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Dualities in quantum information theory

Dualities in quantum information theory. Igor Devetak CSI, EE-S, USC. quant-ph/0505138. FQRS. TIME REVERSAL. RESOURCE REVERSAL. FF. FQSW. SOURCE-CHANNEL DUALITY. SIMULATES. TO PRECISION. …. !. [Schumacher ’95]. Schumacher (quantum) compression. Ref.

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Dualities in quantum information theory

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

  2. FQRS TIME REVERSAL RESOURCE REVERSAL FF FQSW SOURCE-CHANNEL DUALITY

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

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

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

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

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

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

  9. Quantum reverse Shannon FQRS TIME REVERSAL RESOURCE REVERSAL FF FQSW SOURCE-CHANNEL DUALITY

  10. The Feedback Father (FF) Alice Bob

  11. The Feedback Father (FF) Alice Bob

  12. The Feedback Father (FF) FF cf. FQRS

  13. Resource reversal duality: FQRS & FF

  14. Quantum reverse Shannon FQRS TIME REVERSAL RESOURCE REVERSAL FF FQSW SOURCE-CHANNEL DUALITY 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. Ref Source [Abeyesinghe, Devetak, Hayden, Winter] Fully quantum Slepian Wolf (FQSW) Alice Bob

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

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

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

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

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

  22. FQSW FQRS Ref Source Alice Bob

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

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

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