Trade-offs between Entanglement and Communication

• URL: http://arxiv.org/abs/2306.01233v1
• Date: Fri, 2 Jun 2023 01:49:39 GMT
• Title: Trade-offs between Entanglement and Communication
• Authors: Srinivasan Arunachalam and Uma Girish
• Abstract summary: We show that quantum simultaneous protocols with $tildeTheta(k5 log3 n)$ qubits of entanglement can exponentially outperform two-way randomized protocols with $O(k)$ qubits of entanglement. Prior to our work, only a relational separation was known.
• Score: 5.88864611435337
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the advantages of quantum communication models over classical communication models that are equipped with a limited number of qubits of entanglement. In this direction, we give explicit partial functions on $n$ bits for which reducing the entanglement increases the classical communication complexity exponentially. Our separations are as follows. For every $k\ge 1$: $Q\|^*$ versus $R2^*$: We show that quantum simultaneous protocols with $\tilde{\Theta}(k^5 \log^3 n)$ qubits of entanglement can exponentially outperform two-way randomized protocols with $O(k)$ qubits of entanglement. This resolves an open problem from [Gav08] and improves the state-of-the-art separations between quantum simultaneous protocols with entanglement and two-way randomized protocols without entanglement [Gav19, GRT22]. $R\|^*$ versus $Q\|^*$: We show that classical simultaneous protocols with $\tilde{\Theta}(k \log n)$ qubits of entanglement can exponentially outperform quantum simultaneous protocols with $O(k)$ qubits of entanglement, resolving an open question from [GKRW06, Gav19]. The best result prior to our work was a relational separation against protocols without entanglement [GKRW06]. $R\|^*$ versus $R1^*$: We show that classical simultaneous protocols with $\tilde{\Theta}(k\log n)$ qubits of entanglement can exponentially outperform randomized one-way protocols with $O(k)$ qubits of entanglement. Prior to our work, only a relational separation was known [Gav08].

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