Quantum Theory in Finite Dimension Cannot Explain Every General Process

Explore a conference talk from TQC 2023 (Theory of Quantum Computation, Communication and Cryptography) that delves into the limitations of finite-dimensional quantum theory in explaining general processes with finite memory. Learn about groundbreaking research demonstrating how certain processes requiring finite-dimensional explanations cannot be fully explained through classical probability or quantum mechanics alone. Discover new families of processes defined by generalized probabilistic theory (GPT) dynamics that transcend both quantum and classical finite-dimensional explanations. Examine specific examples involving qubits and qutrits that lack classical finite-dimensional realizations, including cases previously introduced as functions of infinite-dimensional Markov chains. Gain insights into the memory size requirements for classical models attempting to realize noisy qubit processes, presented through detailed mathematical frameworks and theoretical proofs.