Counting processes provide a fundamental description of stochastic events ranging from photon detection to clock ticks. A central question is how accurately such events can be timed when only finite memory resources are available. Here, we investigate this problem within a general framework of finite-dimensional classical and quantum counting processes. We derive a rigorous finite-memory variance bound obeyed by every classical $d$-state counting process, which is tight and saturated by a discrete Erlang-type ladder process. Through numerical optimization, we identify quantum counting processes that violate this classical bound, achieving smaller first-tick fluctuations than any classical process with the same memory size and mean tick time. For the qubit case, we further derive an analytical large-mean bound within a single-Kraus no-tick family, showing that the quantum advantage persists asymptotically within this class. The optimized quantum processes exhibit coherent conditioned dynamics and approach a continuous-time quantum-jump description as the mean increases. Our results establish a finite-memory quantum advantage in temporal precision and connect discrete-time counting processes with continuous-time quantum timekeeping.
How complex can the responses of a quantum device become as it runs longer with a fixed internal memory? We quantify this complexity through sequential response capacity: how many adaptive testing stages, each using a fresh run, can continue to separate possible processes by a prescribed gap in response probabilities....
Simulating open quantum systems reveals how environmental coupling shapes relaxation, excitation transport, and the dynamics of quantum correlations. On quantum hardware, dissipative channels add operations and might seem to increase cost. However, we show that a broad class of Pauli noise, including depolarization, ca...
Armando Angrisani, Ricard Puig, Y. Teng et al.· 0 citations
At the heart of every atomic clock is a quantum coherent emitter, the laser, that could in principle be treated autonomously. While their frequency or phase stability is typically studied in the semiclassical regime of a large number of emitted quanta, recent works on autonomous quantum clocks suggest that the few-quan...
Nonlinear dynamics generate non-Gaussian states and operations, but they also make continuously monitored quantum systems difficult to track. A quantum filter performs this task by compressing a noisy measurement record into a set of evolving variables that predict future observables. For Gaussian dynamics, this compre...
Markovian open-system dynamics have widespread applications throughout quantum information science, including algorithmic state preparation. Their convergence is commonly quantified using the worst case global trace distance between the evolving and stationary states. However, this criterion can be unnecessarily string...
Štěpán Šmíd, Richard Meister, Mario Berta et al.· 1 citation
The quantum first-passage problem involves stochastic trajectories conditioned on measurement outcomes. The timing statistics of such trajectories remain largely unexplored in open quantum systems. Here, we investigate the first-passage time to an energy threshold for a ubiquitous model: a harmonic oscillator driven by...
Joseph M. Ryan, Simon Gorbaty, S. Teitsworth et al.· 0 citations
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