Least Variable Quantum Counting Processes

• URL: http://arxiv.org/abs/2608.26240v1
• Date: Wed, 26 Aug 2026 18:00:00 GMT
• Title: Least Variable Quantum Counting Processes
• Abstract summary: We find a finite-memory quantum advantage in temporal precision and connect discrete-time counting processes with continuous-time quantum timekeeping.<n>Our results establish a finite-memory quantum advantage in temporal precision and connect discrete-time counting processes with continuous-time quantum timekeeping.
• Score: 0.27185251060695437
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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