This paper presents a measure of single-mode nonclassicality using a quantum resource theory. The authors show that the measure is the first resource-theoretic measure that quantifies the ability of a state to perform useful tasks, e.g., phase sensing in a Mach Zehnder interferometer, which can also be used to lower bound the nonclassicality experimentally
This paper presents a measure of single-mode nonclassicality using a quantum resource theory. The authors show that the measure is the first resource-theoretic measure that quantifies the ability of a state to perform useful tasks, e.g., phase sensing in a Mach Zehnder interferometer, which can also be used to lower bound the nonclassicality experimentally
Quantifying nonclassicality of a bosonic mode is an important but challenging task in quantum optics. Recently, a nonclassicality measure based on the concept of operational resource theory has been proposed [W. Ge, K. Jacobs, S. Asiri, M. Foss-Feig, and M. S. Zubairy, Phys. Rev. Res. 2, 023400 (2020)], which shows several crucial properties as a resource for quantum metrology. Here we apply the measure to evaluate and categorize different classes of nonclassical states. We discover a class of states that can achieve the maximum nonclassicality in the asymptotic limit of a large mean number of excitations. These states can provide the same sensitivity in place of a squeezed vacuum in a sensing scheme, e.g., the laser interferometer gravitational-wave observatory (LIGO) experiments. We also discover that the nonclassicality of certain states can be greatly improved with a single-photon addition. In addition, we explore some examples on how to evaluate analytically the nonclassicality of mixed states, which are in general difficult to calculate due to the convex roof nature of the measure. Our results will be useful for preparing and utilizing nonclassical states for applications in precision-sensing tasks, such as quadrature sensing and phase sensing in a Mach-Zehnder interferometer.
The operational resource theory (ORT) measure is a nonclassicality measure for bosonic states, notable for its resource-theoretic properties and connection to metrology. However, it can be difficult to evaluate, being linked to an optimization problem for mixed states. Here, we present ORT measure calculations for mixed states with photon-number coherence. We give exact formulas governing the ORT measure of a broad class of rank-two mixed states, and numerical solutions for some higher-rank states. We also compare the nonclassicality of these states to their metrological power, thus showing in what regimes the metrological power manages to saturate the ORT bound. Throughout, we consider the role of coherence. In particular, we show that nonclassicality and metrological power never increase under bosonic dephasing, but may plateau in a manner similar to entanglement sudden death. Nevertheless, lowering photon-number coherence more freely can sometimes yield more nonclassical and metrologically useful states.
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.
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 of bosonic modes are important resources for quantum-enhanced technologies. However, quantifying nonclassicality of these states, in particular mixed states, can be a challenge. Here we present results of quantifying the nonclassicality of a bosonic mode in a mixed Fock state via the operational resource theory measure [Phys. Rev. Res. 2, 023400 (2020)], which relates nonclassicality to metrological advantage. Generally speaking, evaluating a resource-theoretic measure for mixed states is challenging, since it involves finding a convex roof. However, we show that our problem can be reduced to a linear programming problem. By analyzing the results of numerical optimization, we are able to extract analytical results for the case where three or four neighboring Fock states have nonzero population. Interestingly, we find that such a mode can be in distinct phases, depending on the populations. Finally, we demonstrate how our method is generalizable to density matrices of higher ranks. Our findings suggest a viable method for evaluating nonclassicality of arbitrary mixed bosonic states and potentially for solving other convex roof optimization problems.
In this review, the authors introduce the notion of quantum nonclassicality of light and the role of nonclassicality in optical quantum metrology. The first part of this paper focuses on defining and characterizing the notion of nonclassicality and how it may be quantified in radiation fields. Several prominent examples of nonclassical light are also discussed. The second part of this paper deals with quantum metrology through the lens of nonclassicality. The authors introduce key concepts such as the Quantum Fisher information, the Cramér-Rao bound, the standard quantum limit, and the Heisenberg limit and discuss how nonclassical light may be exploited to beat classical limitations in high precision measurements. The discussion here will be largely theoretical, with some references to specific experimental implementations.