arXiv subjects

Graeme D. Berk

Publications and source records attributed to Graeme D. Berk.

6 recordsLinked to original sources

arXiv2026

How much randomness in a quantum process can be explained using memory?

For a stochastic process describing observations of a dynamical system, complexity science provides systematic methods to decompose the information produced into true irreducible randomness, and that which corresponds to structure superficially disguised as random but can in fact be learned and predicted. Such methods then equip vital tools for prediction, control and inference of the system's internal structure. However, quantum analogs remain underdeveloped due to the inherent complications of invasive measurements and quantum correlations. By harnessing the Choi state representation of process tensors which encode multi-time input-output relations, we formulate a convergent measure of irreducible randomness in stationary quantum stochastic processes. This directly enables a measure of temporal correlations which lower bounds the memory resources required to replicate the process via a recurrent quantum circuit.

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arXiv2026

Quantum Circuit Fragments and Link Products in Continuous Variables

Quantum circuits are often drawn as complete processes, with fixed inputs and outputs. In many quantum-information tasks, however, the natural object is only a fragment of such a circuit: an unknown source of non-Markovian noise to be probed, a subroutine to be inserted into a larger algorithm, or an agent implementing an adaptive strategy. In finite dimensions, the link product provides a systematic means to analyze how such circuit fragments interact and compose. Here, we develop the corresponding framework for continuous-variable systems. We introduce continuous-variable circuit fragments and associated link products that stitch such fragments together into larger processes. We show that the formalism simplifies substantially in the Gaussian regime, where link products can be evaluated efficiently using covariance-matrix representations. We use the formalism to construct non-Markovian processes and adaptive agent-environment interactions from modular components. This extends the quantum-comb toolkit to continuous variables, providing systematic methods for adaptive sensing, non-Markovian noise mitigation, and higher-order quantum circuit design.

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arXiv2025

Quantifiers of Noise Reducibility Under Restricted Control

The correlation structure of multitime quantum processes - succinctly described by quantum combs - is an important resource for many quantum information protocols and control tasks. Inspired by approaches for quantum states, we introduce quantifiers of the practical utility of quantum processes that satisfy monotonicity properties, thus overcoming shortcomings in previous state-motivated approaches. Applying these quantifiers to the problem of noise reduction of a quantum process under open-loop control, they are shown to represent the largest amount of temporal mutual information that a process can possibly exhibit. In addition, we study their resource composition behaviour and connect them to the recently introduced notion of generalised comb divergences. Finally, in light of these new quantifiers, we re-interpret the numerical findings of npj Quantum Information 9, 104 (2023) on the relationship of dynamical decoupling and non-Markovian memory, which were based on insufficient resource quantifiers, and show that its main conclusion - the interpretation of dynamical decoupling as a resource distillation - still holds.

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arXiv2025

Monotones in Resource Theories for Dynamical Decoupling

In arXiv:2110.02613, we presented a generalised dynamical resource theory framework that enabled noise reduction techniques including dynamical decoupling (DD) to be studied. While this fundamental contribution remains correct, it has been found that the main resource quantifiers we employed to study these resource theories -- based on the relative entropies between Choi states of multitime processes -- are not monotonic under the allowed transformations. In this letter we detail modified relative entropy-based resource quantifiers, prove that they are indeed monotonic in our resource theories. We re-interpret our numerical results in terms of these new relative entropy monotones, arriving at the same empirical conclusions: DD can be understood as temporal resource distillation, and improvements to noise reduction via our multitimescale optimal dynamical decoupling (MODD) method coincide with a decrease in the corresponding non-Markovianity monotone.

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arXiv2021

Extracting Quantum Dynamical Resources: Consumption of Non-Markovianity for Noise Reduction

Noise is possibly the most formidable challenge for quantum technologies. As such, a great deal of effort is dedicated to developing methods for noise reduction. One remarkable achievement in this direction is dynamical decoupling; it details a clear set of instructions for counteracting the effects of quantum noise. Yet, the domain of its applicability remains limited to devices where exercising fast control is possible. In practical terms, this is highly limiting and there is a growing need for better noise reduction tools. Here we take a significant step in this direction, by identifying the crucial ingredients required for noise suppression and the development of methods that far outperform traditional dynamical decoupling techniques. Using resource theoretic methods, we show that the key resource responsible for the efficacy of dynamical decoupling, and related protocols, is non-Markovianity (or temporal correlations). Using this insight, we then propose two methods to identify optimal pulse sequences for noise reduction. With an explicit example, we show that our methods enable a more optimal exploitation of temporal correlations, and extend the timescales at which noise suppression is viable by at least two orders of magnitude. Importantly, the corresponding tools are built on operational grounds and are easily implemented in the current generation of quantum devices.

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arXiv2021

Resource theories of multi-time processes: A window into quantum non-Markovianity

We investigate the conditions under which an uncontrollable background processes may be harnessed by an agent to perform a task that would otherwise be impossible within their operational framework. This situation can be understood from the perspective of resource theory: rather than harnessing 'useful' quantum states to perform tasks, we propose a resource theory of quantum processes across multiple points in time. Uncontrollable background processes fulfil the role of resources, and a new set of objects called superprocesses, corresponding to operationally implementable control of the system undergoing the process, constitute the transformations between them. After formally introducing a framework for deriving resource theories of multi-time processes, we present a hierarchy of examples induced by restricting quantum or classical communication within the superprocess - corresponding to a client-server scenario. The resulting nine resource theories have different notions of quantum or classical memory as the determinant of their utility. Furthermore, one of these theories has a strict correspondence between non-useful processes and those that are Markovian and, therefore, could be said to be a true 'quantum resource theory of non-Markovianity'.

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