Part 2 Aditi HarishChandra Research Institute India Outline Communication Secure Communication Quantum Cryptography Communication Without security Classical info transmission Quantum state ID: 398729
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Slide1
Quantum Communication Part 2
Aditi Harish-Chandra Research Institute, IndiaSlide2
Outline
Communication
Secure Communication
Quantum Cryptography
Communication
Without security
Classical info
transmission
Quantum state
transmissionSlide3
DC Capacity: Known/Unknown
Single Sender – Single ReceiverMany Senders – Single Receiver
Solved
Slide4
Dense Coding Network 3Slide5
Distributed DC: Two receivers
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)Slide6
Distributed DC: Two receivers
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)
LOCC
i
1
i
2Slide7
Distributed DC: Two receivers
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)Slide8
Distributed DC: Two receivers
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)
Alices
send her particles to BobsSlide9
Distributed DC: Two receiversBob (B
1)Bob (B2
)
Bobs task: gather info
abt
i
k by LOCCSlide10
Distributed DC: Two receiversBob (B
1)Bob (B2
)
Bobs task: gather info
abt
i
k by LOCC
LOCCSlide11
C = Max
Distributed DC: Two receiversSlide12
C = Max
Max
LOCC
Holevo
bound
Maximization over all encodings i.e. over all {pi, Ui
}Distributed DC: Two receiversSlide13
C = Max
Max
LOCC
Holevo
bound
Maximization over all encodings i.e. over all {pi, Ui
}
Badziag, Horodecki, ASD, Sen, PRL’03Distributed DC: Two receiversSlide14
C = Max
Max
LOCC
Holevo
bound
Maximization over all encodings i.e. over all {pi, Ui
}
Bruss, D’Ariano, Lewenstein, Macchiavello, ASD, Sen, PRL’ 04
Distributed DC: Two receiversSlide15
DC Capacity: Known/Unknown
Single Sender – Single ReceiverMany Senders – Single Receiver
Solved
Slide16
DC Capacity: Known/Unknown
Single Sender – Single ReceiverMany Senders – Single Receiver
Solved
Many Senders – Two ReceiversSlide17
DC Capacity: Known/Unknown
Single Sender – Single ReceiverMany Senders – Single Receiver
Solved
Many Senders – Two Receivers
Partially Solved Slide18
DC Capacity: Known/Unknown
Single Sender – Single ReceiverMany Senders – Single Receiver
Solved
Many Senders – Two Receivers
Partially Solved
Many Senders – Many Receivers
Not Solved Slide19
Outline
Communication
Secure Communication
Quantum Cryptography
Communication
Without security
Classical info
transmission
Quantum state
transmissionSlide20
Quantum Dense CodingTask: Classical info transmission
Quantum Dense CodingSlide21
Quantum Dense CodingTask: Classical info transmissionMedium: Quantum State
Quantum Dense CodingSlide22
Quantum Dense CodingTask: Classical info transmissionMedium: Quantum State
Task: quantum state/info
transmission
Task: Quantum state/info
transmission
Quantum Dense CodingSlide23
Quantum Dense CodingTask: Classical info transmissionMedium: Quantum State
Task: Quantum state/info
transmission
Medium: Quantum State
Quantum Dense CodingSlide24
Task: Classical info transmissionMedium: Quantum State
Task: Quantum state/info
transmission
Medium: Quantum State
Quantum Dense Coding
Quantum TeleportationSlide25
Quantum TeleportationBennett, Brassard, Crepeau, Jozsa
, Peres, Wootters, PRL 1993Slide26
Quantum TeleportationTask: Sending arbitrary quantum stateSlide27
Quantum Teleportation
Task: Sending Slide28
Quantum Teleportation
Task: Sending Slide29
Quantum TeleportationTask: Sending
Classical: Infinite communication Slide30
Quantum TeleportationTask: Sending
Classical: Infinite communication Slide31
Quantum Teleportation
A
in
B
Alice
BobSlide32
Quantum Teleportation
A
in
B
Alice
Bob
Alice performs measurements on “in’’ and ASlide33
Quantum Teleportation
A
in
B
Alice
BobAfter measurementSlide34
Quantum Teleportation
A
in
B
Alice
BobAfter measurement
2 bits of classical comm.
sent by Alice to BobSlide35
Quantum Teleportation
A
in
B
Alice
BobAfter measurement
Bob performs unitarySlide36
Quantum Teleportation
A
in
B
Alice
BobAfter measurement
State is with BobSlide37
Moral
Classical
Quantum
Vs.
Task: sending arbitrary quantum state
Infinite classical comm2 bits of classical commSlide38
Moral
Classical
Quantum
Task: sending arbitrary quantum state
Infinite classical
comm2 bits of classical commVs. Slide39
Is it magic?Slide40
Is it magic?
Of course not!Slide41
Is it magic?
Ingredient: Quantum MechanicsSlide42
Is it magic?
Entangled statesSlide43
What is entanglement?
Unentangled
/Useless states
:
Entangled/Useful states
:Slide44
What is entanglement?
Unentangled
/Useless states
:
Entangled/Useful states
:Slide45
What is entanglement?
Unentangled
/Useless states
:
Entangled/Useful states
:Slide46
Is it just theory?Slide47
ExperimentsSlide48
PhotonsSlide49
Photons
143 Km TeleportationSlide50
~100KMSlide51
Entanglement Swapping
Zukowski, Zeilinge, Horne, Ekert, PRL 71, 4287 (’93)Slide52
Entanglement Swapping
Zukowski, Zeilinge, Horne, Ekert, PRL 71, 4287 (’93)Slide53
Photons
PhotonsSlide54
Photons
PhotonsSlide55
IONSSlide56
IONS
14 ions entangledSlide57
ION Entangled States
Phys. Rep. 2008Slide58
Quantum Teleportation between Light and MatterSlide59
Quantum Teleportation between Light and MatterSlide60
Quantum Teleportation between Light and Matter
Polzik’s group, Nature 443, 557 (’06)Slide61
Quantum Teleportation between Light and Matter Polzik’s group, Nature 443, 557 (’06)Slide62
IONS: TeleportationSlide63
IONS: TeleportationSlide64
IONS: TeleportationSlide65
IONS: TeleportationSlide66
NMR
Entangled states in NMRSlide67
Teleportation by NMRSlide68
Teleportation by NMR
Nielsen, Knill, Laflamme, Nature 395 (’98)Slide69
Optical LatticesSlide70
Optical Lattices
Entangled states in
Optical latticesSlide71
Optical Lattices
Entangled states in
Optical latticesSlide72
Optical Lattices
Resonating valence bond states in
Optical latticesSlide73
Teleportation: Neutral Atoms
Wu, Yang,
Shen
,
Zheng
, J. Phys. B: At. Mol. Opt. Phys. 46,185502 (’13)Slide74
Teleportation: Spin chain1. Initially the spin chain is in the ground state: Slide75
Teleportation: Spin chain1. Initially the spin chain is in the ground state:
2. Alice places an arbitrary state at her end: Slide76
Teleportation: Spin chain1. Initially the spin chain is in the ground state:
2. Alice places an arbitrary state at her end: 3. The state evolves according to some Hamiltonian: Slide77
Teleportation: Spin chain1. Initially the spin chain is in the ground state:
2. Alice places an arbitrary state at her end: 3. The state evolves according to some Hamiltonian:
4. Bob receives the state after some time.
Bose, PRL(’03),
Subrahmanyam
, PRA (’03)Slide78
Many other systems …….Slide79
Teleportation for arbitrary statesSlide80
AB
Alice & Bob share a state Slide81
AB
Alice & Bob share a state Slide82
Ain
B
Task: To send to Bob
single copy of is available
C
dSlide83
Ain
B
Allowed operations: LOCCSlide84
Ain
B
Not allowed operations: exchange
qubitsSlide85
Ain
B
Alice & Bob perform some LOCC, T, Slide86
Ain
B
Alice & Bob perform some LOCC, T, and create at Bob’s sideSlide87
Ain
B
Alice & Bob perform some LOCC, T, and create at Bob’s side
Check its closeness with Slide88
AinB
Quantify closeness:
integration over all inputs
Teleportation fidelitySlide89
Singlet Fraction: : max singlet fraction from by LOCC
Bennett,
Divincenzo
,
Smolin
, Wootters, PRA 54, 3824 (’97)MPR Horodeccy, PRA 60, 1888 (’99)M.A. Nielsen, quant-ph/0205035Slide90
Singlet Fraction: : max singlet fraction from by LOCC
Horodeccy
, PRA
60
, 1888 (’99)
Nielsen, arXiv: 0205035Verstreate, Verschele, PRL 90, 097901 (’03) Slide91
Popescu, PRL 72, 797 (’94)
Alice & Bob share separable state, then
f
max
=2/3Slide92
Tele Capacity: Known/Unknown
Single Sender – Single Receiverdd
Solved
Slide93
Teleportation Network 1Slide94
Teleportation: Monogamy
Alice
Debu
Charu
Nitu
....BobSenders
ReceiverSlide95
Teleportation: Monogamy
Alice
Debu
Charu
Nitu
....BobSenders
Receiver
Teleportation monogamyFaithful teleportation cannot be freely performedSlide96
Teleportation: MonogamyTele mono ineq:
Lee and Park, PRA 79, 054309(’09) Slide97
Teleportation: MonogamyHolds for pure
states:Lee and Park, PRA 79, 054309(’09) Slide98
Teleportation: MonogamyHolds for pure
states:Lee and Park, PRA 79, 054309(’09)
Follows from monogamy of concurrence squared in 2
dSlide99
Teleportation: MonogamyDoes Not hold for mixed
states:Lee and Park, PRA 79, 054309(’09) Slide100
Teleportation Network 2Slide101
Teleportation Network
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)ASD, U. Sen, PRA 81, 012308 (’01)Slide102
Teleportation Network
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)ASD, U. Sen, PRA 81, 012308 (’01)Slide103
Teleportation Network
Alice (A
1
)
Alice (A
2)Bob (B1)Bob (B2)ASD, U. Sen, PRA 81, 012308 (’01)Establish relation between capacity & entanglement Slide104
Tele Capacity: Known/Unknown
Single Sender – Single Receiverdd
Solved
Slide105
Tele Capacity: Known/Unknown
Single Sender – Single Receiverdd
Solved
Many Senders – single Receiver
Not Solved Slide106
Tele Capacity: Known/Unknown
Single Sender – Single Receiverdd
Solved
Many Senders – single Receiver
Not Solved Many Senders – many ReceiverNot Solved Slide107
Single Sender – Single Receiver
Many Senders – Single Receiver
Solved
Many Senders – Two Receivers
Many Senders – Many ReceiversPartially Solved Not Solved Classical info transmit
known/Unknown
Quantum info transmissionSingle Sender – Single Receiverdd Solved Many Senders – Single ReceiverNot Solved Many Senders – Many ReceiversNot Solved Slide108
QIC@HRISlide109