Quantum statistical mechanics and the ghosts of modality

James S. Albertson

Garnet N. Ord

Quantum mechanics appears to contain ghosts from both classical statistical mechanics and special relativity. On one hand, both the Dirac and Schrödinger equations have classical analogs that emerge directly from classical statistical mechanics, unimpeded by major problems of interpretation. On the other hand, the formal analytic continuation that takes these classical equations to the quantum version introduces a velocity dependent phase. However, among classical theories, only in relativistic mechanics does one find path-dependent phase in the form of relativistic time dilation. This paper explores the idea that if we start with statistical mechanics and special relativity we can discover a version of the quantum algorithm and show that at least some of the resulting ghosts are direct descendants of those connected with the birth of the differential calculus.

Wolfgang Elsäßer

Ghost metrology is a measurement modality exploiting correlations of photons. At ICTON 2017 [1], we had demonstrated ghost imaging by using a novel, extremely compact superluminescent diode source based on Amplified Spontaneous Emission and exhibiting photon bunching. Here, we now demonstrate that amplified spontaneous emission light emitted both by a spectrally broad-band semiconductor-based superluminescent diode and an erbium-doped fibre amplifier (EDFA) exhibit spectral photon correlations in the spirit of the Hanbury-Brown & Twiss (HBT) experiment, however now in the spectral domain. We then apply these spectral photon correlations within two proof-of-principal ghost spectroscopy experiments, one at an absorption band of trichloromethane (chloroform) at 1214 nm and another one at 1533nm at acetylene (C2H2) reproducing the characteristic absorption features. This ghost spectroscopy work fills the gap of a hitherto missing analogy between the spatial and the spectral domain in classical ghost modalities. Finally, by exploiting polarization correlations of light from an EDFA we succeed in reconstructing a hidden, camouflaged polarization in a ghost polarimetry experiment in close analogy to ghost imaging and ghost spectroscopy. Via these successfully demonstrated results, we are contributing towards a broader dissemination of correlated photon ghost modalities, hence paving the way towards more applications which exploit their favourable advantages.

Uduzei F. Edgal, David L. Huber

Fazilah Nothlawala, Chané Moodley, Neelan Gounden +2 more

Quantum ghost imaging harnesses entangled photon pairs to form images using light that never directly interacts with the object. Conventional approaches rely on pixelated detectors or spatial masks, where the resolution is fundamentally limited by the pixel size and thus bounded by the Rayleigh criterion. In this work, we present a modal approach that replaces pixel-based detection with measurements in a basis of structured modes. By reconstructing images through tailored spatial modes, we decouple resolution from the physical limitations of detectors and instead tie it to the system’s optical precision and computational control. We demonstrate that even non-orthogonal modal sets can achieve high fidelity image reconstruction by exploiting modal sparsity, significantly reducing the number of required measurements. Using phase-only approximations of Hermite-Gaussian modes, we avoid the loss associated with complex amplitude modulation while retaining high reconstruction fidelity. The result is a high-resolution, high-efficiency quantum ghost imaging technique powered by structured light, opening new possibilities for photon-efficient imaging in low-light and quantum-limited regimes, such as biological microscopy and remote sensing.