Maximal Adaptive-Decision Speedups in Quantum-State Readout

Abstract

The average time T required for high-fidelity readout of quantum states can be significantly reduced via a real-time adaptive decision rule. An adaptive decision rule stops the readout as soon as a desired level of confidence has been achieved, as opposed to setting a fixed readout time t f . The performance of the adaptive decision is characterized by the "adaptive-decision speedup," t f =T. In this work, we reformulate this readout problem in terms of the first-passage time of a particle undergoing stochastic motion. This formalism allows us to theoretically establish the maximum achievable adaptive-decision speedups for several physical two-state readout implementations. We show that for two common readout schemes (the Gaussian latching readout and a readout relying on state-dependent decay), the speedup is bounded by 4 and 2, respectively, in the limit of high single-shot readout fidelity. We experimentally study the achievable speedup in a real-world scenario by applying the adaptive decision rule to a readout of the nitrogen-vacancy-center (NV-center) charge state. We find a speedup of ≈2 with our experimental parameters. In addition, we propose a simple readout scheme for which the speedup can, in principle, be increased without bound as the fidelity is increased. Our results should lead to immediate improvements in nanoscale magnetometry based on spin-to-charge conversion of the NV-center spin, and provide a theoretical framework for further optimization of the bandwidth of quantum measurements.

Spin Readout Techniques of the Nitrogen-Vacancy Center in Diamond

“…Here, is the true positive rate, implying a false negative rate , whereas is the false positive rate. The readout fidelity, a measure of the confidence in a given measurement outcome, is defined in terms of these two error rates as [ 28 , 29 ]: The fidelity takes values between 50% and 100%, assuming an optimal threshold condition has been selected.…”

“…Together with low-temperature resonance-fluorescence readout, real-time detection protocols have been essential for the achievement of heralded entanglement [ 107 ] and partial measurements [ 106 ], since they boost the readout fidelity while reducing unwanted backaction. Similarly, hidden Markov models can improve the performance of room-temperature, single-shot charge-state readout [ 29 ]. These results imply that significant improvements should be achievable for room-temperature applications using real-time signal processing in conjunction with nuclear-assisted or SCC readout protocols.…”

Einstein-Podolsky-Rosen paradox implies a minimum achievable temperature

“…The physical consequences of the measurement rate will become increasingly important as quantum experiments push for greater control. [46] However, they also present a new probe of the measurement rule and energytime uncertainty principle for quantum mechanics. For the micromaser, the rate seems to be the number of atoms sent through the cavity per unit time -since every atom that leaves the cavity is measured via its interaction with the outside environment.…”

“…One of the primary motivations for this work has been to derive a firm theoretical foundation for analyzing timesequences of measurements in hopes of better understanding the role of the environment in decoherence. [37][38][39][40][41][42][43][44][45][46] The present paper provides a new way of understanding the gap between the Lindblad operators describing the quantum master equation and the physical processes responsible for decoherence. Rather than unravelling the Lindblad equation, we choose a physical process and show how a Lindblad equation emerges.…”

Real-Time Charge Initialization of Diamond Nitrogen-Vacancy Centers for Enhanced Spin Readout

“…We model the charge probe process using a photon distribution model accounting for transitions between NV − and the neutral (NV 0 ) charge state [28,31,32]. The model assumes that the charge dynamics of the NV center can be reduced to a two-state system with emission rates γ − and γ 0 , and charge transition rates for ionization (negative to neutral, Γ Ion ) and recombination (neutral to negative, Γ Rec ); see Fig.…”