Aditi Sen De HarishChandra Research Institute India Outline Communication Secure Communication Quantum Cryptography Communication Outline Communication Secure Communication Quantum Cryptography ID: 398731
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Slide1
Quantum Communication
Aditi Sen(De)Harish-Chandra Research Institute, IndiaSlide2
Outline
Communication
Secure Communication
Quantum Cryptography
CommunicationSlide3
Outline
Communication
Secure Communication
Quantum Cryptography
Communication
Without security
Classical info
transmission
Quantum state
transmissionSlide4
Outline
Communication
Secure Communication
Quantum Cryptography
Communication
Without security
Classical info
transmission
Quantum state
transmissionSlide5
Outline
Communication
Secure Communication
Quantum Cryptography
Communication
Without security
Classical info
transmission
Quantum state
transmissionSlide6
CommunicationSlide7
CommunicationSlide8
What is Communication?
At least 2 parties
Sender
Receiver
Alice
BobCommunication is a process by which information is sent by a sender to a receiver via some medium.Slide9
What is Communication?
At least 2 parties
Sender
Receiver
Alice
BobCommunication is a process by which information is sent by a sender to a receiver via some medium.Slide10
What is Communication?
At least 2 parties
Sender
Receiver
Alice
BobCommunication is a process by which information is sent by a sender to a receiver via some medium.Slide11
What is Communication?
At least 2 parties
Sender
Receiver
Alice
BobCommunication is a process by which information is sent by a sender to a receiver via some medium.Slide12
What is Communication?
At least 2 parties
Sender
Receiver
Alice
Boba process by which information is sent by a sender to a receiver via some medium.Slide13
What is Communication?Alice (Encoder)
Sends
encodes
Bob (Decoder) receives & decodesSlide14
What is Communication?
information must
be
encoded
in, and decoded from a physical system.encoding/Decodingred-green balls,sign of charge of a particle.Only orthogonal states
Quantum World:
Nonorthogonal states
Classical World
“Information is
physical”
---Landauer Slide15
What is Communication?
information must
be
encoded
in, and decoded from a physical system.encoding/Decodingred-green balls,sign of charge of a particle.Only orthogonal states
Quantum World:
Nonorthogonal states
Classical World
“Information is
physical”
---Landauer Slide16
What is Communication?
information must
be
encoded
in, and decoded from a physical system.encoding/decodingred-green balls,sign of charge of a particle.Only orthogonal states
Quantum World:
Nonorthogonal states
Classical World
“Information is
physical”
---Landauer Slide17
What is Communication?
information must
be
encoded
in, and decoded from a physical system.encoding/decodingred-green balls,sign of charge of a particle.Only orthogonal states
Quantum World:
Nonorthogonal states
Classical World
“Information is
physical”
---Landauer Slide18
What is Communication?
information must
be
encoded
in, and decoded from a physical system.encoding/decodingred-green balls,sign of charge of a particle.Only orthogonal states
Quantum World:
Nonorthogonal states
Classical World
“Information is
physical”
---Landauer
Do quantum states advantageous?Slide19
Classical Information Transmission
via Quantum StatesPart 1Slide20
Quantum Dense Coding
Bennett &
Wiesner
, PRL 1992Slide21
Classical Protocol
Sunny
Snowing
Windy
RainingSlide22
Classical Protocol
Sunny
Snowing
Windy
RainingSlide23
Classical Protocol
Sunny
WindySlide24
Classical Protocol
Sunny
Snowing
Windy
RainingSlide25
Classical Protocol
Sunny
Snowing
Windy
RainingSlide26
Classical Protocol
Sunny
Snowing
Windy
Raining
2 bitsSlide27
Classical Protocol
Sunny
Snowing
Windy
Raining
2 bits
Classical computer unit:
Bit = one of {0, 1}Slide28
Classical Protocol
Message
Sunny
Snowing
Windy
RainingEncoding
Decoding
Distinguishable by colorAliceBob
Sending
00
01
10
11Slide29
Classical Protocol
Message
Sunny
Snowing
Windy
RainingEncoding
Decoding
Distinguishable by colorAliceBob 2 bits 4 dimension Slide30
What
abt Quantum?Slide31
Quantum Protocol
Message
Sunny
Snowing
Windy
RainingAliceBob
B
A
Singlet stateSlide32
Message
Sunny
Snowing
Windy
Raining
AliceBob
B
A
I
U
Alice performs unitary on her particleSlide33
Message
Sunny
Snowing
Windy
Raining
AliceBob
B
A
I
U
Creates 4 orthogonal states
Singlet, Triplets
Alice performs unitary on her particleSlide34
Message
Sunny
Snowing
Windy
Raining
AliceBob
B
A
I
U
Alice sends her particle to BobSlide35
Message
Sunny
Snowing
Windy
Raining
AliceBobIAB
Bob has 2 particles:
one of the triplets or singletSlide36
Message
Sunny
Snowing
Windy
Raining
AliceBobIAB
Decoding
4 orthogonal statesPossible to distinguishSlide37
Message
Sunny
Snowing
Windy
Raining
AliceBobIAB
Decoding
4 orthogonal statesPossible to distinguishDecodes messageSlide38
Message
Sunny
Snowing
Windy
Raining
AliceBobIAB
Decoding
4 orthogonal statesPossible to distinguish 2 bits 2 dimension Slide39
Moral
Classical
Quantum
Vs.
Task: sending 2 bits
Encoding: 4 Dimensions Encoding: 2 Dimensions Slide40
Moral
Classical
Quantum
Vs.
Task: sending 2 bits
Encoding: 4 Dimensions Encoding: 2 Dimensions Bennett & Weisner, PRL 69, 2881 (’92).Slide41
Dense Coding
for arbitrary stateHiroshima, J. Phys. A ’01;
Ziman
&
Buzek
, PRA ’03, Bruss, D’Ariano, Lewenstein, Macchiavello, ASD, Sen, PRL’ 04Slide42
B
A
Alice & Bob share a state Slide43
B
A
Alice’s aim:
to send classical info
i
EncodingSlide44
B
A
Alice’s aim:
to send classical info
i
which occurs with probability p
i
EncodingSlide45
U
i
B
A
Alice performs p
i
,
U
i
EncodingSlide46
U
i
B
A
Alice performs p
i
,
U
i
she produces the ensemble
E
= {p
i
,
r
i
}
EncodingSlide47
U
i
B
A
Alice performs p
i
,
U
i
she produces the ensemble
E
= {p
i
,
r
i
}
EncodingSlide48
U
i
B
A
Alice performs p
i
,
U
i
she produces the ensemble
E
= {p
i
,
r
i
}
Alice sends her particle to Bob
SendingSlide49
A
B
Alice
Bob
DecodingSlide50
A
B
Alice
Bob’s task:
Gather info
abt iDecodingSlide51
A
B
Alice
Bob’s task:
Gather info
abt iDecoding
Bob measures and obtains outcome j with
prob
qjSlide52
A
B
Alice
Bob’s task:
Gather info
abt iDecoding
Post measurement ensemble:
E
|j= {pi|j, i|j}Slide53
A
B
Alice
Bob’s task:
Gather info
abt iDecoding
Post measurement ensemble:
E
|j= {pi|j, i|j}
Mutual information:
iSlide54
A
B
Alice
Bob’s task:
Gather info
abt iDecodingMutual information:
i
Iacc = max I(i:M)Slide55
A
B
Alice
Bob’s task:
Gather info
abt i= Maximal classical information from E= {pi, r
i}.Decoding
Iacc = max I (i:M)Slide56
Holevo Theorem 1973
Initial ensemble
E
= {p
i
, ri}Slide57
Holevo Theorem 1973
Initial ensemble E = {p
i
,
r
i}Slide58
Holevo Theorem 1973
Initial ensemble E = {p
i
,
r
i}
d: dimension of
r
i
Slide59
Holevo Theorem 1973
Initial ensemble E = {p
i
,
r
i}
Bit per
qubitSlide60
A
B
Alice
Bob’s task:
Gather info
abt iAccessible information = Maximal classical information from E = {pi
, ri}.
DecodingSlide61
DC
CapacityDense coding capacity:
m
aximization over all encodings i.e. over all {pi, U
i }
C = Max Iacc Slide62
DC
CapacityDense coding capacity:
m
aximization over all encodings i.e. over all {pi, U
i }
C = Max Iacc = Max Holevo quantity obtained by BobSlide63
DC
CapacityDense coding capacity:
m
aximization over all encodings i.e. over all {pi, U
i }
C = Max Iacc = Max Holevo quantity obtained by Bob
Holevo
can be achieved asymptotically
Schumacher, Westmoreland, PRA
56,
131 (’97)Slide64
DC
CapacityDense coding capacity:
m
aximization over all encodings i.e. over all {pi,
Ui
}C = Max Iacc = Max Slide65
DC
CapacityDense coding capacity:
m
aximization over all encodings i.e. over all {pi,
Ui
}C = Max Iacc = Max Slide66
C =
Max
DC CapacitySlide67
C =
Max
DC CapacitySlide68
C =
Max
DC CapacitySlide69
DC Capacity
C
=
log
2 dA + S(ρB) - S(ρAB) Slide70
DC Capacity
C
=
log
2 dA + S(ρB) - S(ρAB) I
B = S(
ρB) - S(ρAB) > 0A state is dense codeableSlide71
Classification of states
Entangled
S
DCIn 22, 23 Slide72
DC Capacity:
Known/Unknown
Single Sender – Single Receiver
Solved
Slide73
Dense Coding
NetworkSlide74
Why quantum dense coding network?
Point to point communication has limited commercial useSlide75
Why quantum dense coding network?
To build a quantum computer,or communication network Slide76
Why quantum dense coding network?
To build a quantum computer,or communication network,
classical info transmissionSlide77
Why quantum dense coding network?
To build a quantum computer,or communication network,
classical info transmission
via quantum state in networkSlide78
Dense Coding Network 1Slide79
Dense Coding Network
Bob
Debu
Charu
Nitu
....Alice
ReceiversSenderSlide80
Dense Coding Network
Bob
Debu
Charu
Nitu
....Alice
ReceiversSender
Task:
Alice
individually
sends
classical info to all the receiversSlide81
Dense Coding Network
Bob
Debu
Charu
Nitu
....Alice
ReceiversR. Prabhu, A. K. Pati
, ASD, U. Sen, PRA ’ 2013R. Prabhu, ASD, U. Sen, PRA’ 2013R. Nepal, R. Prabhu, ASD, U. Sen, PRA’ 2013SenderSlide82
Dense Coding Network
Bob
Debu
Charu
Nitu
....Alice
ReceiversR. Prabhu, A. K. Pati
, ASD, U. Sen, PRA ’ 2013R. Prabhu, ASD, U. Sen, PRA’ 2013R. Nepal, R. Prabhu, ASD, U. Sen, PRA’ 2013Sender
Ujjwal’s
Talk
Prabhu’s
TalkSlide83
Dense Coding Network 2Slide84
Dense Coding Network
Alice
Debu
Charu
Nitu
....Bob
SendersReceiverSlide85
Dense Coding Network
Alice
Debu
Charu
Nitu
....Bob
SendersReceiver
Several senders & a single receiverSlide86
Dense Coding Network
Alice
Debu
Charu
Nitu
....Bob
SendersReceiver
Task: All senders send classical info {ik, k=1,2, ..N} to a receiverSeveral senders & a single receiverSlide87
Dense Coding Network
Alice
Debu
Charu
Nitu
....Bob
SendersReceiver
Task: All senders send classical info {ik, k=1,2, ..N} to a receiverSlide88
Dense Coding Network
Alice
Debu
Charu
Nitu
....Bob
SendersReceiver
senders perform Uik, k=1,2, ..N on her parts Slide89
Dense Coding Network
Alice
Debu
Charu
Nitu
....Bob
SendersReceiver
Senders create ensemble Slide90
Dense Coding Network
Alice
Debu
Charu
Nitu
....Bob
SendersReceiver
Senders create ensemble Slide91
Dense Coding Network
Alice
Debu
Charu
Nitu
....Bob
SendersReceiver
Senders send ensemble to Bob Slide92
Dense Coding Network
Alice
Debu
Charu
Nitu
....Bob
SendersReceiver
Bob’s task: gather info abtSlide93
DC
Capacity networkDC capacity network
m
aximization over all encodings i.e. over all {p{i},
U{i}
}C = Max Iacc = Max Holevo quantity obtained by BobSlide94
DC
Capacity Network
C
=
Bruss, D’Ariano, Lewenstein, Macchiavello, ASD, Sen, PRL’ 04Bruss, Lewenstein, ASD, Sen, D’Ariano, Macchiavello, Int. J. Quant. Info. ’05Slide95
DC
Capacity Network
C
=
Bruss, D’Ariano, Lewenstein, Macchiavello, ASD, Sen, PRL’ 04Bruss, Lewenstein, ASD, Sen, D’Ariano, Macchiavello, Int. J. Quant. Info. ’05Tamoghna’s PosterSlide96
DC Capacity:
Known/Unknown
Single Sender – Single Receiver
Many Senders – Single Receiver
Solved
Slide97
Dense Coding Network 3Slide98
Distributed DC: Two receivers
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)Slide99
Distributed DC: Two receivers
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)
LOCC
i
1
i
2Slide100
Distributed DC: Two receivers
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)Slide101
Distributed DC: Two receivers
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)
Alices
send her particles to BobsSlide102
Distributed DC: Two receivers
Bob (B1)
Bob (B
2
)
Bobs task: gather info
abt
ik by LOCCSlide103
Distributed DC: Two receivers
Bob (B1)
Bob (B
2
)
Bobs task: gather info
abt
ik by LOCC
LOCCSlide104
C
= Max
Distributed DC: Two receiversSlide105
C
= Max
Max
LOCC Holevo boundMaximization over all encodings i.e. over all {pi, Ui
}Distributed DC: Two receiversSlide106
C
= Max
Max
LOCC Holevo boundMaximization over all encodings i.e. over all {pi, Ui
}
Badziag, Horodecki, ASD, Sen, PRL’03Distributed DC: Two receiversSlide107
C
= Max
Max
LOCC Holevo boundMaximization over all encodings i.e. over all {pi, Ui
}
Bruss, D’Ariano, Lewenstein, Macchiavello, ASD, Sen, PRL’ 04
Distributed DC: Two receiversSlide108
DC Capacity:
Known/Unknown
Single Sender – Single Receiver
Many Senders – Single Receiver
Solved
Slide109
DC Capacity:
Known/Unknown
Single Sender – Single Receiver
Many Senders – Single Receiver
Solved
Many Senders – Two ReceiversSlide110
DC Capacity:
Known/Unknown
Single Sender – Single Receiver
Many Senders – Single Receiver
Solved
Many Senders – Two Receivers
Partially Solved Slide111
DC Capacity:
Known/Unknown
Single Sender – Single Receiver
Many Senders – Single Receiver
Solved
Many Senders – Two Receivers
Partially Solved
Many Senders – Many ReceiversNot Solved Slide112