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

2. Content Local channels Comparison Entanglement-annihilating

3. CEQIP’2011 Local channels E1E1 E2E2

4. CEQIP’2011 Comparison The aim is to distinguish between  non-identical channels  twin-identical channels -distance between channels:

5. CEQIP’2011 Scheme

6. CEQIP’2011 Local two-qubit channels Matrix representation for one channel

7. CEQIP’2011 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’ +1 – All channels ‘same’ ‘different’

8. CEQIP’2011 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’ +1 +0.25 0

9. Entanglement-annihilating behaviour

10. CEQIP’2011

11. What does EA mean? is entanglement-annihilating if the output state is separable for all input states is entanglement-breaking if the state is disentangled with respect to partitioning ‘1+2’|‘anc' for any input state and ancillary system.

12. CEQIP’2011 Properties

13. CEQIP’2011 Two depolarizing channels Entanglement-breaking

14. CEQIP’2011 Two depolarizing channels Entanglement-annihilating

15. CEQIP’2011 Two depolarizing channels

16. CEQIP’2011 Pauli channels

17. CEQIP’2011 Lemma

18. CEQIP’2011 Corollary 1

19. CEQIP’2011 How is Corollary 1 useful?

20. CEQIP’2011 Corollary 2

21. CEQIP’2011

23. 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

24. CEQIP’2011 Conclusion Local channels ask many questions important for practical Quantum Information Are participants similar to local channels? Let us try answer them…

25. Thank you for listening!