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arXiv:1804.09355 · Physical Review Letters

Nonclassicality as a Quantifiable Resource for Quantum Metrology

Hyukjoon Kwon, Kok Chuan Tan, Tyler J. Volkoff, Hyunseok Jeong

Published Feb 1, 2019• 165 citations
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Abstract

We establish the nonclassicality of continuous-variable states as a resource for quantum metrology. Based on the quantum Fisher information of multimode quadratures, we introduce the metrological power as a measure of nonclassicality with a concrete operational meaning of displacement sensitivity beyond the classical limit. This measure belongs to the resource theory of nonclassicality, which is nonincreasing under linear optical elements. Our Letter reveals that a single copy, highly nonclassical quantum state is intrinsically advantageous when compared to multiple copies of a quantum state with moderate nonclassicality. This suggests that metrological power is related to the degree of quantum macroscopicity. Finally, we demonstrate that metrological resources useful for nonclassical displacement sensing tasks can be always converted into a useful resource state for phase sensitivity beyond the classical limit.

DOI
10.1103/physrevlett.122.040503

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We establish the nonclassicality of continuous-variable states as a resource for quantum metrology. Based on the quantum Fisher information of multimode quadratures, we introduce the metrological power as a measure of nonclassicality with a concrete operational meaning of displacement sensitivity beyond the classical limit. This measure belongs to the resource theory of nonclassicality, which is nonincreasing under linear optical elements. Our Letter reveals that a single copy, highly nonclassical quantum state is intrinsically advantageous when compared to multiple copies of a quantum state with moderate nonclassicality. This suggests that metrological power is related to the degree of quantum macroscopicity. Finally, we demonstrate that metrological resources useful for nonclassical displacement sensing tasks can be always converted into a useful resource state for phase sensitivity beyond the classical limit.
We discuss the relationship between quantum coherence of finite dimensional systems and nonclassical quantum light. We demonstrate that quantifying the quantum coherence between coherent states always leads to a quantifier of nonclassicality that monotonically decreases under linear optical operations. This allows us to introduce a resource theory of nonclassicality based on linear optics that closely parallels the resource theory of coherence. Finally, we discuss the metrological power of a quantum state, which quantifies how sensitive a quantum state is to displacement operations. It is then shown that the metrological power leads to a nonclassicality monotone.
Abstract It is well-known that the precision of a phase measurement with a Mach-Zehnder interferometer employing strong classic light can be greatly enhanced with the addition of weak nonclassical light. In the context of quantifying nonclassicality, the amount by which a nonclassical state can enhance precision in this way has been termed its ’metrological power’. To-date, the enhancement provided by weak nonclassical states has been calculated only for specific measurement configurations. Here we are able to optimize over all measurement configurations to obtain the maximum enhancement that can be achieved by any single or multi-mode nonclassical state together with strong classical states, for local and distributed quantum metrology employing any linear or nonlinear single-mode unitary transformation. Our analysis reveals that the quantum Fisher information for quadrature-displacement sensing is the sole property that determines the maximum achievable enhancement in all of these different scenarios, providing a unified quantification of the metrological power.
Nonclassical states enable metrology with a precision beyond that possible with classical physics. Both for practical applications and to understand non-classicality as a resource, it is useful to know the maximum quantum advantage that can be provided by a nonclassical state when it is combined with arbitrary classical states. This advantage has been termed the power of a quantum state. A key open question is whether the metrological powers for the metrology of different quantities are related, especially metrology of force (acceleration) and phase shifts (time). Here we answer this question for all single-mode states, both for local and distributed metrology, by obtaining complete expressions for the metrological powers for the metrology of essentialy any quantity (any single-mode unitary transformation), as well as the linear networks that achieve this maximal precision. This shows that the metrological powers for all quantities are proportional to a single property of the state, which for pure states is the quadrature variance, maximized over all quadratures.
Genuinely quantum states of a harmonic oscillator may be distinguished from their classical counterparts by the Glauber-Sudarshan P representation-a state lacking a positive P function is said to be nonclassical.In this paper, we propose a general operational framework for studying nonclassicality as a resource in networks of passive linear elements and measurements with feed forward.Within this setting, we define new measures of nonclassicality based on the quantum fluctuations of quadratures, as well as the quantum Fisher information of quadrature displacements.These measures lead to fundamental constraints on the manipulation of nonclassicality, especially its concentration into subsystems, that apply to generic multimode non-Gaussian states.Special cases of our framework include no-go results in the concentration of squeezing and a complete hierarchy of nonclassicality for single-mode Gaussian states.
Cubic phase states provide the essential non-Gaussian resource for continuous-variable quantum computing. We show that they also offer significant potential for quantum metrology, surpassing the phase-sensing sensitivity of all Gaussian states at equal average photon number. Optimal sensitivity requires only moderate initial squeezing, and the non-Gaussian advantage remains robust against loss and detection noise. We identify optimal measurement strategies and show that several experimentally relevant preparation schemes surpass Gaussian limits, in some cases reaching the sensitivity of cubic phase states. Our results establish cubic phase states as a promising resource for quantum-enhanced precision measurements beyond Gaussian limits.