A family of loss-tolerant quantum coin flipping protocols

TL;DR

This paper introduces a family of loss-tolerant quantum strong coin flipping protocols with varying qubit numbers, achieving biases below previous limits and showing bias reduction with more qubits, based on numerical evidence.

Contribution

It presents new loss-tolerant quantum coin flipping protocols that improve bias performance as the number of qubits increases, supported by semi-definite programming analysis.

Findings

Bias of 0.4 with one qubit

Bias of 0.3975 with two qubits

Bias decreases with more qubits, but at a diminishing rate

Abstract

We present a family of loss-tolerant quantum strong coin flipping protocols; each protocol differing in the number of qubits employed. For a single qubit we obtain a bias of 0.4, reproducing the result of Berl\'{i}n et al. [Phys. Rev. A 80, 062321 (2009)], while for two qubits we obtain a bias of 0.3975. Numerical evidence based on semi-definite programming indicates that the bias continues to decrease as the number of qubits is increased but at a rapidly decreasing rate.