26th Australian Institute of Physics Congress and the Australian and New Zealand Conference on Optics and Photonics

Using Randomness to Bound Memory in Quantum Stochastic Processes

Not scheduled

20m

Belinda Hutchinson Building (The University of Sydney )

Contributed Oral AIP | Quantum Science and Technology (QST)

Description

To an observer with limited memory, even highly structured processes can appear random. This points to a fundamental interplay between randomness and temporal correlations present in a complex system's behavior. In characterizing this interplay, it is crucial to evaluate how much of a system's behavior is irreducibly random, and the minimum memory cost to simulate it perfectly. Classically, the former is quantified by the entropy rate which measures the rate of information production, while the latter is bounded by the excess entropy which captures the information shared between the past and future. Together, these metrics govern optimal performance across diverse fields—from predicting complex systems, to extracting thermodynamic work, and even classifying systems along the spectrum between order and chaos.

We anticipate these relations to carry over to the quantum regime, where such questions are increasingly important to understand. Real-world quantum devices inevitably leak information into their environments and function as open, and often non-Markovian, system. When temporal correlations are mistaken for noise in such systems, consequences can be severe. For example, the inability to control multi-time non-Markovian noise represents a critical bottleneck in scaling fault-tolerant quantum computers. Thus there are abundant opportunities in improving quantum technologies by identifying and exploiting such hidden structures. These scenarios face the core questions: is that noise irreducible or superficial---can it in fact be revealed as hidden structure with sufficient resources?

Here, we answer these questions by formalizing the quantum entropy rate and excess entropy of quantum stochastic processes. We show their physical significance through a lower bound on the memory cost any recurrent quantum circuit must incur to correctly model the process. Importantly, the quantum excess entropy, which is shown to be equal to the QMI between the past and future, is derived by accumulating the total superficial randomness beyond the quantum entropy rate.