[Paper Review] Beating the Shot-Noise Limit with Sources of Partially-Distinguishable Photons

Patrick M. Birchall, Javier Sabines-Chesterking+3 more|arXiv (Cornell University)|Mar 2, 2016

Quantum Information and Cryptography1 references3 citations

TL;DR

This paper demonstrates that quantum-enhanced phase sensitivity—scaling beyond the shot-noise limit—can be achieved using partially-distinguishable photons, not requiring fully indistinguishable sources. By experimentally controlling photon distinguishability via temporal delay, the authors show that Heisenberg-limited scaling persists as long as there is non-zero indistinguishability, significantly reducing the technical barrier for practical quantum metrology.

ABSTRACT

Quantum metrology promises high-precision measurements beyond the capability of any classical techniques, and has the potential to be integral to investigative techniques. However, all sensors must tolerate imperfections if they are to be practical. Here we show that photons with perfectly overlapped modes, which are therefore fully indistinguishable, are not required for quantum-enhanced measurement, and that partially-distinguishable photons do not have to be engineered to mitigate the adverse effects of distinguishability. We quantify the effect of distinguishability on quantum metrology experiments, and report results of an experiment to verify that two- and four-photon states containing partially-distinguishable photons can achieve quantum-enhanced sensitivity with low-visibility quantum interference. This demonstrates that sources producing photons with mixed spectral states can be readily utilized for quantum metrology.

Motivation & Objective

• To investigate whether quantum metrological advantages can be achieved with partially-distinguishable photons, which are easier to generate than fully indistinguishable ones.
• To quantify the impact of photon distinguishability on quantum interference and phase sensitivity in interferometric measurements.
• To demonstrate experimentally that non-classical phase sensitivity persists even with low-visibility quantum interference.
• To show that distinguishability is a distinct source of error from loss and phase diffusion, and does not necessarily destroy Heisenberg scaling.
• To reduce the technological barrier for quantum metrology by proving that highly indistinguishable photon sources are not required for quantum advantage.

Proposed method

• Controlled distinguishability between photon pairs and four-photon states was introduced via a variable temporal delay in a Mach-Zehnder interferometer.
• Quantum interference fringes were measured by scanning the phase θ over [0, 2π), with coincidence rates recorded for varying levels of distinguishability.
• Fisher information F was extracted from fitted interference fringes using the Cramér-Rao bound, with F′ = F/(2n) used to normalize per-photon sensitivity.
• Background noise effects were modeled and accounted for in the analysis, particularly in the four-photon case.
• Theoretical predictions were compared with experimental data, with the indistinguishability parameter I′(x) used to characterize the degree of interference.
• A four-photon state's expected Fisher information at extreme distinguishability (I′=0) and perfect indistinguishability (I′=1) was estimated using experimental data and the method of Nagata et al. (2007).

Experimental results

Research questions

• RQ1 Can quantum metrology achieve Heisenberg-limited scaling with partially-distinguishable photons, even when indistinguishability is low?
• RQ2 How does the degradation of phase sensitivity scale with increasing photon distinguishability in a multi-photon interferometric setup?
• RQ3 Is the effect of distinguishability on quantum advantage separable from other imperfections like photon loss and phase diffusion?
• RQ4 Can practical photon sources with mixed spectral states be used effectively in quantum metrology without requiring full indistinguishability?
• RQ5 To what extent can background noise and low-visibility interference affect the extraction of supra-classical Fisher information in multi-photon states?

Key findings

• The two-photon experiment showed approximately linear degradation of Fisher information with increasing distinguishability, consistent with theoretical predictions.
• For the four-photon state, Fisher information decreased from the predicted Heisenberg-limited value at I′=1 to the classical limit at I′=0, confirming sustained quantum advantage.
• The experimentally estimated four-photon Fisher information at x=0 (maximum indistinguishability) was Λ₄ = 0.480 ± 0.005, supporting the predicted scaling.
• Despite background noise, the interference fringes maintained high contrast near θ=0, enabling supra-classical sensitivity.
• The results demonstrate that any non-zero indistinguishability enables a quantum advantage, even in the absence of other ideal conditions.
• The study confirms that distinguishability is a distinct and manageable source of error, separate from loss and phase diffusion, and does not preclude Heisenberg scaling.