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arXiv:0906.1027 · Physical Review A

Entanglement is not a critical resource for quantum metrology

Todd Tilma, Shinichiro Hamaji, William J. Munro, Kae Nemoto

Published Feb 11, 2010• 48 citations
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Abstract

We investigate high-precision measurements beyond the standard quantum limit, utilizing nonclassical states. Although entanglement was considered a resource for achieving the Heisenberg limit in measurements, we show that any advantage expected from using entanglement is dependent on the measurement in question. We investigate several measurement scenarios and illustrate the role of entanglement as a resource for quantum high-precision measurement. In particular, we demonstrate that there is a regime wherein entanglement not only does not help, but prevents the achievement of the fundamental limit.

DOI
10.1103/physreva.81.022108

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Entanglement is generally considered necessary for achieving the Heisenberg limit in quantum metrology. We construct analogues of Dicke and GHZ states on a single N+1N+1N+1 dimensional qudit that achieve precision equivalent to symmetrically entangled states on NNN qubits, showing that entanglement is not necessary for going beyond the standard quantum limit. We define a measure of non-classicality based on quantum Fisher information and estimate the achievable precision, suggesting a close relationship between non-classical states and metrological power of qudits. Our work offers an exponential reduction in the physical resources required for quantum-enhanced parameter estimation, making it accessible on any quantum system with a high-dimensional Hilbert space.
Quantum metrology is studied in the presence of quantum correlation. The quantum correlation measure based on quantum Fisher information enables us to gain a deeper insight on how quantum correlations are instrumental in setting metrological precision. Our analysis shows that not only the entanglement but also the quantum correlation plays important roles to enhance precision in quantum metrology. Even in the absence of entanglement, quantum correlation can be exploited as the resource to beat standard quantum limit and reach Heisenberg limit in metrology. Clearly unraveling the role of quantum correlations, the tighter bounds on the metrological precision are derived.
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As a cornerstone of quantum science and technology, quantum precision measurement aims to transcend the standard quantum limit (SQL) and achieve sensitivities unattainable by classical approaches by harnessing distinctive quantum resources such as entanglement, squeezing and non-Gaussianity. Within this framework, Gaussian states have historically played a central role, underpinning a series of seminal experimental advances; however, their utility in metrology is fundamentally bounded by theoretical constraints that preclude unlimited gains in measurement precision. In contrast, a growing body of recent research has revealed that non-Gaussian states–endowed with stronger quantum correlations and more pronounced non-classical characteristics — can significantly surpass Gaussian counterparts in key tasks such as phase estimation, quantum imaging and quantum sensing. Under specific conditions, these states even exhibit the potential to approach or saturate the ultimate Heisenberg limit. This review offers a comprehensive overview of the theoretical underpinnings, representative preparation methodologies, experimental progress and emerging applications of non-Gaussian states in quantum metrology. Special attention is devoted to illustrating their transformative potential for the development of next-generation quantum sensors and high-precision measurement instruments, while also addressing prevailing challenges and delineating promising future research trajectories in this rapidly advancing field.
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