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arXiv:1605.09168 · New Journal of Physics

Unravelling the noise: the discrimination of wave function collapse models under time-continuous measurements

Marco G. Genoni, O S Duarte, Alessio Serafini

Published Oct 24, 2016• 16 citations
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Abstract

Inspired by the notion that environmental noise is in principle observable, while fundamental noise due to spontaneous localization would not be, we study the estimation of the diffusion parameter induced by wave function collapse models under continuous monitoring of the environment. We take into account finite measurement efficiencies and, in order to quantify the advantage granted by monitoring, we analyse the quantum Fisher information associated with such a diffusion parameter, identify optimal measurements in limiting cases, and assess the performance of such measurements in more realistic conditions.

DOI
10.1088/1367-2630/18/10/103040

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Inspired by the notion that environmental noise is in principle observable, while fundamental noise due to spontaneous localization would not be, we study the estimation of the diffusion parameter induced by wave function collapse models under continuous monitoring of the environment. We take into account finite measurement efficiencies and, in order to quantify the advantage granted by monitoring, we analyse the quantum Fisher information associated with such a diffusion parameter, identify optimal measurements in limiting cases, and assess the performance of such measurements in more realistic conditions.
Inspired by the notion that environmental noise is in principle observable, while fundamental noise due to spontaneous localization would not be, we study the estimation of the diffusion parameter induced by wave function collapse models under continuous monitoring of the environment. We take into account finite measurement efficiencies and, in order to quantify the advantage granted by monitoring, we analyse the quantum Fisher information associated with such a diffusion parameter, identify optimal measurements in limiting cases, and assess the performance of such measurements in more realistic conditions.
One of the most fundamental principles of quantum mechanics is the collapse of the wave function upon measurement. Here, we present a novel approach called Noise vs Noise that enables continuous tracking of a quantum particle (specifically, an electron in a double-slit experiment) without causing wave function collapse. Instead of directly interacting with the particle, we introduce a well-defined reference noise field into the medium. The electron perturbs this noise through its electric field, and by analyzing the noise distortion, we extract information about the electron’s position and velocity. Numerical simulations demonstrate that the wave function remains intact (correlation = 1.0000) while achieving positional accuracy on the order of 10−8 m and velocity estimates within the correct order of magnitude (106 m/s). The uncertainty product ∆x · ∆p remains above the Heisenberg limit (ħ/2), confirming that the method re- spects quantum mechanical principles while offering a gentle measurement paradigm. This work opens new possibilities for quantum sensing, continuous monitoring, and fundamental tests of quantum mechanics.
Mainstream literature on spontaneous wave function collapse never reflects on or profit from the formal coincidence and conceptual relationship with standard collapse under time-continuous quantum measurement (monitoring). I propose some easy lessons of standard monitoring theory which would make spontaneous collapse models revise some of their claims. In particular, the objective detection of spontaneous collapse remains impossible as long as the correct identification of what corresponds to the signal in standard monitoring is missing from spontaneous collapse models, the physical detectability of the “signal” is not stated explicitly and, finally, the principles of physical detection are not revealed.
We derive an alternative formulation of the stochastic master equation describing the evolution of quantum systems continuously measured via homodyne detection in a squeezed-thermal environment. This formulation allows us to identify two distinct collapse operators, corresponding respectively to the monitored and unmonitored channels, and to express the quantum state evolution directly in terms of Kraus-like operators. As a consequence, it facilitates the application of advanced numerical methods that account for higher-order corrections and discrete-time monitoring, and it also enables the efficient numerical evaluation of Cramér-Rao bounds in parameter estimation problems. To demonstrate the latter, we evaluate the Fisher information of the continuous homodyne monitoring for qubit frequency estimation in the presence of a squeezed-thermal bath. Our results show that exponential scaling of the steady-state Fisher information rate with squeezing is retained even at non-zero temperature.
Mainstream literature on spontaneous wave function collapse never reflects on or profits from the formal coincidence and conceptual relationship with standard collapse under time-continuous quantum measurement (monitoring). I propose some easy lessons of standard monitoring theory which would make spontaneous collapse models revise some of their claims. In particular, the objective detection of spontaneous collapse remains impossible as long as the correct identification of what corresponds to the signal in standard monitoring is missing from spontaneous collapse models, the physical detectability of the "signal" is not stated explicitly and, finally, the principles of physical detection are not revealed.
We consider the estimation of parameters encoded in the measurement record of a continuously monitored quantum system in the jump unraveling, corresponding to a single-shot scenario, where information is continuously gathered. Here, it is generally difficult to assess the precision of the estimation procedure via the Fisher Information due to intricate temporal correlations and memory effects. In this paper we provide a full set of solutions to this problem. First, for multi-channel renewal processes we relate the Fisher Information to an underlying Markov chain and derive a easily computable expression for it. For non-renewal processes, we introduce a new algorithm that combines two methods: the monitoring operator method for metrology and the Gillespie algorithm which allows for efficient sampling of a stochastic form of the Fisher Information along individual quantum trajectories. We show that this stochastic Fisher Information satisfies useful properties related to estimation on a single run. Finally, we consider the case where some information is lost in data compression/post-selection and provide tools for computing the Fisher Information in this case. All scenarios are illustrated with instructive examples from quantum optics and condensed matter.