Communication complexity of entanglement assisted multi-party computation
Ruoyu Meng, Aditya Ramamoorthy
TL;DR
This work investigates zero-error multi-party function computation with entanglement-assisted communication for prime $n$, introducing a generalized inner product function with a structured promise. It presents a quantum protocol that uses $m$ shared entangled $n$-dimensional states and the quantum Fourier transform to achieve a communication cost of $(n-1)\log n$ bits, significantly outperforming a classical protocol that requires $(n-1)^2 \log n^2$ bits; an ILP-based lower bound and numerical ILP experiments establish a strict quantum advantage. The results connect finite-field structure with quantum processing to quantify when entanglement yields provable benefits in distributed computation. Overall, the paper provides a concrete separation between quantum and classical communication costs in a multi-party, zero-error setting and offers algorithmic tools for lower-bounding classical protocols via ILP.
Abstract
We consider a quantum and classical version multi-party function computation problem with $n$ players, where players $2, \dots, n$ need to communicate appropriate information to player 1, so that a "generalized" inner product function with an appropriate promise can be calculated. The communication complexity of a protocol is the total number of bits that need to be communicated. When $n$ is prime and for our chosen function, we exhibit a quantum protocol (with complexity $(n-1) \log n$ bits) and a classical protocol (with complexity $(n-1)^2 (\log n^2$) bits). In the quantum protocol, the players have access to entangled qudits but the communication is still classical. Furthermore, we present an integer linear programming formulation for determining a lower bound on the classical communication complexity. This demonstrates that our quantum protocol is strictly better than classical protocols.