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arXiv:2309.13572 · npj Quantum Information

Causal asymmetry of classical and quantum autonomous agents

Spiros Kechrimparis, Mile Gu, Hyukjoon Kwon

Published Sep 1, 2026• 0 citations
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Abstract

Why is it that a ticking clock typically becomes less accurate when subject to outside noise but rarely the reverse? Here, we formalise this phenomenon by introducing process causal asymmetry—a fundamental difference in the amount of past information an autonomous agent must track to transform one stochastic process to another over an agent that transforms in the opposite direction. We then illustrate that this asymmetry can surprisingly reverse when agents possess a quantum memory. Thus, the spontaneous direction in which processes get ‘simpler’ may be different, depending on whether quantum information processing is allowed or not.

DOI
10.1038/s41534-026-01335-7

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Why is it that a ticking clock typically becomes less accurate when subject to outside noise but rarely the reverse? Here, we formalise this phenomenon by introducing process causal asymmetry—a fundamental difference in the amount of past information an autonomous agent must track to transform one stochastic process to another over an agent that transforms in the opposite direction. We then illustrate that this asymmetry can surprisingly reverse when agents possess a quantum memory. Thus, the spontaneous direction in which processes get ‘simpler’ may be different, depending on whether quantum information processing is allowed or not.
Causal asymmetry is one of the great surprises in predictive modeling: The memory required to predict the future differs from the memory required to retrodict the past. There is a privileged temporal direction for modeling a stochastic process where memory costs are minimal. Models operating in the other direction incur an unavoidable memory overhead. Here, we show that this overhead can vanish when quantum models are allowed. Quantum models forced to run in the less-natural temporal direction not only surpass their optimal classical counterparts but also any classical model running in reverse time. This holds even when the memory overhead is unbounded, resulting in quantum models with unbounded memory advantage.
Causal asymmetry is one of the great surprises in predictive modeling: The memory required to predict the future differs from the memory required to retrodict the past.There is a privileged temporal direction for modeling a stochastic process where memory costs are minimal.Models operating in the other direction incur an unavoidable memory overhead.Here, we show that this overhead can vanish when quantum models are allowed.Quantum models forced to run in the less-natural temporal direction not only surpass their optimal classical counterparts but also any classical model running in reverse time.This holds even when the memory overhead is unbounded, resulting in quantum models with unbounded memory advantage.
We consider a very general class of theories, process theories, which capture the underlying structure common to most theories of physics as we understand them today (be they established, toy or speculative theories). Amongst these theories, we will be focusing on those which are `causal', in the sense that they are intrinsically compatible with the causal structure of space-time -- as required by relativity. We demonstrate that there is a sharp contrast between these theories and the corresponding time-reversed theories, where time is taken to flow backwards from the future to the past. While the former typically feature a rich gamut of allowed states, the latter only allow for a single state: eternal noise. We illustrate this result by considering of the time-reverse of quantum theory. We also derive a strengthening of the result in PRL 108, 200403 on signalling in time-reversed theories.
We consider devices with two inputs and two outputs, Alice and Bob each having access to one input and one output. To such a device we associate time-reverses by exchanging the roles of the inputs and the outputs. We find that there are devices which admit a local hidden variable representation, but for which time-reverses enable perfect signaling between Alice and Bob. That is, a `perfect channel in one time direction' becomes a `non-channel in the other direction'. Also, for PR boxes time-reverses enable signaling between Alice and Bob, but never as a perfect channel. These results undermine the representation of causal structures as partial orders or similar `time-symmetric structures', as is often assumed in search of a theory of quantum gravity. They also provide new insights into the structure of the polytope of generalized probabilistic correlations, and contribute to the growing area of research into quantum information processing in relativistic spacetimes.
Whether winning blackjack or navigating busy streets, achieving desired outcomes requires agents to execute adaptive strategies, strategies where actions depend contextually on past events. In complexity science, this motivates memory as an operational quantifier of complexity: given two strategies, the more complex one demands the agent to track more about the past. Here, we show that conclusions about complexity fundamentally depend on whether agents can process and store quantum information. Thus, while classical agents might find Strategy A more complex to execute than Strategy B, quantum agents can reach the opposite conclusion. We derive sufficient conditions for such contradictory conclusions and illustrate the phenomenon across multiple scenarios. As a byproduct, our results yield an information-theoretic lower bound on the minimal memory required by any agent - classical or quantum - to execute a given strategy.
Atomic frequency standards have achieved steadily increasing precision over the past seventy years, enabled in part by feedback mechanisms that stabilise their output. In parallel, the timekeeping capabilities of quantum systems have been explored within the recently developed ticking-clock framework, which models clocks as dynamical systems producing a stochastic sequence of ticks. However, a theoretical description that unifies these perspectives and incorporates feedback into autonomous quantum clocks has been lacking. We introduce a framework for feedback-controlled clockworks in which classical information extracted from the tick sequence is used to influence the subsequent dynamics of the clock. We show that such feedback preserves the core structural features of self-timing and clockwork independence that characterise autonomous ticking clocks. We further identify the signal-to-noise ratio S\mathfrak{S}S as the fundamental figure of merit for assessing the performance of feedback-controlled clocks. Applying our framework to two representative architectures, we prove that classical clockworks cannot surpass the optimal signal-to-noise ratio achievable without feedback. In contrast, for quantum clockworks we present numerical evidence that feedback can provide a genuine and robust performance enhancement, improving the maximal attainable signal-to-noise ratio. We provide additional numerical evidence, suggesting that the magnitude of the improvement strongly depends on the amount and type of the stored, classical information. These results establish feedback as a potentially essential ingredient in pushing the fundamental limits of timekeeping in the quantum regime.