Quantum holography is a well established theory of mathematical physics based on harmonic analysis on the Heisenberg Lie group G. The geometric quantization is performed by projectivization of the complexified coadjoint orbit picture of the unitary dual G of G in order to achieve a geometric adjustment to special relativity theory. It admits applications to various imaging modalities such as synthetic aperture radar (SAR), and most importantly for the field of non-invasive medical diagnosis, to the clinical imaging modality of magnetic resonance tomography (MRI). Quantum holography explains the quantum teleportation phenomenon through Einstein-Podolsky-Rosen (EPR) channels which is a consequence of the non-locality of quantum physics. It specifically reveals what was before unobservable in special relativity, namely the light in flight (LIF) recording processing by ultra fast laser pulse trains. Finally, it provides a Lie group theoretical approach to the Kruskal coordinatized Schwarzschild manifold of quantum cosmology with large scale applications to general relativity theory such as gravitational instanton symmetries and the theory of black holes. The direct spinorial detection of gravitational wavelets emitted by the binary radio pulsar PSR 1913+16 will also be based on the principles of quantum holography.
Quantum holography is a well established theory of mathematical physics based on harmonic analysis on the Heisenberg Lie group G. The geometric quantization is performed by projectivization of the complexified coadjoint orbit picture of the unitary dual G of G in order to achieve a geometric adjustment to special relativity theory. It admits applications to various imaging modalities such as synthetic aperture radar (SAR), and most importantly for the field of non-invasive medical diagnosis, to the clinical imaging modality of magnetic resonance tomography (MRI). Quantum holography explains the quantum teleportation phenomenon through Einstein-Podolsky-Rosen (EPR) channels which is a consequence of the non-locality of quantum physics. It specifically reveals what was before unobservable in special relativity, namely the light in flight (LIF) recording processing by ultra fast laser pulse trains. Finally, it provides a Lie group theoretical approach to the Kruskal coordinatized Schwarzschild manifold of quantum cosmology with large scale applications to general relativity theory such as gravitational instanton symmetries and the theory of black holes. The direct spinorial detection of gravitational wavelets emitted by the binary radio pulsar PSR 1913+16 will also be based on the principles of quantum holography.
Quantum holography is a well established theory of mathematical physics based on harmonic analysis on the Heisenberg Lie group G. The geometric quantization is performed by projectivization of the complexified coadjoint orbit picture of the unitary dual Ĝ of G in order to achieve a geometric adjustment of the quantum scenario to special relativity theory. It admits applications to various imaging modalities such as synthetic aperture radar (SAR) in the microwave range, and, most importantly for the field of non-invasive medical diagnosis, to the clinical imaging modality of magnetic resonance tomography (MRI) in the radio frequency range. Quantum holography explains the quantum teleportation phenomemon through Einstein-Podolsky-Rosen (EPR) channels which is a consequence of the non-locality of phase coherent quantum field theory, the concept of absolute simultaneity of special relativity theory which provides the Einstein equivalence of energy and Fitzgerald-Lorentz dilated mass, and the perfect quantum holographic replication process of molecular genetic information processing. It specifically reveals what was before unobservable in quantum optics, namely the interference phenomena of matter wavelets of Bose-Einstein condensates, and what was before unobservable in special relativity, namely the light in flight (LIF) recording processing by ultrafast laser pulse trains. Finally, it provides a Lie group theoretical approach to the Kruskal coordinatized Schwarzschild manifold of relativistic cosmology with large scale applications to general relativity theory such as gravitational instanton symmetries and the theory of black holes. The direct spinorial detection of gravitational wavelets emitted by the binary radio pulsar PSR 1913+16 and known only by anticipatory system computation so far will also be based on the principles of quantum holography applied to very large array (VLA) radio interferometers.
Coherent wavelets form a unified basis of the multichannel perfect reconstruction analysis-synthesis filter bank of high resolution radar imaging and clinical magnetic resonance imaging (MRI). The filter bank construction is performed by the Kepplerian temporospatial phase detection strategy which allows for the stroboscopic and synchronous cross sectional quadrature filtering of phase histories in local frequency encoding multichannels with respect to the rotating coordinate frame of reference. The Kepplerian strategy and the associated filter bank construction take place in symplectic affine planes which are immersed as coadjoint orbits of the Heisenberg two-step nilpotent Lie group G into the foliated three-dimensional real projective space $\mbox{\bf P}\bigl(\mbox{\bf R}\times\mbox{\rm Lie}(G)^{\star}\bigr)$. Due to the factorization of transvections into affine dilations of opposite ratio, the Heisenberg group G under its natural sub-Riemannian metric acts on the line bundle realizing the projective space $\mbox{\bf P}\bigl(\mbox{\bf R}\times \mbox{\rm Lie}(G)^{\star}\bigr)$. Its elliptic non-Euclidean geometry without absolute quadric, associated to the unitary dual G^, governs the design of the coils inside the bore of the MRI scanner system. It determines the distributional reproducing kernel of the tracial read-out process of quantum holograms excited and coexisting in the MRI scanner system. Thus the pathway of this paper leads from Keppler's approach to projective geometry to the Heisenberg approach to the sub-Riemannian geometry of quantum physics, and finally to the enormously appealing topic of ensemble quantum computing.
Coherent wavelets form a unified basis of the multichannel perfect reconstruction analysis-synthesis filter bank of high resolution radar imaging and clinical magnetic resonance imaging (MRI). The filter bank construction is performed by the Kepplerian temporospatial phase detection strategy which allows for the stroboscopic and synchronous cross sectional quadrature filtering of phase histories in local frequency encoding multichannels with respect to the rotating coordinate frame of reference. The Kepplerian strategy and the associated filter bank construction take place in symplectic affine planes which are immersed as coadjoint orbits of the Heisenberg two-step nilpotent Lie group G into the foliated three-dimensional real projective space $\mbox{ P}\bigl(\mbox{ R}\times\mbox{Lie}(G)^{\star}\bigr)$. Due to the factorization of transvections into affine dilations of opposite ratio, the Heisenberg group G under its natural sub-Riemannian metric acts on the line bundle realizing the projective space $\mbox{ P}\bigl(\mbox{ R}\times \mbox{ Lie}(G)^{\star}\bigr)$. Its elliptic non-Euclidean geometry without absolute quadric, associated to the unitary dual G^, governs the design of the coils inside the bore of the MRI scanner system. It determines the distributional reproducing kernel of the tracial read-out process of quantum holograms excited and coexisting in the MRI scanner system. Thus the pathway of this paper leads from Keppler's approach to projective geometry to the Heisenberg approach to the sub-Riemannian geometry of quantum physics, and finally to the enormously appealing topic of ensemble quantum computing.
The holographic transform H is thought of as the sesquilinear mapping which assigns to the elements of the tensor product vector space L2(R) @ L2(R) the matrix coefficient function of the linear Schrodinger representation of the three-dimensional real Heisenberg nil-potent Lie group. - It is the purpose of the present paper to study the quantum mechanical approach to optical holography including optical phase conjugation, electron holography, and computerized tomographic methods in high resolution imaging radar, for instance synthetic-aperture imaging radar like side-looking airborne SAR, and space shuttle SAR. The aspect common to these techniques is the geometric encoding of the two-wave mixing u @ v by the interference pattern H(u,v;.,.) in the holographic plane R @ R performed simultaneously for the amplitude and the phase by the holographic transform H.
Over the past few decades, medical imaging has revolutionized the way clinicians diagnose, monitor, and treat diseases. However, despite significant advancements in imaging resolution, contrast, and computational reconstruction, several challenges remain unresolved — especially in terms of early-stage detection, noise reduction, and functional imaging at the cellular or molecular level. In recent years, quantum physics has emerged as a disruptive force with the potential to drastically enhance medical imaging technologies through the application of its fundamental principles such as quantum superposition, entanglement, tunneling, and spin dynamics. This research explores the intersection of quantum mechanics and medical imaging engineering, with a primary focus on how quantum phenomena are being utilized to elevate the performance and capability of key imaging modalities like Magnetic Resonance Imaging (MRI), Positron Emission Tomography (PET), and optical-based quantum imaging. The study presents an in-depth analysis of how quantum concepts are applied in practice — such as the role of spin alignment and magnetic resonance in MRI, the use of entangled photon pairs in PET scanning, and the integration of quantum dots in high-contrast optical imaging. Beyond existing technologies, the paper investigates cutting-edge developments including quantum-enhanced sensors, quantum computing for real-time image reconstruction, and the promise of quantum artificial intelligence in image interpretation. By analyzing both theoretical frameworks and experimental findings, the study highlights the significant advantages that quantum technologies bring — such as improved spatial resolution, higher signal-to-noise ratio, and reduced patient exposure to radiation. Despite its promise, the integration of quantum physics into medical imaging is not without challenges. The research discusses limitations such as system decoherence, scalability, clinical costs, and the gap between laboratory research and clinical deployment. In conclusion, this paper argues that while still emerging, the application of quantum physics holds transformative potential for the future of diagnostic imaging, and could ultimately lead to more accurate, efficient, and personalized healthcare.
Medical imaging, a cornerstone of modern diagnostics that underpins early disease detection and personalized therapy, continues to confront fundamental physical limitations inherent to conventional modalities, including suboptimal sensitivity and specificity, limited resolution, and ionizing radiation risks. Quantum imaging, leveraging principles such as entanglement, superposition, and quantum sensing, has emerged as a transformative paradigm with the potential to transcend these limitations. This review systematically summarizes the physical principles, technological advancements, and major clinical applications of quantum technologies in medical imaging. We elaborate on several cutting-edge modalities, including quantum dot probes for targeted imaging and surgical navigation, wearable magnetoencephalography facilitated by optically pumped magnetometers, quantum-enhanced magnetic resonance imaging with nanoscale resolution, quantum optical coherence tomography with dispersion cancellation, photon-counting computed tomography for superior spectral imaging, and nuclear medicine imaging that can visualize the molecular microenvironment. Additionally, the roles of quantum computing and quantum artificial intelligence in accelerating and optimizing the image analysis workflow are also discussed. Furthermore, we analyze the technical bottlenecks and translational barriers that currently hinder the widespread clinical implementation of these emerging technologies. Finally, we outline promising future research directions to accelerate clinical translation, underscoring the transformative potential of quantum medical imaging to advance precision diagnostics and personalized medicine.