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From Notices of the AMS

Top row shows Alice and Bob on an untrusted quantum network with an eavesdropper present, and a trusted classical channel. They are each with a secret bit string. Bottom row shows Alice and Bob on a trusted quantum network with no eavesdropper. They are each with a random bit.
Quantum key distribution (top) and quantum coin-flipping (bottom).

The Mathematics of Quantum Coin-Flipping

by Carl A. Miller
Communicated by Emilie Purvine

Mathematical models are the lenses by which mathematics reflects the world we live in, and thus they are fundamental for progress in scientific applications. And yet, science is fluid, and a lot of growth happens when fundamental assumptions are changed. This kind of growth is exemplified in the subject of quantum information. Quantum physics alters basic rules of information processing and leads to new results in computing and communication.

The scenario of two-party coin-flipping illustrates how the answer to a problem can change simply depending on the nature of the model. Let's suppose that two parties, Alice and Bob, are connected by a communication channel and wish to flip a coin together. Alice wants the outcome of the coin flip to be "0,"and Bob wants the outcome to be "1." Alice and Bob are permitted to send messages back and forth to one another, and at the end of the communication they will each broadcast bits, denoted X and Y respectively, declaring what they each believe the outcome of the coin flip to be.

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Also in Notices
Applications of PDEs and Stochastic Modeling to Protein Transport in Cell Biology
Euclidian Traveller in Hyperbolic Worlds
 

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2023

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