Skip to Main Content

Advancing Research. Creating Connections.

The American Mathematical Society is dedicated to advancing research and connecting the diverse global mathematical community through publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs.

Learn more and join »

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.

Read more »

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

More from Notices »


News from the AMS

More News »

Feature Stories

More Feature Stories »




2-3 January

January 2-3, 2023

AMS Short Course: Polynomial systems, homotopy continuation and applications

3 January

January 3, 2023

Workshop for Department Chairs and Leaders

4-7 January

January 4-7, 2023

2023 Joint Mathematics Meetings (JMM)

With fifteen partner organizations offering paper sessions, panels, workshops, student activities, and invited addresses, each day of JMM 2023 will provide an array of offerings — truly something for everyone.

18-19 March

March 18-19, 2023

Spring Southeastern Sectional Meeting

Georgia Institute of Technology, Atlanta, GA

1-2 April

April 1-2, 2023

Spring Eastern Sectional Meeting

Meeting virtually

15-16 April

April 15-16, 2023

Spring Central Sectional Meeting

University of Cincinnati, Cincinnati, OH

6-7 May

May 6-7, 2023

Spring Western Sectional Meeting

California State University, Fresno, Fresno, CA

Member Journals

Notices of the American Mathematical Society Bulletin of the American Mathematical Society

Math in the Media

Math in the Media

Stay up-to-date with mathematics in current events and get ideas for classroom activities!
Also read Tony Phillips' deeper dives into recent mathematical developments.