Classification of the quantum measurement based on correlations between a quantum memory (instead of a classical memory) and a measured quantum system results in a new class of measurement interactions. We experimentally demonstrate this with qubits.
Abstract Quantum mechanics is usually formulated with an implicit assumption that agents who can observe and interact with the world are external to it and have a classical memory. However, there is no accepted way to define the quantum–classical cut and no a priori reason to rule out fully quantum agents with coherent quantum memories. In this work, we introduce an entirely quantum notion of measurement, called a sensation, to account for quantum agents that experience the world through quantum sensors. Sensations eschew probabilities and instead describe a deterministic flow of quantum information. We quantify the information gain and disturbance of a sensation using concepts from quantum information theory and find that sensations always disturb at least as much as they inform. Viewing measurements as sensations could lead to a new understanding of quantum theory in general and to new results in the context of quantum networks.
An agent monitors a complex environment, receiving one observation at each time step and eventually deciding how to label the resulting sequence. Does the sequence indicate an anomaly, and if so, of what type? Does it signal market instability, and to what degree? This is the setting of online multi-class classification: the input arrives sequentially, the full history is never available at once, and the agent must retain any past information relevant to the eventual decision. As the environment becomes more complex, the memory needed to track this information can grow rapidly without bound. Here, we introduce families of such multi-class classification games and show that any exact classical agent requires memory that grows without bound, whereas exact quantum agents can solve all tasks in the family with bounded memory. This separation is sharp: any classical agent using less than the required memory, under suitable input distributions, performs arbitrarily close to random guessing. Moreover, our quantum constructions are provably memory minimal, allowing us to derive the exact classical and quantum memory complexities to perform such tasks. In doing so, we establish an unbounded separation between classical and quantum memory cost for online multi-class classification.
Adaptive agents realise complex reactive behaviours by using a memory of past input stimuli and output actions to guide structured future responses. Quantum adaptive agents can operate while storing less information in memory than optimal classical counterparts; yet, this does not necessarily translate into a reduced dimension of the memory that must be physically realised. We introduce a route-truncate-repair procedure that can convert entropic quantum memory advantages into reductions in memory dimension. Routing a reference input process through an agent yields a temporal matrix product state representation whose canonical bond is identified with the joint reference--agent memory. Truncating the agent's share of this bond and locally repairing the resulting dynamics produces a smaller, physically-valid agent that remains capable of responding to arbitrary input sequences. A fidelity-divergence certificate quantifies the resulting trade-off between accuracy and memory dimension. Benchmark adaptive processes exhibit substantial dimension reduction whilst preserving the underlying behaviour with high fidelity. The construction extends to feedback and coherent quantum interactions, with accuracy guarantees under arbitrary adaptive interrogation for a class of agents. For a resettable clock, four quantum memory dimensions attain an input--output fidelity divergence rate first matched with eleven states in our search over classical reduced models. These results establish a route from entropic memory advantages to practical, dimension-reduced adaptive quantum agents.