1. Ankit Garg Princeton Univ. Joint work with Mark Braverman Young Kun Ko Princeton Univ. Princeton Univ. Jieming Mao Dave Touchette Princeton Univ. Univ. of Waterloo and Perimeter Institute Near Optimal Bounds on Bounded-Rounded Quantum Communication Complexity of Disjointness

2. Quantum Communication Complexity Alice Bob

3. Quantum Protocols Alice Bob Send C 1

4. Quantum Protocols Alice Bob Send C 2

5. Quantum protocols

6. Quantum communication complexity [Yao ‘93]

7. Disjointness

11. Quantum Information Theory 101

12. Classical Information Cost [CSWY `01, BJKS-04, BBCR-10] A B Protocol π

13. Quantum Information Cost A B Protocol π Quantum Protocol Issues: 1.No concept of transcript. 2.Reversible computing.

14. Quantum Information Cost [Touchette `14] Account for forgetting of information.

15. Quantum Information Cost [Touchette `14] Information sent by Alice Information forgotten by Alice

16. Quantum Information Complexity

20. QIC of AND

21. Why is it hard?

22. Proof idea

23. Complete reduction

24. Continuity of QIC

25. Conclusion and Open Problems

26. We prove this if the goal is to compute boolean functions.

27. Thank You