User:Wnelson4/sandbox

Assumptions
There are a few assumptions that must be made for this protocol to work properly. The first is that Alice can create each state independent of Bob, and with an equal probability. Second, for the first bit that Bob successfully measures, his basis and bit are both random and completely independent of Alice. The last assumption, is that when Bob measures a state, he has a uniform probability to measure each state, and no state is easier to be detected than others. This last assumption is especially important because if Alice were aware of Bob's inability to measure certain states, she could use that to her advantage.

Cheating
The key issue with coin flipping is that it occurs between two distrustful parties. These two parties are communicating some distance from each other and must agree on a winner or loser with each having a 50 percent chance of winning. However, since they are distrustful of one another, cheating is likely to occur. Cheating can occur in a number of ways, such as claiming they lost some of the message when they do not like the result, or increasing the average number of photons contained in each of the pulses.

For Bob to cheat, he would have to be able to guess Alice’s basis with a probability greater than ½. In order to accomplish this, Bob would have to be able to determine a train of photons randomly polarized in one basis from a train of photons polarized in another basis.

Alice, on the other hand, could cheat in a couple of different ways, but she has to be careful because Bob could easily detect it. When Bob sends a correct guess to Alice, she could convince Bob that her photons are actually polarized the opposite of Bob’s correct guess. Alice could also send Bob a different original sequence of qubits than she actually used in order to beat Bob.

Detecting a third-party
Single photons are used to pass the information from one player to the other (qubits). In this protocol, the information is encoded in the single photons with polarization directions of 0, 45, 90, and 135 degrees, non-orthogonal quantum states. When a third party attempts to read or gain information on the transmission, they alter the photon’s polarization in a random way that is likely detected by the two players because it does not match the pattern exchanged between the two legitimate users.

Experimental
As mentioned in the history section, scientists at the LTCI in Paris have experimentally carried out a quantum coin flipping protocol. Previous protocols called for a single photon source or an entangled source to be secure. However, these sources are why it is difficult for quantum coin flipping to be implemented. Instead, the researchers at LTCI used the effects of quantum superposition rather than a single photon source, which they claim makes implementation easier with the standard photon sources available.

The researchers used the Clavis2 platform developed by IdQuantique for their protocol, but needed to modify the Clavis2 system in order for it to work for the coin flipping protocol. The experimental setup they used with the Clavis2 system, involves a two-way approach. Light is pulsed at 1550 nanometres is from Bob to Alice. Alice then encodes her information with a phase modulator, and uses a Faraday mirror to attenuate and reflect the pulses back to Bob. Using two high quality single photon detectors and a phase modulator, Bob chooses a measurement basis to detect the pulses from Alice.

They replaced the detectors on Bob’s side because of the low detection efficiencies of the previous detectors. When they replaced the detectors, they were able to show a quantum advantage on a channel for over 15 km. A couple of other challenges the group faced was reprogramming the system because photon source attenuation was high and performing system analyses to identify losses and errors in system components. With these corrections, the scientists were capable of implementing a coin flipping protocol by introducing a small honest abort probability, the probability that two honest participants cannot obtain a coin flip at the end of the protocol, but at a short communication distance.