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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 1: Basics
1
TELECOM ParisTech Ecole Nationale Supérieure des Télécommunications
(ENST)✔ Since 1878…✔ Belong to
❏ Ministry of Economy and Industry❏ ParisTech (Paris Institute of Technology)❏ Institut Télécom
✔ Graduate level electrical curriculum❏ Engineering and computer science❏ 600 students toward engineering degree❏ Selective national wide admission contest❏ Acceptance upon degree
✔ PhD Program❏ 350 students toward PhD Degree❏ Doctoral School : EDITE (Computer Science,
Telecommunications and Electronics)
2Quantum Communication Part 1: Basics Philippe Gallion!
2
TELECOM ParisTech, in few words
✔ The leading Engineering School in ICT, in France✔ Top 3rd to 7th in national rankings of Engineering Schools inFrance (among 250)✔ Highly international
❏ 42% international students❏ 64 partner Universities
✔ High professor/student Ratio : 1/7✔ 205 full-time professors for 1500 students✔ Innovation
❏ 130 sustainable companies ❏ 1000 jobs created since 1999
✔ Strong links with industry
3Quantum Communication Part 1: Basics Philippe Gallion
Where are we located ?
4
Télécom ParisTech
Quantum Communication Part 1: Basics Philippe Gallion
3
Four Teaching and Research Departments
✔ Communication & Electronics (Mine)❏ Digital Communications❏ Optoelectronics and Optical Communications❏ Microwaves and Radio Communications❏ Digital and analog electronics integration
✔ Computer Science & Networking
✔ Signal and Image processing
✔ Economics, Management & Social Sciences
5Quantum Communication Part 1: Basics Philippe Gallion
Outline …(for today)
✔ 1. Introduction✔ 2. Classical Cryptography (CC)✔ 3. Basics Concepts for Quantum Cryptography (QC)✔ 4. Quantum Cryptography Protocols✔ 5. Security and Attack Strategies✔ 6. Conclusion
Tomorrow : …. Quantum receiver and implementation
6Quantum Communication Part 1: Basics Philippe Gallion
4
What optical signal at quantum levels for ? 1 Space communications
✔ Low photon numbers ❏ Low transmitted power ❏ Strong attenuation
✔ Applications ❏ Airborne❏ Satellite-to-ground ❏ Inter satellite❏ Space to ground❏ Planetary, deep space
V. Chan, IEEE-JLT 2003
7Quantum Communication Part 1: Basics Philippe Gallion
What optical signal at quantum levels for ? 2 - Quantum cryptography
✔ Information is supported by single photon
❏ The quantum aspect appears
❏ Measurement destroys the quantum system
❏ Non duplication ( non cloning) of unknown state
Security !
8Quantum Communication Part 1: Basics Philippe Gallion
5
Alice is the message sender
Bob is the receiverEve is the
eavesdropper
Alice in wonderland
(Lewis Caroll)Bob Marley the Reagee Music
StarCranach’ the Elder (Germain Painting)
Traditional Cryptography Starring
9Quantum Communication Part 1: Basics Philippe Gallion
Outline
✔ 1. Introduction✔ 2. Classical Cryptography (CC)✔ 3. Basics Concepts for Quantum Cryptography (QC)✔ 4. Quantum Cryptography Protocols✔ 5. Security and Attack Strategies✔ 6. Conclusion
10Quantum Communication Part 1: Basics Philippe Gallion
6
Encryption
Decryption
Cryptosystem (or Ciphers)
Message + Key Cryptogram
Cryptogram + Key Message
✔ Decryption without the key is:❏ « Impossible » (nothing is)❏ Difficult (growing exponentially with the key length)❏ « Easy » (growing polynomially with the key length )
✔ Key is a secret shared by Alice & Bob
11Quantum Communication Part 1: Basics Philippe Gallion
Secret Key (Symmetrical) Cipher - 1
✔ Principles❏ Single key for encryption and decryption ❏ Alice encrypts with this secret key ❏ Bob decrypts with this secret key
✔ Only Computational Security❏ More secure than asymmetrical ciphers at a given Key
length✔ Data Encryption Standard (DES)
❏ 56 bits❏ Used for e-commerce….
12Quantum Communication Part 1: Basics Philippe Gallion
7
TEXT Q CASCII 1 0 0 0 1 0 1 1 1 0 0 0 0 1+ KEY 0 1 1 0 0 1 1 0 1 1 0 0 1 1
ENCODEDMESSAGE
1 1 1 0 1 1 0 1 0 1 0 0 1 0
+KEY 0 1 1 0 0 1 1 0 1 1 0 0 1 1ASCII 1 0 0 0 1 0 1 1 1 0 0 0 0 1TEXT Q C
0 10 0 11 1 0
Secret Key (Symmetrical) Cipher - 2
✔ Exclusive OR or XOR, or addition modulo 2
✔ Two consecutive additions return to the initial message
13Quantum Communication Part 1: Basics Philippe Gallion
“One Time Pad” Necessity (Vernan Code)
✔ Eve’s recording of allows to start knowledge of the message
✔ The addition of 2 messages scrambled with the same key is the sum of the 2 messages
✔ Perfectly secure for “One Time Pad” (OTP)
✔ Key of the same length than the message
14Quantum Communication Part 1: Basics Philippe Gallion
8
✔ Security secret key systems using one time pad (OTP)❏ Key distribution problem
Quantum Key Distribution (QKD)
✔ Teleportation (secure faithful copy transfer) possible
❏ System state description possible with arbitrary precision❏ Secure transmission with a key with appropriated length❏ Bob can in principle reconstruct a copy of the system❏ Original system is not affected❏ Many copies are possible
Hello Dolly !
Classical Systems
15Quantum Communication Part 1: Basics Philippe Gallion
Outline
✔ 1. Introduction✔ 2. Classical Cryptography (CC)✔ 3. Basics Concepts for Quantum Cryptography (QC)✔ 4. Quantum Cryptography Protocols✔ 5. Security and Attack Strategies✔ 6. Conclusion
16Quantum Communication Part 1: Basics Philippe Gallion
9
“…and it may well be doubted
whether human ingenuity can construct an enigma of
the kind which human ingenuity may
not, by proper application,
resolve.”
Edgar Allan PoeThe Gold-Bug, Tales of Mystery
and Ratiocination, 1843
17Quantum Communication Part 1: Basics Philippe Gallion
Classical Physics Basics
✔ Determinism❏ The state of a system at a given time is totally
determinate by previous state❏ Statistical imprecision is a consequence of the formalism❏ Not of the system nature
✔ Objectivity❏ Reality exists independently from its observation
✔ Completeness❏ Each element of the reality have a theoretical counterpart
Only based on macroscopic experience !18Quantum Communication Part 1: Basics Philippe Gallion
10
Quantum Physics Basics
✔ Principle of indetermination (Heisenberg)❏ Indeterminism inherent to the nature
✔ The wave nature (de Broglie, Schrödinger)❏ Describing probabilities
✔ Principle of complementary (Bohr)❏ Wave and corpuscular nature are two (classical) perspectives ❏ Its is a duality❏ It is NOT dualism❏ But not a classical particle or a particle wave !
✔ Principle of correspondence (Ehrenfest)❏ Quantum mechanics and classical one agree as the quantum
nature disappears❏ Classical mechanics is a limit
19Quantum Communication Part 1: Basics Philippe Gallion
What is a Quantum Communication System ?
✔ There is no information without physical representation✔ Information is supported by a quantum system
❏ Individual photon❏ Coherent state…
✔ Ensemble systems are (semi) classical and do not work✔ Information is encoded by using
❏ Polarization❏ Phase ❏ Frequency❏ …
✔ Other parts of the communications channel are classical❏ Optical fiber❏ Free space
20Quantum Communication Part 1: Basics Philippe Gallion
11
✔ A Quantum state is the superposition of its eigenstates
✔ A measurement converts a quantum state into one of its eigenstate
❏ The measurement result is the corresponding eigenvalue❏ The probability of this result is IαiI 2
✔ Only eigenstates are kept unchanged✔ Consequences
❏ Except for the eigenstates, measurement destroys the system❏ Simultaneous and precise measurements may be impossible❏ Duplication of unknown quantum state impossible
Quantum Physics Basics
21
A = a1 A1 + a2 A2 with ai = Ai A
A Ai
Quantum Communication Part 1: Basics Philippe Gallion
Schrödinger’s Cat Paradox✔ When does
❏ The wave function collapse ?❏ The superposition disappears ?❏ The cats dies ?
✔ At the (eventually microscopic) killing process ❏ Linked to physic ?
✔ At the box opening ❏ linked to observation and conscience ?
✔ Problem with Cartesian dualism : mental/physical✔ Monism : reduction to a single “substance” (Spinoza)
❏ Idealism (Platon, Leibnitz, Hegel …)• The superposition disappears with the conscience intervention
❏ Materialism (Epicure, Marx…)• The superposition disappears with the microscopic killing process
✔ Idealism/materalism “Superposition” interpretation 22Quantum Communication Part 1: Basics Philippe Gallion
12
Quantum FishAndré Breton 1924
✔ The fish is melted out in the water✔ It is only defined by a concentration✔ When does the quantum fish appear?
❏ When biting the bait? Materialism ?❏ When seen by the fisher man ? Idealism ?
23Quantum Communication Part 1: Basics Philippe Gallion
1
0
1
0
Classical Bit v.s. Quantum BitClassical Bit :
Any macroscopic 2-state system
✔ Exclusive states : 0 or 1 at a given time
✔ States exist independently of measurement
✔ p(1) + p(0) = 1
✔ Measurement keeps the system unchanged
Quantum Bit (QB)Any 2-level quantum system
✔ 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
Ensemble average
24Quantum Communication Part 1: Basics Philippe Gallion
13
Quantum Bit (QB)
✔ 2 dimensions✔ n qubits belongs to a 2n
dimension space
I 0 >
IQB>
I 1 >continuousvariable
0 1
Classical Bit v.s. Quantum Bit - 2/2
Classical Bit (CB)
✔ 1 dimension✔ Areas selected for bit
value representation✔ 2 possibilities✔ n bits belongs to an n
dimension space
25Quantum Communication Part 1: Basics Philippe Gallion
Qbit Communication System using Simple Eigenstate Encoding
✔ Polarization (i.e. spin) is an example❏ Any 2-level system acts in the same way
✔ Q bit are used : IQB > =α I0> + β I1>✔ Simple eigenstate information encoding
❏ α =1 for bit 0 and β =0 ❏ α =0 for bit 1 and β =1
✔ Bit discrimination by simple polarization splitting❏ A 2 detector arrangement is mandatory❏ Correct detection probabilities are equal to 1❏ Error free transmission
I 0 >
IQB>
I 1 >
Detector 1
Detector 2
Polarizingsplitter I0>
I1>
€
! = 0" = 1
Where is the Rub ?✔ Eve can
❏ Intercept, ❏ Detect the same way….and get the key❏ Resend to Bob
✔ Simple eigenstate encoding not relevant✔ Protocol required for QKD
26Quantum Communication Part 1: Basics Philippe Gallion
14
✔ 2 qubits lead to a 4 dimension basisI00>, I01>, I10>, I11>
✔ Some combinations are combination of separated (non correlated) qubit states
I01>+ I11>= (I0>+ I1>) I1>
✔ Some of them are notI00>+ I11>
✔ n qubits belongs to a 2n dimensions space❏ Enhanced complexity❏ n classical bits only belongs to a n dimensions space
✔ Great interest for quantum information processing€
00 + 01 = 0 ⊗ 0 + 1( )00 + 10 = 0 + 1( ) ⊗ 0
00 + 11 = 2 entangled states
01 + 10 = 2 entangled states
01 + 11 = 0 + 01( ) ⊗ 1
10 + 11 = 1 ⊗ 0 + 1( )
Qbit Association
27Quantum Communication Part 1: Basics Philippe Gallion
✔ Entanglement, Verschränkung (i.e.“arm in arm”)✔ Quantum « super correlation » ≠ classical correlation✔ 2 photon parametric generation
✔ The individual photon have a random polarization
✔ When both measured they have always orthogonal polarization
ψ AB =12
↑A→ B + → A ↑
B[ ]
ψ =12
↑ + →[ ]
Photon A,ω
Photon B,ω
2ω χ(2)
Entangled States - 1
28Quantum Communication Part 1: Basics Philippe Gallion
15
Entangled States - 2
✔ Measurement on one instantaneously influences the other❏ No matter how far apart they may be❏ In opposition with the theory of relativity❏ Einstein, Podolski, Rosen (EPR) paradox (1935)❏ Hidden variables❏ Bell’s inequality violation (1964)❏ Demonstrated experimentally by Clauser (1976) & Aspect (1981)❏ Quantum mechanics completeness (no hidden variable)
✔ They have interacted in the past❏ They constitute a single quantum object
✔ They have some locally inaccessible information in common ❏ This information cannot be accessed in any experiment performed on
either of them alone
29Quantum Communication Part 1: Basics Philippe Gallion
✔ 4 quantum states , forming 2 basis are used
✔ Binary value attributions on each basis✔ Simultaneous observations using the 2 basis are
impossible✔ Alice and Bob can select any basis✔ Basis coincidence allows correct bit detection✔ Basis anti-coincidence
p(0) = p(1)= 1/2 whatever is the transmitted bit✔ A second detection is impossible (quantum demolition)
I0>
I90> I45>I135>
Using 2 Conjugated Basis
€
! =12
" + #( ) and $ =12
" − #( )
30Quantum Communication Part 1: Basics Philippe Gallion
16
€
0 00 11 11 0
"
#
$ $ $ $
%
&
' ' ' '
=
1 0 0 00 1 0 00 0 0 10 0 1 0
(
)
* * * *
+
,
- - - -
0 00 11 01 1
"
#
$ $ $ $
%
&
' ' ' '
€
x b → x x
€
α 0 + β 1( ) b →α 0 0 + β 1 1 ≠ α 0 + β 1( ) α 0 + β 1( )
Original
CopyCloning
✔ Classical state cloning (controlled XOR gate)
✔ Cloning impossibility for superposed states
✔ Except for α = β = 1/2
31Quantum Communication Part 1: Basics Philippe Gallion
Quantum Teleportation
✔ Under complete system knowledge, the problem turns to a classical one❏ Knowledge implies Ψ collapse❏ Duplication of unknown quantum state impossible
✔ Quantum state transfer from Alice to Bob requires:❏ The sharing many entangled qubits ❏ A classical communication channel❏ A quantum teleportation protocol
✔ The quantum teleportation result is:❏ Alice’s system destruction without knowledge for herself❏ Bob get an isomorphic, but unknown, system
32Quantum Communication Part 1: Basics Philippe Gallion
17
Outline
✔ 1. Introduction✔ 2. Classical Cryptography (CC)✔ 3. Basics Concepts for Quantum Cryptography (QC)✔ 4. Quantum Cryptography Protocols
❏ BB84 Protocol❏ Eckert Protocol❏ Continuous variable protocol❏ ….
✔ 5. Security and Attack Strategies✔ 6. Conclusion
33Quantum Communication Part 1: Basics Philippe Gallion
I0>
I90> I45>I135>
Bennett-Brassard 1984 (BB84)✔ 4 quantum states , forming 2 basis for the same space
✔ Simultaneous observations using the 2 basis are impossible
✔ Binary value attributions
✔ Alice and Bob can select any basis✔ Basis coincidence allows correct bit detection✔ Basis anti-coincidence leads to p(0) = p(1)= 1/2 after detection,
whatever is the transmitted bit✔ A second detection Eve is impossible (quantum demolition)
34Quantum Communication Part 1: Basics Philippe Gallion
18
BB84/QKD : Initial Alice to Bob Transmission on the Quantum Channel
✔ 1 - Alice chooses a random series of bits✔ 2 - Alice sends each bit with a random bases choice✔ 3 - Bob detects each bit using another random choice of the basesResulting BER is 25%
1 0 1 0 0 1 1 1
Quantum Chanel
0
011
35Quantum Communication Part 1: Basics Philippe Gallion
BB84/QKD : Reconciliation on the Public Classical Channel
✔ 4 - Bob publicly announces his series of bases choices (not the measurement result!)
✔ 5 - Alice publicly announces the bases coincidences i.e. the bits correctly detected by Bob
✔ 6 - Bob & Alice use this bit sequence as the key: ReconciliationTheoretical BER is 0%
1 0 1 0 1
Classical Chanel
36Quantum Communication Part 1: Basics Philippe Gallion
19
BB84/QKD : Key Distillation on the Public Classical Channel
✔ 7 - Error correction✔ 8 - Privacy amplificationAt the expense of the key length reduction !
Classical Chanel
But systems impairments and Eve intervention turn to BERAnd Eve have catch some information about the key
37Quantum Communication Part 1: Basics Philippe Gallion
1 Qubit BB84 Protocol
✔ Neither Alice and Bob decide of the key✔ Key is a result of random basis choice
coincidences in a random series of bits✔ Security relies on
❏ Quantum demolition measurement❏ Non cloning
✔ Phase, frequency or polarization may be used
38Quantum Communication Part 1: Basics Philippe Gallion
20
✔ Classical systems average out the quantum character✔ Quantum system must be used✔ 2 representations of the 2 binary symbols on 2 conjugated bases
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
Encoding Information on a Single Photon
0
0
1
1
1
0
0
1
0
1 0
1
1 Base 1
0 Base 2
0
1
39Quantum Communication Part 1: Basics Philippe Gallion
Foiling Eavesdroppers
1 - Alice sends each bit with a first random basis choice2 - Eve detects each bit using a second random choice of the basis3 - Bob detects each bit using a third random choice of the basis4 - many error thanks to wrong basis5 - Bob and Alice are able to detect error by telling each other a
portion of it
40Quantum Communication Part 1: Basics Philippe Gallion
21
Using QC
✔ Retrospect security ❏ Useful for the message itself❏ Solves the key distribution problem because intercepted key
may be discarded✔ Conventional (classical channel) may be used in OTP
41Quantum Communication Part 1: Basics Philippe Gallion
!
Common
Source
2 Qubit Ekert (EPR) Protocol
✔ The 2 qubits are in the same state chosen randomly among the 4 states of the BB84 protocol❏ The source announces the base❏ Alice & Bob only consider compatible basis measurements❏ Equivalent to BB84 protocol❏ But the source may be controlled by Eve!
✔ The 2 qubits are emitted as an entangled state❏ Reduction of basis coincidence probability
!!
! !
42Quantum Communication Part 1: Basics Philippe Gallion
22
Outline
✔ 1. Introduction✔ 2. Classical Cryptography (CC)✔ 3. Basics Concepts for Quantum Cryptography (QC)✔ 4. Quantum Cryptography Protocols✔ 5. Security and Attack Strategies
❏ QBER Amplification❏ Privacy Amplication
✔ 6. Conclusion
43Quantum Communication Part 1: Basics Philippe Gallion
Improving the QBER of Sifted Keys
✔ The shared key contains error thanks to❏ Technical imperfections❏ Eve’s intervention
✔ QBER is usually in the few percent range❏ Corrected with a posteriori classical error correction❏ Implying a key reduction❏ Public channel is used to distill a shorter key without error
✔ QBER differs from BER usually in the 10-9 range❏ Corrected a priori using FEC and over heading of the signal
44Quantum Communication Part 1: Basics Philippe Gallion
23
✔ Alice randomly chooses pairs of bits✔ Alice compute their sum modulo 2 (XOR)✔ Alice publicly announces:
❏ The result❏ The rank of the 2 bits
✔ For same results Alice and Bob❏ Keep the first bit❏ Throw away the second to avoid Eve information improvement
✔ For wrong results they throw away the 2 bits
€
p→ p2
p2 + (1− p)2 < p pour p < 12
Both wrong Both OK
A Simple, but low Performance, Algorithmfor QBER Improvement
45Quantum Communication Part 1: Basics Philippe Gallion
Basics of Communication Theory
Sourceentropy H
H(X/Y)
0
MutualInformation I
I(X,Y)
0
Sourceentropy H
H(X)
0
MutualInformation I
0
(a) Non operating channel
(b) Operating channel
H(X)
ü No communication channel
q The available information H (entropy) remains stored in the right vessel (a)
ü Moving down the vessel of the right side
q Reduces the available source information
q Increases of the same amount the mutual information (b).
46
I(X,Y ) = H (X)−H (X /Y )
Quantum Communication Part 1: Basics Philippe Gallion
24
!
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
bina
ry e
ntro
py
probabity
Basics of Communication Theory
No communicationp =1/2
Source Entropy H(X)
Mutual Information I(X,Y)
Conditional Entropy H(X/Y)
Probability after communication
€
H 2( p) = − p log2 p − (1− p)log2(1− p)Binary entropy :
47Quantum Communication Part 1: Basics Philippe Gallion
!
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
bina
ry e
ntro
py
probabity
✔ Improving mutual information difference
✔ Public channel is used✔ Key is shortened
€
I(Alice,Eve)
€
I(Alice,Bob) ≈1€
ΔI
Bit probability for Eve
€
ΔI = I(Alice,Bob) − I(Alice,Eve)
Privacy Amplification
48Quantum Communication Part 1: Basics Philippe Gallion
25
A Simple, but low Performance, Algorithmfor Privacy Amplification
✔ Alice randomly chooses pairs of bits✔ Alice compute their sum modulo 2 (XOR)✔ Alice does not announce the result✔ Alice only announces the rank of the 2 bits✔ Alice and Bob replace the 2 bits by their sum modulo 2
✔ Heuristic demonstration:❏ Eve only knows one of the two bits: Its sum contains no more
information p = 1/2❏ Eve knows the two bits with probability p : the probability turn to p2 +(1-p)2< p for p >1/2
✔ Performant when p for Eve is close to 1/2
49Quantum Communication Part 1: Basics Philippe Gallion
Eve knows Nothing
Privacy vanishes out
Perfect security
€
34log2 3−1
Quantum Unconditional Security✔ Security rely on
❏ Non cloning❏ Quantum demolition
✔ Ensemble systems❏ Average the quantum behavior❏ Are (semi) classical
✔ Information must supported by quantum system❏ Individual photon❏ Coherent state
A Simple Attack Strategy: Random interception with probability ω and resend
Eve tries to attack the QDK
!
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
IAEIABIAB-IAE
Mut
ual i
nfor
mat
ion
Interception Probability
50Quantum Communication Part 1: Basics Philippe Gallion
26
Some Other Attack Strategies
✔ Selection of an other base✔ Using teleportation✔ Photon number splitting (PNS)✔ Performances limited by
❏ the channel imperfection❏ the available time for a key sharing❏ Eve resources
51Quantum Communication Part 1: Basics Philippe Gallion
Outline
✔ 1. Introduction✔ 2. Classical Cryptography (CC)✔ 3. Basics Concepts for Quantum Cryptography (QC)✔ 4. Quantum Cryptography Protocols✔ 5. Security and Attack Strategies✔ 6. Conclusion
52Quantum Communication Part 1: Basics Philippe Gallion
27
About Unconditional Security
✔ QKD is the only protocol to provide it
✔ Considered as limited only by the principles of physics ❏ What about the resources that could realistically have Eve on a
given time scale ❏ Where is the better emergence probability
• For the technologies usually evoked in unconditional security? • For technology that would collapse the traditional security systems ?
✔ Quantum layer approach is not sufficient to achieve an end-to-end security up to the application layer ❏ Attack on the quantum layer is an heavy strategy mistake for Eve ❏ Conventional integrated electronics circuits are very vulnerable to
the so-called side-channel attacks
✔ Needs very limited v.s. security on demand✔ Confining into academics or thought experiments ?
53Quantum Communication Part 1: Basics Philippe Gallion
From the promises of physics of the last century…toward quantum security engineering✔ Implementation of the physical layer is demonstrated
❏ 1550nm wavelength operation without photon counter❏ Standard optical fiber❏ One way system, in single optical fiber❏ Off-the shelf and low cost optoelectronics components
✔ End to end approach already started❏ True Random Number Generators (for symbols & bases)
• 100 to 1000 time faster than the application data rate• Robust against attacks
❏ Raw key processing• Electronics interface• Buffering for key material management• Secured electronics processing
❏ Application interface• Key distillation using public channel• Key management• Upper layer interface
54
Will be discussedWednesday
Quantum Communication Part 1: Basics Philippe Gallion
28
Thank You for the Quality
of Your Listening
55Quantum Communication Part 1: Basics Philippe Gallion
Quantum Acception
✔ Latin : how much✔ Kant :
❏ Things as they appear (phenomenal) may differ from things as they are and persist in being (noumenal)
❏ Quantum is the invariant of the substance and the object of measurement
✔ Classical Physic : Corpuscular❏ Determinism inherent to the nature, ❏ Indeterminism only inherent to the formalism (statistics)
✔ Planck, Einstein, Bohr, Sommerfeld : defined quantities✔ Quantum Physics
❏ Indeterminism inherent to the nature❏ Principle of indetermination
56Quantum Communication Part 1: Basics Philippe Gallion
29
Goals of Cryptography✔ Making communications interaction as safe as
perfectly secret personal meeting
✔ Confidentiality✔ Identification
❏ Credit card number❏ PINs
✔ Authentication, Digital Signature
✔ Non-repudiation
57Quantum Communication Part 1: Basics Philippe Gallion
Quantum information
Quantum Information
✔ Quantum information processing❏ Quantum Processors❏ Quantum Algorithm
✔ Quantum Communication❏ Teleportation❏ Quantum Cryptography
58Quantum Communication Part 1: Basics Philippe Gallion
30
Basics of Communication Theory 1/3Intrinsic source
propertiesSource perception
through thecommunication channel
Communication channeleffect
Signal probability Probability
€
p(x)
Conditional Probability
€
p(x / y)
€
p(x / y) > p(x)
Improved probability
For a given occurrence xof the input
InformationI(x) = − log2 p(x)
Low probability resultsin large information
Conditional information
€
I(x / y) = −log2 p(x / y)
Residual sourceinformation
Mutual information
€
I(x,y) = I(x) − I(x /y)
Decay of the sourceinformation
Ensemble averageoverall the possible
occurrences
Source entropy
€
H(X) = I(x) x
Potential informationavailable from the
source
Conditional entropy
€
H(X /Y ) = I(x / y) x,y
Residual sourceinformation after
communication process
Average mutualinformation
I(X,Y) = H(X) − H(X /Y)
Decay of the sourceentropy provided by thecommunication process
59Quantum Communication Part 1: Basics Philippe Gallion
✔ Information is encoded as CW modulation of two optical field quadrature (EX, EY) or (A, ϕ)
✔ Security relies on❏ Non simultaneous precision
measurements❏ Non cloning
✔ Conversion into digital signal for❏ Privacy amplification❏ Error Correction
✔ Squeezing or EPR correlation are not required
✔ Chaos cryptography is an other way
Continuous Variable Protocol
60Quantum Communication Part 1: Basics Philippe Gallion