Quantum Nonlocality under Latency Constraints

Code for the paper Quantum Nonlocality under Latency Constraints by Dawei Ding, Zhengfeng Ji, Pierre Pocreau, Mingze Xu, and Xinyu Xu.

Overview

This repository implements optimization tools for analyzing quantum advantages in LC games. The code computes classical and quantum bounds on game values when communication between parties is restricted by physical latency limitations.

Key features:

• NPA hierarchy for upper bounds on quantum correlations
• Seesaw algorithm for optimizing quantum strategies on LC games
• Classical deterministic strategy optimization
• Analysis of different latency constraints and layout of parties (no communication, one-round, merged parties)

Repository Structure

.
├── NPA/                         # NPA hierarchy implementation
│   ├── hierarchy.py             # SDP hierarchy for quantum bounds
│   ├── operator.py              # Measurement operator representation
│   └── canonicalOp.py           # Canonical monomial ordering
│
├── NetworkSeesaw/               # Seesaw optimization for quantum strategies
│   ├── seesaw.py                # Main seesaw algorithm
│   ├── quantumStrategy.py       # Quantum strategy with communication
│   ├── QCFO.py                  # Quantum Circuit with Fixed Order
│   ├── QCFO_utils.py            # Utility functions for QCFOs
│   └── data/                    # Storage for optimized strategies
│
├── latency_plot.py              # Simulation and latency plot (Table 4 and Fig. 13)
├── game.py                      # Definition of nonlocal games, and computation of classical value
├── random_XOR_game.py           # Random XOR game example (Table 2)
└── extended_XOR_games.py        # Extended XOR games analysis (Sec. 4.2.2, Table 6)

Installation

Requirements

pip install numpy cvxpy networkx matplotlib scipy toqito dill pandas

Required packages:

• numpy - Numerical computing
• cvxpy - Convex optimization
• networkx - Graph structures for communication networks
• matplotlib - Plotting
• toqito - Quantum information toolkit
• dill - Serialization for saving strategies
• scipy - Scientific computing
• pandas - Data analysis

Solvers:

• MOSEK (recommended) - Commercial solver with free academic licenses
• SCS (fallback) - Open-source SDP solver

Install MOSEK following instructions at mosek.com