Ankit Garg Princeton Univ. Joint work with Mark Braverman Young Kun Ko Princeton Univ. Princeton Univ. Jieming Mao Dave Touchette Princeton Univ. Univ.

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Presentation transcript:

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

Quantum Communication Complexity Alice Bob

Quantum Protocols Alice Bob Send C 1

Quantum Protocols Alice Bob Send C 2

Quantum protocols

Quantum communication complexity [Yao ‘93]

Disjointness

Quantum Information Theory 101

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

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

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

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

Quantum Information Complexity

QIC of AND

Why is it hard?

Proof idea

Complete reduction

Continuity of QIC

Conclusion and Open Problems

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

Thank You

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