1 / 24

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.

reuel
Download Presentation

Dualities in quantum information theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related