dualities in quantum information theory igor devetak csi, ee-s, usc quant-ph/0505138
DESCRIPTION
Schumacher (quantum) compression Alice Bob Ref SIMULATES TO PRECISION… test state [Schumacher ’95] !TRANSCRIPT
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Dualities in quantum information theory
Igor DevetakCSI, EE-S, USC
quant-ph/0505138
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FQRS
FF FQSW
RESOURCEREVERSAL
TIMEREVERSAL
SOURCE-CHANNEL DUALITY
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Schumacher (quantum) compression
Alice
Bob
Ref
SIMULATES TO PRECISION …
test state
[Schumacher ’95] !
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Schumacher (quantum) compression
Alice
Bob
Ref
Would not work on anyother input!
test state
[Schumacher ’95]
asymptotic
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Fully quantum reverse Shannon (FQRS)
cf. Schumacher compression
[Devetak, Hayden, Leung, Shor] !
feedback channel
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Quantum reverse Shannon (QRS)
QRS
FQRS
Rule I
[Bennett, Devetak, Harrow, Shor, Winter]
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FQRS
Alice
Bob
Ref
SIMULATES TO PRECISION …
[Devetak, Hayden, Leung, Shor]
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FQRS
Alice
Bob
Ref
[Devetak, Hayden, Leung, Shor]
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FQRS
FF FQSW
RESOURCEREVERSAL
TIMEREVERSAL
SOURCE-CHANNEL DUALITY
Quantum reverse Shannon
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The Feedback Father (FF)
Alice
Bob
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Alice
Bob
The Feedback Father (FF)
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The Feedback Father (FF)
FF
cf. FQRS
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Resource reversal duality: FQRS & FF
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FQRS
FF FQSW
RESOURCEREVERSAL
TIMEREVERSAL
SOURCE-CHANNEL DUALITY
Quantum reverse Shannon
Father
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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”)
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Fully quantum Slepian Wolf (FQSW)
Alice
Bob
Ref
Source
[Abeyesinghe, Devetak, Hayden, Winter]
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FQSW
Bob
Alice
Ref
Source
[Abeyesinghe, Devetak, Hayden, Winter]
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FQSW
ED QSW
Mother FQSW
[Abeyesinghe, Devetak, Hayden, Winter]
= state merging[Horodecki, Oppenheim, Winter ’05]
[Devetak, Winter 03]
[Devetak, Harrow, Winter 03]
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FQRS
FF FQSW
RESOURCEREVERSAL
TIMEREVERSAL
SOURCE-CHANNEL DUALITY
Quantum reverse Shannon
Father Mother
State merging
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Source-channel duality: FQSW & FF
FF
cf. FQSW
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Time-reversal duality: FQSW & FQRS
FQRS
cf. FQSW
interchange A & B:
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Alice
Bob
Ref
Source
FQSW
FQRS
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FQSW
FF
FQRS
Summary: Quantum, distributed, closed & relative
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FQRS
FF FQSW
RESOURCEREVERSAL
TIMEREVERSAL
SOURCE-CHANNEL DUALITY
Quantum reverse Shannon
Father Mother
State merging
QuantumDistributedClosed Relative