Editing Quantum Weak Coin Flipping (section)

==Further Information==

# The QWCF protocol by Spekkens and Rudolph is optimal, i.e., it achieves the minimum possible bias for any QWCF protocol, which is ϵ=sin(θ/2).
# This protocol is cheat-sensitive, i.e., if a dishonest party tries to cheat by deviating from the protocol, the honest party can detect it with some probability and abort the protocol.
# This protocol is based on entanglement swapping, i.e., the parties exchange qubits that are entangled with their own qubits, and then perform a Bell measurement on their qubits to obtain a shared random bit.
# The mentioned protocol is similar to the Quantum Strong Coin Flipping (QSCF) protocol by Ambainis, but with a different choice of states and measurements. The QSCF protocol by Ambainis uses the states ∣+⟩=(∣0⟩+∣1⟩)/2 and ∣−⟩=(∣0⟩−∣1⟩)/2, and the measurements {∣0⟩,∣1⟩} and {∣+⟩,∣−⟩}. The QSCF protocol by Ambainis achieves a bias of ϵ=1/2, which is optimal for QSCF, but not for QWCF.
# This protocol can be generalized to a Quantum Weak Dice Rolling (QWDR) protocol, where the parties want to generate a random integer between 1 and N, such that each party has a known and opposite preferred outcome. The QWDR protocol can be implemented by using N orthogonal states and N measurements, and choosing the outcome as the index of the state that matches the measurement.

* [https://arxiv.org/abs/quant-ph/0202118 Quantum Protocol for Cheat-Sensitive Weak Coin Flipping, R.W. Spekkens, T. Rudolph, Physical Review Letters 89, 2002]
* [https://arxiv.org/abs/quant-ph/0204022 A New Protocol and Lower Bounds for Quantum Coin Flipping, A. Ambainis, Journal of Computer and System Sciences, 2004]
* [https://arxiv.org/abs/0711.4114 Quantum weak coin flipping with arbitrarily small bias, C. Mochon, 2007]

<div style='text-align: right;'>''*contributed by Mohammadreza Vali''