Trade-offs between Entanglement and Communication
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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≥ 1: Q^* versus R2^*: We show that quantum simultaneous protocols with Θ̃(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 Θ̃(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 Θ̃(klog 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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