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arXiv:2004.07857

Ultimate limit on time signal generation

Yuxiang Yang, Renato Renner

Published Apr 16, 2020• 5 citations
arXivHTMLPDF

Abstract

The generation of time signals is a fundamental task in science. Here we study the relation between the quality of a time signal and the physics of the system that generates it. According to quantum theory, any time signal can be decomposed into individual quanta that lead to single detection events. Our main result is a bound on how sharply peaked in time these events can be, which depends on the dimension of the signal generator. This result promises applications in various directions, including information theory, quantum clocks, and process simulation.

DOI
10.48550/arxiv.2004.07857

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The generation of time signals is a fundamental task in science. Here we study the relation between the quality of a time signal and the physics of the system that generates it. According to quantum theory, any time signal can be decomposed into individual quanta that lead to single detection events. Our main result is a bound on how sharply peaked in time these events can be, which depends on the dimension of the signal generator. This result promises applications in various directions, including information theory, quantum clocks, and process simulation.
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Abstract Combining quantum sensing with quantum computing can lead to quantum computational sensing (QCS) protocols that are able to more efficiently extract task-specific information from physical signals than is possible otherwise. In this paper, we present, in theory and numerical simulations, the application of two quantum algorithms—quantum signal processing and quantum neural networks—to various binary and multiclass machine-learning classification tasks in sensing. Here, sensing operations are interleaved with computing operations, giving rise to nonlinear functions of the sensed signals. Our approach to optimizing QCS protocols takes into account quantum sampling noise and allows us to engineer protocols that can yield accurate results with as few as just a single measurement shot. In all cases, we have been able to show a regime of operation where a quantum computational sensor can achieve higher accuracy than a conventional quantum sensor for a given budget of sensing time, with a simulated accuracy advantage of >20 percentage points for some tasks. We also present protocols for performing nonlinear tasks using Hamiltonian-engineered bosonic systems and quantum signal processing with hybrid qubit-bosonic systems, and empirically show an advantage when the received signal has a limited mean photon number.
We develop a Fisher-informational reformulation of physical time in which clock time is not regarded as a fundamental ontological substance, but as an emergent calibration of causally ordered distinguishability among physical states. The operational starting point is that clocks do not measure time itself; rather, they instantiate reproducible physical processes whose distinguishable states are correlated with other events. We introduce a causal-informational parameter, denoted by Lambda_F, defined as an accumulated Fisher-geometric distance along a causally admissible trajectory in state space. In classical statistical systems, this parameter is generated by the Fisher information metric; in quantum systems, the corresponding construction is associated with quantum Fisher information, the Bures metric, and the Fubini-Study geometry of projective Hilbert space. The manuscript distinguishes model-dependent Fisher information from quantum Fisher information, clarifies the reparameterization of Schrodinger dynamics, and gives explicit examples involving a qubit clock, an exponential decay process, and a Fisher characterization of clock quality. The proposal is positioned relative to relational time, the Page-Wootters mechanism, thermal time, quantum speed-limit relations, information geometry, and the problem of time in quantum gravity. We do not claim that relational or emergent time is new. The specific contribution is the use of Fisher distinguishability as an operational precursor from which ordinary clock time can be reconstructed. In this sense, the central statement of the paper is: time is not measured by clocks; clock time is reconstructed from the Fisher distinguishability accumulated along causally ordered physical changes.
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