Deformed Photon States Enhance Phase Estimation in Quantum Interferometry

Research demonstrates photon counting maintains optimal precision for phase estimation within a Mach-Zehnder interferometer, even when utilising realistic, non-ideal light sources modelled by q-deformed photon states. Phase sensitivity increases with greater q-deformation, suggesting improved metrological performance due to non-classical light statistics.

Precise determination of phase – the difference in the timing of wave cycles – underpins numerous technologies, from optical sensing and imaging to gravitational wave detection. Researchers are continually seeking methods to refine these measurements, pushing the limits of precision. A new investigation, detailed in a forthcoming publication, explores the potential of utilising specifically engineered states of light – termed ‘q-deformed’ states – within a Mach-Zehnder interferometer to enhance phase estimation.

Duttatreya and Sanjib Dey, both from the Birla Institute of Technology and Science, Pilani, demonstrate that these non-ideal, non-classical light sources can, counterintuitively, improve measurement sensitivity. Their work, titled ‘Enhanced quantum phase estimation with -deformed nonideal nonclassical light’, utilises a mathematical technique called the Jordan-Schwinger mapping to analyse photon statistics and establish the efficacy of photon counting as an optimal measurement strategy, even with these deformed states.

Enhanced Phase Estimation via q-Deformed Photon States

Precise phase estimation underpins numerous technologies, from gravitational wave detectors – instruments designed to detect ripples in spacetime – to secure quantum communication networks. Current research consistently seeks to overcome the limitations imposed by classical physics and achieve improved measurement sensitivity. A recent investigation focuses on phase estimation within a Mach-Zehnder interferometer, employing q-deformed photon states as realistic models for non-ideal light sources, and demonstrating a pathway to enhanced precision.

The Mach-Zehnder interferometer splits a single beam of light into two paths, recombining them to create interference. The phase shift between the beams, determined by the properties of the medium they traverse, dictates the interference pattern. Accurately measuring this phase shift is crucial in many applications. However, real-world light sources deviate from ideal conditions, introducing noise and limiting precision.

Researchers addressed this by modelling the light source using q-deformed photon states. These states represent a departure from standard quantum descriptions, incorporating a parameter ‘q’ that quantifies the degree of deformation from a standard Poissonian photon number distribution. This deformation alters the statistical properties of the light, influencing the precision with which phase can be estimated.

The investigation employed the Jordan-Schwinger mapping – a mathematical technique used to transform quantum optical problems into equivalent classical statistical mechanics problems – to derive analytical expressions for the probability of detecting a specific number of photons (photon count likelihoods). These expressions facilitated precise calculations of both classical information – a measure of the information obtainable from a measurement – and Fisher information – a quantum mechanical measure of the precision with which a parameter can be estimated.

Results demonstrate a counterintuitive enhancement in phase sensitivity as the degree of q-deformation increases. This arises from the non-classical photon statistics exhibited by these states, challenging conventional expectations that broader photon number distributions necessarily degrade precision. The altered photon number distribution, characteristic of q-deformed states, effectively reduces uncertainty during phase estimation.

The study confirms that photon counting – directly measuring the number of photons detected – consistently remains an optimal measurement strategy, even when dealing with these deformed states. Crucially, classical and Fisher information exhibited exact agreement, signifying that the information obtainable from the measurement process is fully exploited, maximising the precision of the phase estimation.

Researchers derived closed-form expressions for the photon count likelihoods, enabling precise calculations of both classical and Fisher information, and performed Bayesian inference – a statistical method for updating beliefs based on evidence – on simulated detector data to rigorously assess phase estimation performance. This analytical framework provides a robust tool for analysing and optimising quantum measurement strategies employing non-ideal light sources.

The investigation encompassed various q-deformed states, including q-coherent and q-cat states, acknowledging the imperfections inherent in practical quantum systems. The findings suggest that carefully engineered quantum states can outperform classical limits in precision measurement, opening new possibilities for advanced sensing technologies.

This work confirms the utility of q-deformed states in precision measurement applications, leveraging their unique statistical properties to enhance metrological performance and achieve greater sensitivity in interferometric sensing. The ability to accurately measure phase shifts is fundamental to many areas of physics and engineering, and this research represents a significant step forward in achieving that goal.