Quantum Fisher Information Bounds on Precision Limits of Circular Dichroism

Abstract

Circular dichroism (CD) is a widely used technique for investigating optically chiral molecules, especially for biomolecules. It is thus of great importance that these parameters be estimated precisely so that the molecules with desired functionalities can be designed. In order to surpass the limits of classical measurements, we need to probe the system with quantum light. We develop quantum Fisher information matrix (QFIM) for precision estimates of the circular dichroism and the optical rotary dispersion for a variety of input quantum states of light that are easily accessible in laboratory. The Cramer-Rao bounds, for all four chirality parameters are obtained, from QFIM for (a) single photon input states with a specific linear polarization and for (b) NOON states having two photons with both either left polarized or right polarized. The QFIM bounds, using quantum light, are compared with bounds obtained for classical light beams i.e., beams in coherent states. Quite generally, both the single photon state and the NOON state exhibit superior precision in the estimation of absorption and phase shift in relation to a coherent source of comparable intensity, especially in the weak absorption regime. In particular, the NOON state naturally offers the best precision among the three. We compare QFIM bounds with the error sensitivity bounds, as the latter are relatively easier to measure whereas the QFIM bounds require full state tomography.

Quantum Polarimetry

“…2004; Wang and Agarwal, 2021). The QFIM for this measurement has recently been calculated and shown to outperform that of coherent states, especially in the small-absorption regime (Wang and Agarwal, 2021), similar to other attenuation measurement results.…”

“…2004; Wang and Agarwal, 2021). The QFIM for this measurement has recently been calculated and shown to outperform that of coherent states, especially in the small-absorption regime (Wang and Agarwal, 2021), similar to other attenuation measurement results. Then, the ultimate quantum limit for such a measurement was studied by Rudnicki et al (2020), where it was found that certain squeezed states allow for a simultaneous estimate of both ellipsometry parameters that approaches the Heisenberg limit.…”

“…Ellipsometry typically focuses on determining a specific pair of polarization parameters, namely the ratio between two reflection or transmission components and the difference between two phase shifts, which can be cast as the ratio between two diattenuation parameters (1 − 𝑞) /(1 − 𝑟) or 𝑞/𝑟 and a rotation angle about the e 3 axis. This has been studied from a few quantum perspectives (Abouraddy et al, 2001(Abouraddy et al, , 2002Graham et al, 2006;Rudnicki et al, 2020;Toussaint et al, 2002Toussaint et al, , 2004Wang and Agarwal, 2021) that we review here. First, one can show that particular quantum states, such as entangled photon pairs, can be used for measuring these two parameters (Abouraddy et al, 2001(Abouraddy et al, , 2002Graham et al, 2006;Toussaint et al, 2002, It is still possible to approach the lower bound in some parameter regimes (Albarelli et al, 2019).…”

Quantum Fisher Information Perspective on Sensing in Anti-PT Symmetric Systems

“…Following the method discussed in [44], we solve the equations for the individual components separately. In other words, the corresponding SLD gets split as…”