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Sergey Filippov ¹ , Tom áš Ryb á r ² , M ário Ziman² ¹ Moscow Institute of Physics and Technology

Local two-qubit channels: probability-based comparison of constituents and entanglement-annihilating behavior. Sergey Filippov ¹ , Tom áš Ryb á r ² , M ário Ziman² ¹ Moscow Institute of Physics and Technology ² Research Center for Quantum Information, Slovak Academy of Sciences. CEQIP’2011.

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Sergey Filippov ¹ , Tom áš Ryb á r ² , M ário Ziman² ¹ Moscow Institute of Physics and Technology

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  1. Local two-qubit channels:probability-based comparison of constituents and entanglement-annihilating behavior Sergey Filippov¹, Tomáš Rybár², Mário Ziman² ¹Moscow Institute of Physics and Technology ²Research Center for Quantum Information, Slovak Academy of Sciences CEQIP’2011

  2. Content • Local channels • Comparison • Entanglement-annihilating

  3. Local channels B E2 A E1

  4. Comparison The aim is to distinguish between • non-identical channels • twin-identical channels -distance between channels:

  5. Scheme

  6. Local two-qubit channels • Matrix representation for one channel

  7. Example 1 • Input state is • POVM has two effects, corresponding to projectors on symm. and antisymm. subspaces • The output mean value is • Unitary channels • ‘same’ • ‘different’ • All channels • ‘same’ • ‘different’ -1 +1

  8. Example 2 • Input state • POVM has two effects, corresponding to projectors on symm. and antisymm. subspaces • The output mean value is • All channels • ‘same’ • ‘different’ +0.25 -1 0 +1

  9. Entanglement-annihilating behaviour

  10. What does EA mean? • isentanglement-annihilating if the output state isseparable for all input states • is entanglement-breaking if the state is disentangledwith respect to partitioning ‘1+2’|‘anc' for any input state andancillary system.

  11. Properties

  12. Two depolarizing channels • Entanglement-breaking

  13. Two depolarizing channels • Entanglement-annihilating

  14. Two depolarizing channels

  15. Pauli channels

  16. Lemma

  17. Corollary 1

  18. How is Corollary 1 useful?

  19. Corollary 2

  20. Summary • We have considered • Probability-based comparison of qubit channels • Entanglement between qubits involved while passing through a local channel • Problems to investigate • Upper-dimensional systems (qudits) • Continuous-variables • Multipartite systems • Hope you have had some fun 

  21. Conclusion • Local channels ask many questions important for practical Quantum Information • Let us try answer them… • Are participants similar to local channels?

  22. Thank you for listening!

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