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Dualities in quantum information theory Igor Devetak CSI, EE-S, USC quant-ph/0505138.

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Presentation on theme: "Dualities in quantum information theory Igor Devetak CSI, EE-S, USC quant-ph/0505138."— Presentation transcript:

1 Dualities in quantum information theory Igor Devetak CSI, EE-S, USC quant-ph/0505138

2 FQRS FFFQSW RESOURCE REVERSAL TIME REVERSAL SOURCE-CHANNEL DUALITY

3 Schumacher (quantum) compression Alice Bob Ref SIMULATES TO PRECISION… test state [Schumacher ’95] !

4 Schumacher (quantum) compression Alice Bob Ref Would not work on any other input! test state [Schumacher ’95] asymptotic

5 Fully quantum reverse Shannon (FQRS) cf. Schumacher compression [Devetak, Hayden, Leung, Shor] ! feedback channel

6 Quantum reverse Shannon (QRS) QRS FQRS Rule I [Bennett, Devetak, Harrow, Shor, Winter]

7 FQRS Alice Bob Ref SIMULATES TO PRECISION… [Devetak, Hayden, Leung, Shor]

8 FQRS Alice Bob Ref [Devetak, Hayden, Leung, Shor]

9 FQRS FFFQSW RESOURCE REVERSAL TIME REVERSAL SOURCE-CHANNEL DUALITY Quantum reverse Shannon

10 The Feedback Father (FF) Alice Bob

11 Alice Bob The Feedback Father (FF)

12 FF cf. FQRS

13 Resource reversal duality: FQRS & FF

14 FQRS FFFQSW RESOURCE REVERSAL TIME REVERSAL SOURCE-CHANNEL DUALITY Quantum reverse Shannon Father

15 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”)

16 Fully quantum Slepian Wolf (FQSW) Alice Bob Ref Source [Abeyesinghe, Devetak, Hayden, Winter]

17 FQSW Bob Alice Ref Source [Abeyesinghe, Devetak, Hayden, Winter]

18 FQSW ED QSW Mother FQSW [Abeyesinghe, Devetak, Hayden, Winter] = state merging [Horodecki, Oppenheim, Winter ’05] [Devetak, Winter 03] [Devetak, Harrow, Winter 03]

19 FQRS FFFQSW RESOURCE REVERSAL TIME REVERSAL SOURCE-CHANNEL DUALITY Quantum reverse Shannon Father Mother State merging

20 Source-channel duality: FQSW & FF FF cf. FQSW

21 Time-reversal duality: FQSW & FQRS FQRS cf. FQSW interchange A & B:

22 Alice Bob Ref Source FQSW FQRS

23 FQSW FF FQRS Summary: Quantum, distributed, closed & relative

24 FQRS FFFQSW RESOURCE REVERSAL TIME REVERSAL SOURCE-CHANNEL DUALITY Quantum reverse Shannon Father Mother State merging Quantum Distributed Closed Relative

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