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arXiv:2609.25844

Quantum survival in hybrid pursuit dynamics - a lion chasing a lamb problem

P. Held, İ. Yalçınkaya, F. Pegoraro, J. Lammers, F. Schlue, K. Jiráková, S. Barkhofen, B. Brecht, M. Štefaňák, V. Potoček, A. Gábris, I. Jex, C. Silberhorn

quant-phSubmitted Sep 22, 2026• Announced Sep 23, 2026• 0 citations
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Abstract

Measurement and classical randomness usually degrade coherence; controlling where and when a subsystem is monitored can instead make them a tunable resource. We introduce a photonic time-multiplexed quantum walk whose fast reconfigurability enables precise position measurements, allowing us to study this interplay in a hybrid quantum-classical pursuit problem: A quantum walker (lamb) evolves on a line while a classical pursuer (lion) performs a lazy random walk. Each lion trajectory drives a distinct coherent, norm-reducing evolution of the lamb, with capture implemented by measurements at the lion's positions; averaging over the recorded trajectories then synthesizes a decoherent process. Counterintuitively, increasing the lion's mobility does not monotonically suppress survival: over a broad range of hopping probabilities, the lamb survives better than against an immobile predator. Directly observing this local enhancement, we demonstrate a manifestly quantum feature aided rather than hindered by classical stochastic control.

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Measurement and classical randomness usually degrade coherence; controlling where and when a subsystem is monitored can instead make them a tunable resource. We introduce a photonic time-multiplexed quantum walk whose fast reconfigurability enables precise position measurements, allowing us to study this interplay in a hybrid quantum-classical pursuit problem: A quantum walker (lamb) evolves on a line while a classical pursuer (lion) performs a lazy random walk. Each lion trajectory drives a distinct coherent, norm-reducing evolution of the lamb, with capture implemented by measurements at the lion's positions; averaging over the recorded trajectories then synthesizes a decoherent process. Counterintuitively, increasing the lion's mobility does not monotonically suppress survival: over a broad range of hopping probabilities, the lamb survives better than against an immobile predator. Directly observing this local enhancement, we demonstrate a manifestly quantum feature aided rather than hindered by classical stochastic control.
Measurements on a quantum particle unavoidably affect its state, since the otherwise unitary evolution of the system is interrupted by a nonunitary projection operation. To probe measurement-induced effects in the state dynamics using a quantum simulator, the challenge is to implement controlled measurements on a small subspace of the system and continue the evolution from the complementary subspace. A powerful platform for versatile quantum evolution is represented by photonic quantum walks because of their high control over all relevant parameters. However, measurement-induced dynamics in such a platform have not yet been realized. We implement controlled measurements in a discrete-time quantum walk based on time-multiplexing. This is achieved by adding a deterministic outcoupling of the optical signal to include measurements constrained to specific positions resulting in the projection of the walker's state on the remaining ones. With this platform and coherent input light, we experimentally simulate measurement-induced single-particle quantum dynamics. We demonstrate the difference between dynamics with only a single measurement at the final step and those including measurements during the evolution. To this aim, we study recurrence as a figure of merit, that is, the return probability to the walker's starting position, which is measured in the two cases. We track the development of the return probability over 36 time steps and observe the onset of both recurrent and transient evolution as an effect of the different measurement schemes, a signature which only emerges for quantum systems. Our simulation of the observed one-particle conditional quantum dynamics does not require a genuine quantum particle but is demonstrated with coherent light.
Abstract The origin of non-classicality in physical systems and its connection to distinctly quantum features such as entanglement and coherence is a central question in quantum physics. This work analyses this question theoretically and experimentally, linking quantitatively non-classicality with quantum coherence. On the theoretical front, we show when the coherence of an observable is linearly related to the degree of violation of the Kolmogorov condition, which quantifies the deviation from any classical (non-invasive) explanation of the multi-time statistics. Experimentally, we probe this connection between coherence and non-classicality in a time-multiplexed optical quantum walk. We demonstrate exquisite control of quantum coherence of the walker by varying the degree of coherent superposition effected by the coin, and we show a concomitant variation in the degree of non-classicality of the walker statistics, which can be accessed directly by virtue of the unprecedented control on the measurement-induced effects obtained via fast programmable electro-optic modulators.
We investigate the quantum walk on the line when decoherence is introduced through simultaneous measurements of the chirality and the particle position. This decoherence drives the system to a classical diffusive behavior, for which we have obtained analytical expressions for its diffusion coefficient. We show that this coefficient is proportional to the variance of the initially localized quantum random walker just before the first measurement. Through an association of the measurement processes to the collisions in Brownian motion, we show that this treatment provides a smooth connection between the pure classical and quantum limits.
Quantum measurements are crucial for observing the properties of a quantum system, which, however, unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system being subjected to a sequence of projective measurements applied at random times. In the case of independent and identically distributed intervals of time between consecutive measurements, we analytically demonstrate that the survival probability of the system to remain in the projected state assumes a large deviation (exponentially decaying) form in the limit of an infinite number of measurements. This allows us to estimate the typical value of the survival probability, which can therefore be tuned by controlling the probability distribution of the random time intervals. Our analytical results are numerically tested for Zeno-protected entangled states, which also demonstrate that the presence of disorder in the measurement sequence further enhances the survival probability when the Zeno limit is not reached (as it happens in experiments). Our studies provide a new tool for protecting and controlling the amount of quantum coherence in open complex quantum systems by means of tunable stochastic measurements.
The random walk of photons in a tight-binding lattice is known to exhibit diffusive motion similar to classical random walks under decoherence, clearly illustrating the quantum-to-classical transition. In this study, we reveal that the random walk of intense classical light under dephasing dynamics can disentangle quantum and ensemble averaging, making it possible to observe subdiffusive walker dynamics, i.e., a behavior very distinct from both a classical and a quantum walker. These findings are demonstrated through proposing photonic random walk in synthetic temporal lattices, based on pulse dynamics in coupled fiber loops.
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Here the walker has memory of its previous locations and preferentially avoids stepping back to locations where it has previously resided. Classical self-avoiding random walks have found numerous algorithmic applications, most notably in the modelling of protein folding. We consider the analogous problem in the quantum setting - a quantum walk in one dimension with tunable levels of self-avoidance. We complement a quantum walk with a memory register that records where the walker has previously resided. The walker is then able to avoid returning back to previously visited sites or apply more general memory conditioned operations to control the walk. We characterise this walk by examining the variance of the walker's distribution against time, the standard metric for quantifying how quantum or classical a walk is. We parameterise the strength of the memory recording and the strength of the memory back-action on the walker, and investigate their effect on the dynamics of the walk. We find that by manipulating these parameters, which dictate the degree of self-avoidance, the walk can be made to reproduce ideal quantum or classical random walk statistics, or a plethora of more elaborate diffusive phenomena. In some parameter regimes we observe a close correspondence between classical self-avoiding random walks and the quantum self-avoiding walk.