CSHS Quantum Simulation

A simple C++ quantum simulation of the CHSH game and its classical and quantum strategies.

This project demonstrates how quantum strategies outperform classical ones in a well-known theoretical game from quantum information theory.

The CSHS Game

Theoretical framework used to experimentally test concepts from quantum information.

The game involves three entities:

• Alice (player)
• Bob (player)
• Referee

Rules:

1. The referee randomly chooses two bits:
   • x for Alice
   • y for Bob
2. Alice and Bob receive their respective bits without communicating.
3. Alice outputs a bit a, and Bob outputs a bit b.
4. Alice and Bob win if:

a ⊕ b = x ∧ y

Otherwise, they lose.

Classical vs Quantum Strategies

• Classical strategies have a maximum winning probability of 75%.
• Quantum strategies, using entangled states, can achieve a winning probability of 85%.

This simulation compares both approaches and highlights the advantage provided by quantum mechanics.

1) Random Strategy 
2) Copy Strategy 
3) Opposite Strategy 
4) Always zero Strategy 
5) Always one Strategy 
6) Quantum Strategy 

WIN RATE (134000 games played)
1) [##########################........................] 50.1507%
2) [#############.....................................] 24.9358%
3) [#############.....................................] 24.9358%
4) [######################################............] 75.0194%
5) [######################################............] 75.0194%
6) [###########################################.......] 85.3398%

How to build and run

g++ src/*.cpp -I includes -o bin/main && bin/main

References

[1] Riccardo Bassoli, Holger Boche, Christian Deppe, et al.: Quantum Communication Networks, Springer, 2021.