On the Role of Shared Entanglement

Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement analogue" for the famous theorem by Newman, saying that the number of shared random bits required for solving any communication problem can be at most logarithmic in the input length (i.e., using more than O(log n) shared random bits would not reduce the complexity of an optimal solution). In this paper we prove that the same is not true for entanglement. We establish a wide range of tight (up to a polylogarithmic factor) entanglement vs. communication tradeoffs for relational problems. The low end is: for any t > 2, reducing shared entanglement from logt n to o(logt-2 n) qubits can increase the communication required for solving a problem almost exponentially, from O(logt n) to ( n). The high end is: for any > 0, reducing shared enta...

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Dmitry Gavinsky
• Keywords: Communication, Communication Complexity, CORR 2006, Education, Random Bits