications
o refined control techniques for the in-field implementations.
The (MDI) Twin-Field QKD allows us to overcome a bound considered
unsurmountable without quantum repeaters. New techniques for
quantum communications are likely to be imported from other fields.
The path to MDI Quantum Information has just started and we can
expect many more surprising and exciting results along the way!
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James DynesZhiliang Yuan Andrew Shields
George RobertsMirko PittalugaMariella Minder
MDI-QKD team at TREL
…and to you for your attention!
Thanks to…