Abstract

In this work, we investigate the relationship between quantum coherence and multiparameter quantum estimation in a graphene-based system. We focus on the estimation of two relevant physical parameters, namely the temperature T and the wave vector kx, and analyze how their variations affect both quantum coherence and the achievable metrological precision. The minimum variances associated with the estimation process are evaluated through the quantum Cramér–Rao bound within both simultaneous and independent estimation schemes. Our results show that quantum coherence is enhanced in the low-temperature regime and around kx = 0, while it decreases progressively as either the temperature or the wave vector increases. However, the regions where coherence is maximal do not necessarily coincide with those of optimal estimation precision. In particular, the variance associated with temperature estimation exhibits a divergent behavior near T = 0, indicating that the system becomes weakly sensitive to small temperature variations in this regime. By contrast, the estimation of the wave vector kx is more directly related to the coherence properties of the system, with improved precision obtained near kx = 0. Furthermore, we introduce the ratio Γ to compare the total variances obtained from the independent and simultaneous estimation schemes. This quantity provides a useful measure of the relative difference between the two strategies when the parameters are estimated separately or jointly. The behavior of Γ shows that this difference becomes more pronounced for increasing temperature and larger wave-vector values, reflecting the nontrivial role of the multiparameter nature of the estimation problem. These findings demonstrate that quantum coherence can support metrological performance in specific regimes, but it is not sufficient on its own to guarantee optimal precision in multiparameter estimation.

Abstract

In this work, we investigate the relationship between quantum coherence and multiparameter quantum estimation in a graphene-based system. We focus on the estimation of two relevant physical parameters, namely the temperature T and the wave vector kx, and analyze how their variations affect both quantum coherence and the achievable metrological precision. The minimum variances associated with the estimation process are evaluated through the quantum Cramér–Rao bound within both simultaneous and independent estimation schemes. Our results show that quantum coherence is enhanced in the low-temperature regime and around kx = 0, while it decreases progressively as either the temperature or the wave vector increases. However, the regions where coherence is maximal do not necessarily coincide with those of optimal estimation precision. In particular, the variance associated with temperature estimation exhibits a divergent behavior near T = 0, indicating that the system becomes weakly sensitive to small temperature variations in this regime. By contrast, the estimation of the wave vector kx is more directly related to the coherence properties of the system, with improved precision obtained near kx = 0. Furthermore, we introduce the ratio Γ to compare the total variances obtained from the independent and simultaneous estimation schemes. This quantity provides a useful measure of the relative difference between the two strategies when the parameters are estimated separately or jointly. The behavior of Γ shows that this difference becomes more pronounced for increasing temperature and larger wave-vector values, reflecting the nontrivial role of the multiparameter nature of the estimation problem. These findings demonstrate that quantum coherence can support metrological performance in specific regimes, but it is not sufficient on its own to guarantee optimal precision in multiparameter estimation.

Abstract

In this work, we investigate the relationship between quantum coherence and multiparameter quantum estimation in a graphene-based system. We focus on the estimation of two relevant physical parameters, namely the temperature T and the wave vector kx, and analyze how their variations affect both quantum coherence and the achievable metrological precision. The minimum variances associated with the estimation process are evaluated through the quantum Cramér–Rao bound within both simultaneous and independent estimation schemes. Our results show that quantum coherence is enhanced in the low-temperature regime and around kx = 0, while it decreases progressively as either the temperature or the wave vector increases. However, the regions where coherence is maximal do not necessarily coincide with those of optimal estimation precision. In particular, the variance associated with temperature estimation exhibits a divergent behavior near T = 0, indicating that the system becomes weakly sensitive to small temperature variations in this regime. By contrast, the estimation of the wave vector kx is more directly related to the coherence properties of the system, with improved precision obtained near kx = 0. Furthermore, we introduce the ratio Γ to compare the total variances obtained from the independent and simultaneous estimation schemes. This quantity provides a useful measure of the relative difference between the two strategies when the parameters are estimated separately or jointly. The behavior of Γ shows that this difference becomes more pronounced for increasing temperature and larger wave-vector values, reflecting the nontrivial role of the multiparameter nature of the estimation problem. These findings demonstrate that quantum coherence can support metrological performance in specific regimes, but it is not sufficient on its own to guarantee optimal precision in multiparameter estimation.

Abstract

In this work, we investigate the relationship between quantum coherence and multiparameter quantum estimation in a graphene-based system. We focus on the estimation of two relevant physical parameters, namely the temperature T and the wave vector kx, and analyze how their variations affect both quantum coherence and the achievable metrological precision. The minimum variances associated with the estimation process are evaluated through the quantum Cramér–Rao bound within both simultaneous and independent estimation schemes. Our results show that quantum coherence is enhanced in the low-temperature regime and around kx = 0, while it decreases progressively as either the temperature or the wave vector increases. However, the regions where coherence is maximal do not necessarily coincide with those of optimal estimation precision. In particular, the variance associated with temperature estimation exhibits a divergent behavior near T = 0, indicating that the system becomes weakly sensitive to small temperature variations in this regime. By contrast, the estimation of the wave vector kx is more directly related to the coherence properties of the system, with improved precision obtained near kx = 0. Furthermore, we introduce the ratio Γ to compare the total variances obtained from the independent and simultaneous estimation schemes. This quantity provides a useful measure of the relative difference between the two strategies when the parameters are estimated separately or jointly. The behavior of Γ shows that this difference becomes more pronounced for increasing temperature and larger wave-vector values, reflecting the nontrivial role of the multiparameter nature of the estimation problem. These findings demonstrate that quantum coherence can support metrological performance in specific regimes, but it is not sufficient on its own to guarantee optimal precision in multiparameter estimation.