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

What Does Prediction Mean in a Quantum World?

Not scheduled

20m

Belinda Hutchinson Building (The University of Sydney )

Contributed Oral AIP | Quantum Science and Technology (QST)

Speaker

Graeme Berk (Nanyang Technological University)

Description

Prediction is a foundational task across the quantitative sciences and is precisely understood in the classical world. The universe, however, is fundamentally quantum. Then, what does it mean to 'predict' a future whose proper description is neither a definite state nor a probability distribution, but a quantum state, and what resources are required?

The first question turns out to be unexpectedly problematic. Classically, prediction is per-realisation faithfulness: a model outputs the correct probability distribution of what will happen next, given a past, and it does so in every realisation in which that past is observed. Quantum mechanically, this final clause is ill-defined, because density matrices fix no hidden variable for which pure state the model's memory is 'really' in. We are thus compelled towards ontological neutrality—that per-realisation faithfulness holds for all pure states of all ensembles consistent with the memory state. However, doing so appears to strip predictive models of the operational content that privileges them over more general generative ones. We resolve this tension by proving equivalence of our notion of quantum prediction with non-oracularity. The memory of a predictive model contains no 'oracular' information pertaining to its own future beyond that already in the past.

For the second question, we bound the minimum average memory required to implement a quantum model of a quantum process in terms of the forecasting advantage yielded by knowing the past—a Holevo information-derived generalisation of the classical past-future correlation measure known as excess entropy. We then decompose quantum memory into four operationally distinct contributions: excess entropy, oracular information, gauge information, and crypticity. From this, the goal of quantum prediction emerges as an optimisation: maximise the excess entropy that gets encoded into memory, while simultaneously minimising oracular information; predicting efficiently further requires minimising gauge information and crypticity.