Quantum Communication Part 2 : Quantum Receiver · 2018-01-16 · 30/09/15 2 Outline 1.Optical...

30/09/15

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Fiber Optics: Light in Action from Science to Technology

Sept/Oct2015U. Fort Hare, Alice/Hogsback, South Africa

Philippe Gallion

Telecom ParisTech, Ecole Nationale Supérieure des TélecommunicationsCentre Nationale de la Recherche Scientifique, LTCI

Paris, France

Quantum CommunicationPart 2 : Quantum Receiver

1

Outline

1. Optical signal at quantum levels2. Quantum receivers3. Homodyne receiver v.s. photon counting4. Phase control5. Conclusion

Quantum Communication Part 2 : Quantum Receiver Philippe Gallion 2

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Outline



1

0✔  State superposition

❏  0 and 1 at the same time❏  IQB > =α I0> + β I1>

✔  One of the 2 eigenstates is obtained after a measurement❏  IαI2 is the probability to obtain I0> IαI2+ IβI2= 1

✔  Measurement destroys the superposition❏  Quantum demolition

✔  Non cloning unknown state

✔  Information must supported by quantum system❏  Ensemble systems average out the quantum behavior

1

0Quantum Bit (QB) Classical bit

Quantum Bit

Security !


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100km

1photon/ms

1mm radiuspinhole

Single photon energy

✔ Big as compared to the thermal one

❏  In the visible range❏ At fiber telecommunication wavelength

✔ But hard to be directly observed

q Standard old light bulb 100W q Energy efficiency 10%q Distance: 100kmq Pine hole:1mm

1 photon in each millisecond !

€

hν ≈100kT


hν ≈ 40kT

One photon per ms!

Quantum Communication Part 2 : Quantum Receiver Philippe Gallion

Single Photon Sourceü  Reliable single photon sources not yet available

q  Emitting one and only one photon only on requestü  Fainted Poisonnian coherent optical pulses

ü  Multi photon pulses are an opportunity for Eveq  Photon Number Splitting Attack (PNS)

ü  Fainting the pulses leads to empty pulse occurrencesq  Erasures are waited time ( …as time go by)

ü  Trade-off between empty pulses and multiphoton pulsesq  0.2 to 0.6 photon /pulse

!0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

prob

abilit

y

photon number

<n>=0.1

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

prob

abilit

y

photon number

<n> =0.25

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

prob

abilit

y

photon number

<n> =0.50

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

prob

abilit

y

photon number

<n> =1

€

p(n) =< n >n

n!exp− < n >

6

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ü  The minimum energy of a quantized harmonic oscillator

ü  Vacuum fluctuations are independent of the signalq  They exist without signal

ü  Two quadratures equally noisy ü  Impossible to be detected aloneü  Vacuum fluctuations are non elusive

q  Already present at any (evenly unused or hidden!) optical inputq  Provided free of charge at any port of any device

ü  Coherent stateq  Nearly classicalq  Classical determinist wave + vacuum fluctuationq  Produced by good lasersq  Nearly Additional White Gaussian (Circular) Noise

Poisson intensity fluctuationPhase noise

Vacuum fluctuations and Coherent State


En = n+ 12

!

"#

$

%&hν E0 =

hν2

for n = 0, E2

E1

EEFF0

EEFF0

E2

A

ϕE1

EEFF0

Coherent States vs Number States

✔ Single photon source (photon gun) not available so far✔ Fainted coherent state pulses easy to be produced✔ Non orthogonal coherent states may expand as a sum

of number states

✔ Two coherent states overlap

❏  Error free distinction is impossible€

α = exp(− 12α 2) α n

n!n= 0

∞

∑ n

€

α1 α22

= exp(−α1−α

2

2)


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Photons Counters

✔  Avalanche Photodiodes (APD)❏  Biased above breakdown ❏  Single photon trigger 1000 electron avalanche❏  Quenching required and recovery time

✔  Telecom wavelength (1550nm) with SMF pig tail✔  Quantum efficiency 10 to 25% (tradeoff with dark count)✔  Noise

❏  Dark counts proportional to the gated opening time : 10-4 to 10-5 /ns❏  After pulse counts : reduced by a dead time

✔  Speed❏  Gate width 2.5 to 100ns required photon arrival time control

•  Time synchronization,•  Heralded photon

❏  Gate trigger up to 8Mhz✔  Feature

❏  Cooling requires: -50°C❏  Several Kg❏  Several 10K€


Optical Fiber Constraints

ü  1500 nm wavelength mandatory for credibilityq Trial v.s. proof of concept

ü  Low photon counting efficiencyü  Stable optical IC may be used

q Modulatorq Delay line q Coupler…

ü  Polarization instability (PMD)ü  Phase modulation is nearly mandatory

10Quantum Communication Part 2 : Quantum Receiver Philippe Gallion

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ü  Their discrimination at quantum level is the key issue….Polarization Encoding Phase Encoding (QPSK)

Orthogonal states of polarization(Discrimination by polarizer)

Antipodal state of Phase

(Discrimination by interferenceor homodyne detection)

Modulation bandwidth FSK(Discrimination by filters)

Frequency Encoding

2 representations of the 2 binary symbols on 2 conjugated bases

0

0

1

1

1

0

0

1

0

1 0

1

1 Base 1

0 Base 2

0

1



Phase Encoding QKD Receiverü  Bob introduces his bases choice by clockwise or counter clockwise

constellation rotationü  Quadrature Phase Shift Keyed (QPSK) turns to Binary Phase Shift

Keyed (BPSK)

ρ̂ =14αS αS + −αS −αS + jαS jαS + − jαS − jαS( ) ρ̂ =

14αS αS + −αS −αS( )

!

OR

BPSK SignalQPSK Signal

12

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Quantum Classical channels

ü  The propagation media as nothing specialq  The information is encoded on individual quantum particleq  The information is NOT encoded on ensemble of particles

ü  Fiber systems :100km experimentsq  Polarizationq  Attenuation

Half of the photon lost (3dB) after 15 km @1550nm)ü  Free space systems :140 km experiments

q  Diffractionq  Line-of-sightq  Daylightq  Atmosphere

Turbidity, Turbulence


Outline

1. Optical signal at quantum levels2. Quantum receivers for PSK signals3. Homodyne receiver v.s. photon counting4. Phase control5. Conclusion


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ü  Information theory❏  Maximum likehood

✔  Binary Phase Shift Keyed signal❏  Antipodal signals❏  Maximize the distance at given energy❏  Minimize the overlap

✔  As compared with On-of-Keying signals❏  Signal distance is reduced per 2❏  Half of the power is saved

Helström limit

€

α −α = exp(−4NS ) with NS =α 2

€

BErrorR =121− 1− exp −4NS( )( ) ≈ 14 exp −4NS( )

p(s)

s +1 -1 0

+1 -1

€

BErrorR ≈ 14exp −2NS( )

0 is tranmitted

1 is tranmitted


✔  No splitting of signal power ✔  Same local and signal amplitudes✔  Unconditional nulling✔  Error when no photon occurs as 4Ns are expected✔  No error for the nulled signal✔  Super quantum limit✔  Twice the Standard Quantum Limit (SQL)

Idealistic single photon counter Kennedy receiver

Nearly 100%

Input signal

Local Oscillator

Photon Counter N

Nearly 0%

€

BErrorR =12exp −4NS( )

+2 0 +1 +1 -1 + =

Input signal Local Oscillator


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✔  No splitting of signal power ✔  Same local and signal amplitudes✔  Conditional nulling✔  Phase switching of LO✔  Amplitude tuning of LO✔  May reach the Helström bound

Idealistic single photon counter Dolinar receiver

Nearly 100%

Input signal

Local Oscillator

Photon Counter N

Nearly 0%

0 +1 -1 + =

Input signal Local Oscillator


✔  Same local and signal amplitude L=S✔  Half of the signal is wasted✔  Decision taken by detector outputs✔  Erasure rate

❏  No photon is received when NS is expected (Poisson)❏  May occurs for any of the 2 symbols❏  May be discarded at reconciliation in quantum cryptography❏  Turn to an half error rate without coding in digital quantum communication

2 Photon Counters Nulling

Kennedy Receiver

€

N2 =12S ± S( )2

=2S2 = 2NS when 0 is transmitted

0 when 0 is transmitted

" # $

€

N1 =12S ∓ S( )2

=0 when 0 is transmitted

2S2 = 2NS when 0 is transmitted" # $

€

BErasureR = exp −2NS( )

0 1

€

12(S ± S)

D2

Input signal

Local Oscillator

+

D1

N2

N1 S

S

+

€

12(S ∓ S)


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What a Single Photon do when in a 2 Paths

Interferometer ?

Paris, Ile de la Cité Photographed by Yann Arthus-Bertand

✔  The boat (and the photon) go in a single arm

✔  The water (and the wave) flow in the 2 path determinate afterward the boat navigation

✔  «What happens for the hole when the cheese is eaten? » Bertolt Brecht


Two face roman God Janus

Bohr Complementarity Principle

ü  (A.Einstein and) L.Infeld formulationq  «But what is light really? Is it a wave or a

shower of photons?…q  We have two contradictory pictures of reality;

separately neither of them fully explains the phenomena of light, but together they do.»

The Evolution of Physics, 1938.

ü  Lao Tseu formulationq  «The ten thousand things carry yin and embrace yang.

They achieve harmony by combining these forces.»Tao Te Ching 42, vers 500 av.J.C


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✔  50%/50% coupler✔  2 detector output subtraction✔  Total shot noise (Poisson)✔  Signal to noise ratio

✔  Decision by threshold set to 0✔  Bit Error rate (Gaussian)

€

N = N1 − N1 = 2SL = ±2 NSNL

€

ΔN( )2 = N ≈ NL

€

SN

=4NSNL

NL

= 4NS

€

BER =12erfc 2N S( ) ≈ 12 exp −2NS( )

0 1

€

12(S ± L)

D2

Input signal

Local Oscillator

+

D1 +

- N2

N1

N2 – N1 €

N1 =S2 + L2

2+ SL

€

N2 =S2 + L2

2− SL

S

L

+

€

12(L ∓ S)

2 PIN photodiodes strong Local Oscillator

balanced homodyne detection


Quantum receiver Bit Error Rate Asymptotic

approximation Implementation

requirement Comments

Helström limit Dolinar

receiver

€

1 2 1− 1− exp −4NS( )( )

€

1 4exp −4NS( ) Idealist combiner

Single photon counter

Conditional nulling Phase et amplitude feed-

back control Super

homodyne Kennedy receiver

€

1 2exp −4NS( )

€

1 2exp −4NS( ) Super quantum

limit

Idealist combiner Single photon

counter

Unconditional nulling receiver

Thermal noise limitation

Double detector

homodyne Kennedy receiver

€

1 2exp(−2NS )

€

1 2exp(−2NS ) Standard quantum

limit

Realistic balance mixer

2 Photon counters

Unconditional nulling on one of the 2 detectors

Thermal noise limitation

Strong LO homodyne detection

€

1 2erfc 2N S( )

€

1 2exp(−2NS ) Standard quantum

limit

Realistic balance mixer 2 PIN

photodiodes

Strong LO Mixing gain

overcoming thermal noise

Heterodyne detection

€

1 2erfc N S( )

€

1 2exp(−NS ) Idealist combiner

2 PIN photodiodes

Strong LO Mixing gain

overcoming thermal noise

Direct detection of OOK signals

€

1 2exp(−2NS ) Standard Quantum Limit

€

1 2exp(−2NS ) Standard

Quantum Limit

Single PIN thermal noise free

photodiode

Usually impaired by thermal noise or optical

amplification

Comparison of receiver implementations and achievable bit error rate


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Bit

Erro

r Rat

e

!

Comparison and achievable Bit Error Rate

Helström limitSingle detector Kennedy RXStrong oscillator homodyne RX


Outline



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✔  Fainted pulse coherent states❏  Telecommunication wavelength 1550nm❏  Integrated laser and modulator(ILM) 30dB extinction ratio❏  5 ns pulse width❏  4 Mhz repetition rate (limited by photon counters)❏  Calibrate attenuation for operation in the 0.1 to 2 average photon number range

✔  Phase modulation❏  QPSK constellation, turning to BPSK after Bob base selection❏  Mach Zendher interferometer phase modulation

✔  2 Receiver structures compared❏  Balanced super homodyne receiver with ID Quantic photon counters (4 Mhz) ❏  Strong reference balanced homodyne receiver with PIN photodiodes (150Mhz)

✔  Phase referencing❏  Time multiplexed phase reference pulse transmission after 20 ns time delay ❏  Single fiber operation❏  Differential phase and polarization stabilizations only❏  Strong pulsed clock synchronization❏  Orthogonal polarizations for signal and local (30dB extinction ratio improvement)

Our 2 Experimental Set-ups


Photon Counting and Homodyne Detection 2

Alice’s end Bob’s end

4 Mbits/s Clock rate (limited by photon counters)2.5 ns photon counter gate


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Alice

Monitor Alice

Attenuator

H1, H2

Optical Fiber 11km

Isolator Laser

ФA Delay

EOM-A

ФB Delay

EOM-B

Photon Counter1

Photon Counter 2

Bob ФA-ФB

Photon Counting and Super Homodyne Detection with Differential Phase Referencing

✔  Long arm short arms❏  Unmodulated reference pulses❏  Time multiplexed

✔  (Short+short) and (Long+Long) photon paths are disregarded✔  High erasures channel thank to empty pulses

27

28

Photon Counting and Super Homodyne Detection

Histograms for Phase States Dicrimination

✔  2.5 ns photon counter gate duration✔  95% contrast under the most favorable phase matching conditions


28

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PIN Photodiode and Strong LO Homodyne Detection

with differential Phase ReferencingAlice

Monitor Alice

Attenuator

Optical Fiber 11km

Isolator Laser ФA Delay

EOM-A

ФB Delay

EOM-B

Detector 1

Detector 2

Bob ФA-ФB

Decision


30

PIN Photodiode and Strong LO Homodyne Detection with differential Phase Referencing

Experimental and Theoretical Histograms for Different Average Signal Energies

NS from 0.02 to 3 photons

NL = 2.8 105 photons

Pulse durations = 5ns

Overlap control below 0.2ns (10cm of fiber)

Only 0 and π may be distinguished

+π/2 and +π/2 are undistinguishable

NS=0.5

NS=1.5


30

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31

Strong Reference Balanced Homodyne Receiver with PIN Photodiodes

Bit Error Rate as a Function of the Average Photon Number

€

BErrorR =12erfc 2N S( ) ≈ 12 exp −2NS( )


31

Strong Reference Balanced Homodyne Receiver

with PIN PhotodiodesJ Standard PIN photodiode

✔ High speed (GHz)✔ High quantum efficiency(90%)✔ Room Temperature✔ Low cost

L  Strong referenceJ  Noise free mixing gainJ  Clock provided by reference pulsesJ  Decision threshold(s)

✔ Post detection at high signal level✔ Multi level decision possible

J Standard Quantum Limit (SQL)

Super Homodyne Receiver

with Photon Counters

L  Photon counter (gated Geiger APD)✔ Low speed (MHz)✔ Low quantum efficiency (10%)✔ Dark count limit (QBER)✔ Cooling required✔ Quenching required

J No strong referenceL  Decision threshold

✔ At the counter level✔ Trade-off between efficiency and dark count

J Erasure rate at twice the SQL BER

Receiver comparison @1550nm

In any case: Challenging polarization and phase controls required!Quantum Communication Part 2 : Quantum Receiver Philippe Gallion 32

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Outline



1 1

0 0

p(0/1)

p(1/0)

p(0/0)=1-p(1/0))

p(1/1)=1-p(0/1)

input output

=1

= 0

φ =cosφ/2

€

BER = sin2(φ 2) =1−C2

Optical contrast : C =cos φ

φ =sinφ/2

Phase Mismatch

D1

D2

€

p(1/0) = p(0 /1) = sin2(φ 2)

When 1 is transmitted

€

QB = cos(φ 2) 1 + sin(φ 2) 0

Optical contrast: C =1

Phase Mismatch Influence on Super Homodyne with

Photon Counters


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Free-runing Phase Drift of the Balanced Super Homodyne Receiver with Photon Counters

✔  Free-running photon counts of the two detectors✔  CW signal is used✔  The number of photon is measured every 0.2 second✔  Random but strong negative correlated photon counter out-puts ✔  Phase control with <1s time response required


36

Versatile Phase Compensation System (Operating both for super homodyne and Photon counting receiver)

Processing

Detector1

Detector2

PS

∆Ф

Super Homodyne or Photon Counting

Interface

Bit acquisition in real time

Decision (A/D)Phase correction based on

training frame Phase error feedback controller

Raw Key

€

QBERS =12erfc 2ηNB cos

2θE( )

ü  Feedback from a deterministic training frameü  Training Frame including the 4 equiprobable states of the constellationü  Each received bit compared to the expected oneü  Averaged result of 2 quadrature multiplication allows phase mismatch extractionü  Control feedback signal applied on a piezoelectric fiber spool (PS)ü  Forcing phase error down to 0

Bob interferometer


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Phase Drift and QBER of the Balanced Super Homodyne Receiver with Photon Counters

after Phase Control

✔  Phase correction each O.1 seconds✔  < 10° phase control✔  < 10% QBER✔  Residual QBER governed by other system impairments


Phase Drift of the Strong LO Balanced Homodyne Receiver with PIN Photodiodes before and after

Phase Control

✔  5% of the received bits as the “training frame header”✔  Average photon number NS = 0.8✔  Phase correction each 0.1 seconds✔  < 5° phase control


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Outline



Conclusion

✔  Review of quantum receivers structures and performance

✔  Implementation of 2 quantum receivers❏  2 Photon Counters super homodyne receiver ❏  2 PIN Photodiodes strong reference balanced homodyne receiver

•  Inexpensive PIN photo detector receiver

✔  Phase referencing is a key issue❏  Single fiber and one way and time-multiplexed strong reference pulse❏  Relax the end to end phase/polarization to interferometer control❏  Real-time phase drift compensation by training frames

✔  System performance test with 0.02-2.0 photons/bit on average


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Looking ahead for a credible role in the «Security Theater »

ü  The security world is also sometime «Security theater » (Bruce Schneier in his book “Beyond Fear”)

q More intended to provide the feeling of improved securityq  Less than some time doing something efficient to actually improve it

ü  Security is a conservative world q  Up to now the monopole of classical software based security q  It cannot afford any technical risk q  Afraid by disruptive technology

ü  A credible for quantum security requiresq  Infiltration (Trojan horse’s) in classically secured system technology and

cultureClassical and quantum securities osmosisQuantum seeded classical key

q  End-to-end security approachq  Clarification of compatibility with WDM systems


Futureü  Infinite security means infinite cost and no

interestü  Vulnerability & Price have a given productü  The worst is never a certainty (Spinoza)ü  Companies involved

q  AuréaTechnologyq  ID Quantiqueq MagicQ….

ü  As the vine was too high for him to reach the grapes the fox said, “They're sour, I can see it, these grapes are good just for loirs and squirrels!”"THE FOX AND THE GRAPES » Jean de La Fontaine's fable

ü  Now, what about the Edgar Allan Poe sentence ? 42Quantum Communication Part 2 : Quantum Receiver Philippe Gallion

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Thank You (a Second Time) for the Quality of Your Listening


Quantum Communication Part 2 : Quantum Receiver · 2018-01-16 · 30/09/15 2 Outline 1.Optical...

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