Dualities in quantum information theory Igor Devetak CSI, EE-S, USC quant-ph/0505138.
-
Upload
bertina-pierce -
Category
Documents
-
view
216 -
download
0
description
Transcript of Dualities in quantum information theory Igor Devetak CSI, EE-S, USC quant-ph/0505138.
Dualities in quantum information theory
Igor DevetakCSI, EE-S, USC
quant-ph/0505138
FQRS
FF FQSW
RESOURCEREVERSAL
TIMEREVERSAL
SOURCE-CHANNEL DUALITY
Schumacher (quantum) compression
Alice
Bob
Ref
SIMULATES TO PRECISION …
test state
[Schumacher ’95] !
Schumacher (quantum) compression
Alice
Bob
Ref
Would not work on anyother input!
test state
[Schumacher ’95]
asymptotic
Fully quantum reverse Shannon (FQRS)
cf. Schumacher compression
[Devetak, Hayden, Leung, Shor] !
feedback channel
Quantum reverse Shannon (QRS)
QRS
FQRS
Rule I
[Bennett, Devetak, Harrow, Shor, Winter]
FQRS
Alice
Bob
Ref
SIMULATES TO PRECISION …
[Devetak, Hayden, Leung, Shor]
FQRS
Alice
Bob
Ref
[Devetak, Hayden, Leung, Shor]
FQRS
FF FQSW
RESOURCEREVERSAL
TIMEREVERSAL
SOURCE-CHANNEL DUALITY
Quantum reverse Shannon
The Feedback Father (FF)
Alice
Bob
Alice
Bob
The Feedback Father (FF)
The Feedback Father (FF)
FF
cf. FQRS
Resource reversal duality: FQRS & FF
FQRS
FF FQSW
RESOURCEREVERSAL
TIMEREVERSAL
SOURCE-CHANNEL DUALITY
Quantum reverse Shannon
Father
The Source
!
• Passive protagonist – not allowed to code.• Sends inputs to Alice and/or Bob.• Goal: Redirection of channels originating at the Source (“source coding”)
Fully quantum Slepian Wolf (FQSW)
Alice
Bob
Ref
Source
[Abeyesinghe, Devetak, Hayden, Winter]
FQSW
Bob
Alice
Ref
Source
[Abeyesinghe, Devetak, Hayden, Winter]
FQSW
ED QSW
Mother FQSW
[Abeyesinghe, Devetak, Hayden, Winter]
= state merging[Horodecki, Oppenheim, Winter ’05]
[Devetak, Winter 03]
[Devetak, Harrow, Winter 03]
FQRS
FF FQSW
RESOURCEREVERSAL
TIMEREVERSAL
SOURCE-CHANNEL DUALITY
Quantum reverse Shannon
Father Mother
State merging
Source-channel duality: FQSW & FF
FF
cf. FQSW
Time-reversal duality: FQSW & FQRS
FQRS
cf. FQSW
interchange A & B:
Alice
Bob
Ref
Source
FQSW
FQRS
FQSW
FF
FQRS
Summary: Quantum, distributed, closed & relative
FQRS
FF FQSW
RESOURCEREVERSAL
TIMEREVERSAL
SOURCE-CHANNEL DUALITY
Quantum reverse Shannon
Father Mother
State merging
QuantumDistributedClosed Relative